KILLED
proof of input_d9HQBYn39O.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# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished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) InliningProof [UPPER BOUND(ID), 341 ms]
        (16) CpxRNTS
        (17) SimplificationProof [BOTH BOUNDS(ID, ID), 4 ms]
        (18) CpxRNTS
        (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
        (20) CpxRNTS
        (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (22) CpxRNTS
        (23) IntTrsBoundProof [UPPER BOUND(ID), 88 ms]
        (24) CpxRNTS
        (25) IntTrsBoundProof [UPPER BOUND(ID), 4 ms]
        (26) CpxRNTS
        (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (28) CpxRNTS
        (29) IntTrsBoundProof [UPPER BOUND(ID), 143 ms]
        (30) CpxRNTS
        (31) IntTrsBoundProof [UPPER BOUND(ID), 3 ms]
        (32) CpxRNTS
        (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
        (35) IntTrsBoundProof [UPPER BOUND(ID), 90 ms]
        (36) CpxRNTS
        (37) IntTrsBoundProof [UPPER BOUND(ID), 43 ms]
        (38) CpxRNTS
        (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (40) CpxRNTS
        (41) IntTrsBoundProof [UPPER BOUND(ID), 189 ms]
        (42) CpxRNTS
        (43) IntTrsBoundProof [UPPER BOUND(ID), 26 ms]
        (44) CpxRNTS
        (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (46) CpxRNTS
        (47) IntTrsBoundProof [UPPER BOUND(ID), 3709 ms]
        (48) CpxRNTS
        (49) IntTrsBoundProof [UPPER BOUND(ID), 753 ms]
        (50) CpxRNTS
    (51) CompletionProof [UPPER BOUND(ID), 0 ms]
    (52) CpxTypedWeightedCompleteTrs
        (53) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (54) CpxRNTS
(55) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(56) CdtProblem
    (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (88) CdtProblem
    (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (124) CdtProblem
    (125) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (130) CdtProblem
    (131) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 1811 ms]
    (134) CdtProblem
    (135) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) 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:

   from(X) -> cons(X, n__from(s(X)))
   length(n__nil) -> 0
   length(n__cons(X, Y)) -> s(length1(activate(Y)))
   length1(X) -> length(activate(X))
   from(X) -> n__from(X)
   nil -> n__nil
   cons(X1, X2) -> n__cons(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(n__nil) -> nil
   activate(n__cons(X1, X2)) -> cons(X1, X2)
   activate(X) -> X

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:

   from(X) -> cons(X, n__from(s(X)))
   length(n__nil) -> 0'
   length(n__cons(X, Y)) -> s(length1(activate(Y)))
   length1(X) -> length(activate(X))
   from(X) -> n__from(X)
   nil -> n__nil
   cons(X1, X2) -> n__cons(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(n__nil) -> nil
   activate(n__cons(X1, X2)) -> cons(X1, X2)
   activate(X) -> X

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:

   from(X) -> cons(X, n__from(s(X)))
   length(n__nil) -> 0
   length(n__cons(X, Y)) -> s(length1(activate(Y)))
   length1(X) -> length(activate(X))
   from(X) -> n__from(X)
   nil -> n__nil
   cons(X1, X2) -> n__cons(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(n__nil) -> nil
   activate(n__cons(X1, X2)) -> cons(X1, X2)
   activate(X) -> X

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:

   from(X) -> cons(X, n__from(s(X))) [1]
   length(n__nil) -> 0 [1]
   length(n__cons(X, Y)) -> s(length1(activate(Y))) [1]
   length1(X) -> length(activate(X)) [1]
   from(X) -> n__from(X) [1]
   nil -> n__nil [1]
   cons(X1, X2) -> n__cons(X1, X2) [1]
   activate(n__from(X)) -> from(X) [1]
   activate(n__nil) -> nil [1]
   activate(n__cons(X1, X2)) -> cons(X1, X2) [1]
   activate(X) -> X [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:

   from(X) -> cons(X, n__from(s(X))) [1]
   length(n__nil) -> 0 [1]
   length(n__cons(X, Y)) -> s(length1(activate(Y))) [1]
   length1(X) -> length(activate(X)) [1]
   from(X) -> n__from(X) [1]
   nil -> n__nil [1]
   cons(X1, X2) -> n__cons(X1, X2) [1]
   activate(n__from(X)) -> from(X) [1]
   activate(n__nil) -> nil [1]
   activate(n__cons(X1, X2)) -> cons(X1, X2) [1]
   activate(X) -> X [1]

The TRS has the following type information:
from :: s:0 -> n__from:n__nil:n__cons
cons :: s:0 -> n__from:n__nil:n__cons -> n__from:n__nil:n__cons
n__from :: s:0 -> n__from:n__nil:n__cons
s :: s:0 -> s:0
length :: n__from:n__nil:n__cons -> s:0
n__nil :: n__from:n__nil:n__cons
0 :: s:0
n__cons :: s:0 -> n__from:n__nil:n__cons -> n__from:n__nil:n__cons
length1 :: n__from:n__nil:n__cons -> s:0
activate :: n__from:n__nil:n__cons -> n__from:n__nil:n__cons
nil :: n__from:n__nil:n__cons

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:

   length_1
   length1_1

(c) The following functions are completely defined:

   activate_1
   nil
   from_1
   cons_2

Due to the following rules being added:
none

And the following fresh constants: none

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

(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:

   from(X) -> cons(X, n__from(s(X))) [1]
   length(n__nil) -> 0 [1]
   length(n__cons(X, Y)) -> s(length1(activate(Y))) [1]
   length1(X) -> length(activate(X)) [1]
   from(X) -> n__from(X) [1]
   nil -> n__nil [1]
   cons(X1, X2) -> n__cons(X1, X2) [1]
   activate(n__from(X)) -> from(X) [1]
   activate(n__nil) -> nil [1]
   activate(n__cons(X1, X2)) -> cons(X1, X2) [1]
   activate(X) -> X [1]

The TRS has the following type information:
from :: s:0 -> n__from:n__nil:n__cons
cons :: s:0 -> n__from:n__nil:n__cons -> n__from:n__nil:n__cons
n__from :: s:0 -> n__from:n__nil:n__cons
s :: s:0 -> s:0
length :: n__from:n__nil:n__cons -> s:0
n__nil :: n__from:n__nil:n__cons
0 :: s:0
n__cons :: s:0 -> n__from:n__nil:n__cons -> n__from:n__nil:n__cons
length1 :: n__from:n__nil:n__cons -> s:0
activate :: n__from:n__nil:n__cons -> n__from:n__nil:n__cons
nil :: n__from:n__nil:n__cons

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:

   from(X) -> cons(X, n__from(s(X))) [1]
   length(n__nil) -> 0 [1]
   length(n__cons(X, n__from(X'))) -> s(length1(from(X'))) [2]
   length(n__cons(X, n__nil)) -> s(length1(nil)) [2]
   length(n__cons(X, n__cons(X1', X2'))) -> s(length1(cons(X1', X2'))) [2]
   length(n__cons(X, Y)) -> s(length1(Y)) [2]
   length1(n__from(X'')) -> length(from(X'')) [2]
   length1(n__nil) -> length(nil) [2]
   length1(n__cons(X1'', X2'')) -> length(cons(X1'', X2'')) [2]
   length1(X) -> length(X) [2]
   from(X) -> n__from(X) [1]
   nil -> n__nil [1]
   cons(X1, X2) -> n__cons(X1, X2) [1]
   activate(n__from(X)) -> from(X) [1]
   activate(n__nil) -> nil [1]
   activate(n__cons(X1, X2)) -> cons(X1, X2) [1]
   activate(X) -> X [1]

The TRS has the following type information:
from :: s:0 -> n__from:n__nil:n__cons
cons :: s:0 -> n__from:n__nil:n__cons -> n__from:n__nil:n__cons
n__from :: s:0 -> n__from:n__nil:n__cons
s :: s:0 -> s:0
length :: n__from:n__nil:n__cons -> s:0
n__nil :: n__from:n__nil:n__cons
0 :: s:0
n__cons :: s:0 -> n__from:n__nil:n__cons -> n__from:n__nil:n__cons
length1 :: n__from:n__nil:n__cons -> s:0
activate :: n__from:n__nil:n__cons -> n__from:n__nil:n__cons
nil :: n__from:n__nil:n__cons

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:

   n__nil => 0
   0 => 0

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

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

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 1 }-> nil :|: z = 0
   activate(z) -{ 1 }-> from(X) :|: z = 1 + X, X >= 0
   activate(z) -{ 1 }-> cons(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   cons(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   from(z) -{ 1 }-> cons(X, 1 + (1 + X)) :|: X >= 0, z = X
   from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 2 }-> 1 + length1(nil) :|: z = 1 + X + 0, X >= 0
   length(z) -{ 2 }-> 1 + length1(from(X')) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0
   length(z) -{ 2 }-> 1 + length1(cons(X1', X2')) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2')
   length1(z) -{ 2 }-> length(X) :|: X >= 0, z = X
   length1(z) -{ 2 }-> length(nil) :|: z = 0
   length1(z) -{ 2 }-> length(from(X'')) :|: z = 1 + X'', X'' >= 0
   length1(z) -{ 2 }-> length(cons(X1'', X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   nil -{ 1 }-> 0 :|: 


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

(15) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   nil -{ 1 }-> 0 :|: 
   cons(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   from(z) -{ 1 }-> cons(X, 1 + (1 + X)) :|: X >= 0, z = X
   from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X

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

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

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 2 }-> cons(X', 1 + (1 + X')) :|: z = 1 + X, X >= 0, X' >= 0, X = X'
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z = 1 + X, X >= 0, X' >= 0, X = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   from(z) -{ 2 }-> 1 + X1 + X2 :|: X >= 0, z = X, X1 >= 0, X2 >= 0, X = X1, 1 + (1 + X) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 3 }-> 1 + length1(cons(X'', 1 + (1 + X''))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z = 1 + X + 0, X >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 2 }-> length(X) :|: X >= 0, z = X
   length1(z) -{ 3 }-> length(cons(X, 1 + (1 + X))) :|: z = 1 + X'', X'' >= 0, X >= 0, X'' = X
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z = 1 + X'', X'' >= 0, X >= 0, X'' = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 


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

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

(18)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 3 }-> 1 + length1(cons(X'', 1 + (1 + X''))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(cons(X, 1 + (1 + X))) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 


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

(19) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
Found the following analysis order by SCC decomposition:

   { nil }
   { from }
   { cons }
   { activate }
   { length1, length }

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 3 }-> 1 + length1(cons(X'', 1 + (1 + X''))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(cons(X, 1 + (1 + X))) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {nil}, {from}, {cons}, {activate}, {length1,length}

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

(21) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(22)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 3 }-> 1 + length1(cons(X'', 1 + (1 + X''))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(cons(X, 1 + (1 + X))) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {nil}, {from}, {cons}, {activate}, {length1,length}

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

(23) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: nil
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(24)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 3 }-> 1 + length1(cons(X'', 1 + (1 + X''))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(cons(X, 1 + (1 + X))) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {nil}, {from}, {cons}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: ?, size: O(1) [0]

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: nil
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 3 }-> 1 + length1(cons(X'', 1 + (1 + X''))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(cons(X, 1 + (1 + X))) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {from}, {cons}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [0]

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

(27) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 3 }-> 1 + length1(cons(X'', 1 + (1 + X''))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(cons(X, 1 + (1 + X))) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {from}, {cons}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [0]

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: from
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 3 + 2*z

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 3 }-> 1 + length1(cons(X'', 1 + (1 + X''))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(cons(X, 1 + (1 + X))) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {from}, {cons}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [0]
  from: runtime: ?, size: O(n^1) [3 + 2*z]

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: from
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 3 }-> 1 + length1(cons(X'', 1 + (1 + X''))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(cons(X, 1 + (1 + X))) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {cons}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [0]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]

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

(33) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

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

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 3 }-> 1 + length1(cons(X'', 1 + (1 + X''))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(cons(X, 1 + (1 + X))) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {cons}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [0]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]

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

(35) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: cons
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z + z'

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

(36)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 3 }-> 1 + length1(cons(X'', 1 + (1 + X''))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(cons(X, 1 + (1 + X))) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {cons}, {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [0]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: ?, size: O(n^1) [1 + z + z']

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

(37) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: cons
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

(38)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 3 }-> 1 + length1(cons(X'', 1 + (1 + X''))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(cons(X, 1 + (1 + X))) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [0]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']

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

(39) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(40)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 3 }-> s'' :|: s'' >= 0, s'' <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 4 }-> 1 + length1(s) :|: s >= 0, s <= X'' + (1 + (1 + X'')) + 1, z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 4 }-> length(s') :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [0]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: activate
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + 2*z

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

(42)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 3 }-> s'' :|: s'' >= 0, s'' <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 4 }-> 1 + length1(s) :|: s >= 0, s <= X'' + (1 + (1 + X'')) + 1, z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 4 }-> length(s') :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {activate}, {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [0]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  activate: runtime: ?, size: O(n^1) [1 + 2*z]

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

(43) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: activate
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 10

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

(44)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 3 }-> s'' :|: s'' >= 0, s'' <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 4 }-> 1 + length1(s) :|: s >= 0, s <= X'' + (1 + (1 + X'')) + 1, z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 4 }-> length(s') :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [0]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  activate: runtime: O(1) [10], size: O(n^1) [1 + 2*z]

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

(45) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(46)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 3 }-> s'' :|: s'' >= 0, s'' <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 4 }-> 1 + length1(s) :|: s >= 0, s <= X'' + (1 + (1 + X'')) + 1, z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 4 }-> length(s') :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [0]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  activate: runtime: O(1) [10], size: O(n^1) [1 + 2*z]

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: length1
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

Computed SIZE bound using CoFloCo for: length
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

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

(48)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 3 }-> s'' :|: s'' >= 0, s'' <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 4 }-> 1 + length1(s) :|: s >= 0, s <= X'' + (1 + (1 + X'')) + 1, z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 4 }-> length(s') :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [0]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  activate: runtime: O(1) [10], size: O(n^1) [1 + 2*z]
  length1: runtime: ?, size: INF
  length: runtime: ?, size: INF

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

(49) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: length1
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

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

(50)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 3 }-> s'' :|: s'' >= 0, s'' <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 1 }-> z :|: z >= 0
   activate(z) -{ 2 }-> 0 :|: z = 0
   activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X'
   activate(z) -{ 2 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2'
   cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   from(z) -{ 1 }-> 1 + z :|: z >= 0
   from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 2 }-> 1 + length1(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length(z) -{ 4 }-> 1 + length1(s) :|: s >= 0, s <= X'' + (1 + (1 + X'')) + 1, z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(0) :|: z - 1 >= 0
   length(z) -{ 3 }-> 1 + length1(1 + X'') :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0, X'' >= 0, X' = X''
   length(z) -{ 3 }-> 1 + length1(1 + X1 + X2) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2'), X1 >= 0, X2 >= 0, X1' = X1, X2' = X2
   length1(z) -{ 4 }-> length(s') :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 2 }-> length(z) :|: z >= 0
   length1(z) -{ 3 }-> length(0) :|: z = 0
   length1(z) -{ 3 }-> length(1 + X) :|: z - 1 >= 0, X >= 0, z - 1 = X
   length1(z) -{ 3 }-> length(1 + X1 + X2) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0, X1 >= 0, X2 >= 0, X1'' = X1, X2'' = X2
   nil -{ 1 }-> 0 :|: 

Function symbols to be analyzed: {length1,length}
Previous analysis results are:
  nil: runtime: O(1) [1], size: O(1) [0]
  from: runtime: O(1) [2], size: O(n^1) [3 + 2*z]
  cons: runtime: O(1) [1], size: O(n^1) [1 + z + z']
  activate: runtime: O(1) [10], size: O(n^1) [1 + 2*z]
  length1: runtime: INF, size: INF
  length: runtime: ?, size: INF

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

(51) 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:

   length(v0) -> null_length [0]

And the following fresh constants:    null_length

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

(52)
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:

   from(X) -> cons(X, n__from(s(X))) [1]
   length(n__nil) -> 0 [1]
   length(n__cons(X, Y)) -> s(length1(activate(Y))) [1]
   length1(X) -> length(activate(X)) [1]
   from(X) -> n__from(X) [1]
   nil -> n__nil [1]
   cons(X1, X2) -> n__cons(X1, X2) [1]
   activate(n__from(X)) -> from(X) [1]
   activate(n__nil) -> nil [1]
   activate(n__cons(X1, X2)) -> cons(X1, X2) [1]
   activate(X) -> X [1]
   length(v0) -> null_length [0]

The TRS has the following type information:
from :: s:0:null_length -> n__from:n__nil:n__cons
cons :: s:0:null_length -> n__from:n__nil:n__cons -> n__from:n__nil:n__cons
n__from :: s:0:null_length -> n__from:n__nil:n__cons
s :: s:0:null_length -> s:0:null_length
length :: n__from:n__nil:n__cons -> s:0:null_length
n__nil :: n__from:n__nil:n__cons
0 :: s:0:null_length
n__cons :: s:0:null_length -> n__from:n__nil:n__cons -> n__from:n__nil:n__cons
length1 :: n__from:n__nil:n__cons -> s:0:null_length
activate :: n__from:n__nil:n__cons -> n__from:n__nil:n__cons
nil :: n__from:n__nil:n__cons
null_length :: s:0:null_length

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

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

   n__nil => 0
   0 => 0
   null_length => 0

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

(54)
Obligation:
Complexity RNTS consisting of the following rules:

   activate(z) -{ 1 }-> X :|: X >= 0, z = X
   activate(z) -{ 1 }-> nil :|: z = 0
   activate(z) -{ 1 }-> from(X) :|: z = 1 + X, X >= 0
   activate(z) -{ 1 }-> cons(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   cons(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   from(z) -{ 1 }-> cons(X, 1 + (1 + X)) :|: X >= 0, z = X
   from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   length(z) -{ 1 }-> 0 :|: z = 0
   length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   length(z) -{ 1 }-> 1 + length1(activate(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0
   length1(z) -{ 1 }-> length(activate(X)) :|: X >= 0, z = X
   nil -{ 1 }-> 0 :|: 

Only complete derivations are relevant for the runtime complexity.

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

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   length(n__nil) -> 0
   length(n__cons(z0, z1)) -> s(length1(activate(z1)))
   length1(z0) -> length(activate(z0))
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
   activate(n__from(z0)) -> from(z0)
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(z0, z1)
   activate(z0) -> z0
Tuples:
   FROM(z0) -> c(CONS(z0, n__from(s(z0))))
   FROM(z0) -> c1
   LENGTH(n__nil) -> c2
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   NIL -> c5
   CONS(z0, z1) -> c6
   ACTIVATE(n__from(z0)) -> c7(FROM(z0))
   ACTIVATE(n__nil) -> c8(NIL)
   ACTIVATE(n__cons(z0, z1)) -> c9(CONS(z0, z1))
   ACTIVATE(z0) -> c10
S tuples:
   FROM(z0) -> c(CONS(z0, n__from(s(z0))))
   FROM(z0) -> c1
   LENGTH(n__nil) -> c2
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
   NIL -> c5
   CONS(z0, z1) -> c6
   ACTIVATE(n__from(z0)) -> c7(FROM(z0))
   ACTIVATE(n__nil) -> c8(NIL)
   ACTIVATE(n__cons(z0, z1)) -> c9(CONS(z0, z1))
   ACTIVATE(z0) -> c10
K tuples:none
Defined Rule Symbols:   from_1, length_1, length1_1, nil, cons_2, activate_1

Defined Pair Symbols:   FROM_1, LENGTH_1, LENGTH1_1, NIL, CONS_2, ACTIVATE_1

Compound Symbols:   c_1, c1, c2, c3_2, c4_2, c5, c6, c7_1, c8_1, c9_1, c10


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

(57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 9 trailing nodes:
   ACTIVATE(z0) -> c10
   FROM(z0) -> c1
   LENGTH(n__nil) -> c2
   ACTIVATE(n__from(z0)) -> c7(FROM(z0))
   CONS(z0, z1) -> c6
   ACTIVATE(n__nil) -> c8(NIL)
   ACTIVATE(n__cons(z0, z1)) -> c9(CONS(z0, z1))
   NIL -> c5
   FROM(z0) -> c(CONS(z0, n__from(s(z0))))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   length(n__nil) -> 0
   length(n__cons(z0, z1)) -> s(length1(activate(z1)))
   length1(z0) -> length(activate(z0))
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
   activate(n__from(z0)) -> from(z0)
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(z0, z1)
   activate(z0) -> z0
Tuples:
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
S tuples:
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0))
K tuples:none
Defined Rule Symbols:   from_1, length_1, length1_1, nil, cons_2, activate_1

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_2, c4_2


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

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   length(n__nil) -> 0
   length(n__cons(z0, z1)) -> s(length1(activate(z1)))
   length1(z0) -> length(activate(z0))
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
   activate(n__from(z0)) -> from(z0)
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(z0, z1)
   activate(z0) -> z0
Tuples:
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)))
S tuples:
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)))
K tuples:none
Defined Rule Symbols:   from_1, length_1, length1_1, nil, cons_2, activate_1

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(61) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   length(n__nil) -> 0
   length(n__cons(z0, z1)) -> s(length1(activate(z1)))
   length1(z0) -> length(activate(z0))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   cons(z0, z1) -> n__cons(z0, z1)
   nil -> n__nil
Tuples:
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)))
S tuples:
   LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)))
   LENGTH1(z0) -> c4(LENGTH(activate(z0)))
K tuples:none
Defined Rule Symbols:   activate_1, from_1, cons_2, nil

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1))) by 
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   cons(z0, z1) -> n__cons(z0, z1)
   nil -> n__nil
Tuples:
   LENGTH1(z0) -> c4(LENGTH(activate(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
S tuples:
   LENGTH1(z0) -> c4(LENGTH(activate(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
K tuples:none
Defined Rule Symbols:   activate_1, from_1, cons_2, nil

Defined Pair Symbols:   LENGTH1_1, LENGTH_1

Compound Symbols:   c4_1, c3_1


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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH1(z0) -> c4(LENGTH(activate(z0))) by 
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   activate(n__from(z0)) -> from(z0)
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(z0, z1)
   activate(z0) -> z0
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   cons(z0, z1) -> n__cons(z0, z1)
   nil -> n__nil
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
K tuples:none
Defined Rule Symbols:   activate_1, from_1, cons_2, nil

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(67) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   activate(n__from(z0)) -> from(z0)
   activate(n__nil) -> nil
   activate(n__cons(z0, z1)) -> cons(z0, z1)
   activate(z0) -> z0

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   cons(z0, z1) -> n__cons(z0, z1)
   nil -> n__nil
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
K tuples:none
Defined Rule Symbols:   from_1, cons_2, nil

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0))) by 
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   cons(z0, z1) -> n__cons(z0, z1)
   nil -> n__nil
Tuples:
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
S tuples:
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
K tuples:none
Defined Rule Symbols:   from_1, cons_2, nil

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) by 
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   cons(z0, z1) -> n__cons(z0, z1)
   nil -> n__nil
Tuples:
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
S tuples:
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(z0, z1)))
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
K tuples:none
Defined Rule Symbols:   from_1, cons_2, nil

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(z0, z1))) by 
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   cons(z0, z1) -> n__cons(z0, z1)
   nil -> n__nil
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   from_1, cons_2, nil

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0))) by 
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__from(z0)))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   cons(z0, z1) -> n__cons(z0, z1)
   nil -> n__nil
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__from(z0)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__from(z0)))
K tuples:none
Defined Rule Symbols:   from_1, cons_2, nil

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__from(z0)))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)
   cons(z0, z1) -> n__cons(z0, z1)
   nil -> n__nil
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
K tuples:none
Defined Rule Symbols:   from_1, cons_2, nil

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(79) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   from(z0) -> cons(z0, n__from(s(z0)))
   from(z0) -> n__from(z0)

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__nil) -> c4(LENGTH(nil))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
K tuples:none
Defined Rule Symbols:   nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH1(n__nil) -> c4(LENGTH(nil)) by 
   LENGTH1(n__nil) -> c4(LENGTH(n__nil))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
   LENGTH1(n__nil) -> c4(LENGTH(n__nil))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
   LENGTH1(n__nil) -> c4(LENGTH(n__nil))
K tuples:none
Defined Rule Symbols:   nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   LENGTH1(n__nil) -> c4(LENGTH(n__nil))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   nil -> n__nil
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
K tuples:none
Defined Rule Symbols:   nil, cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(85) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   nil -> n__nil

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1)))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
K tuples:none
Defined Rule Symbols:   cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(z0, z1))) by 
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0)))))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(cons(z0, n__from(s(z0))))) by 
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
K tuples:none
Defined Rule Symbols:   cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace LENGTH1(n__from(z0)) -> c4(LENGTH(cons(z0, n__from(s(z0))))) by 
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   cons(z0, z1) -> n__cons(z0, z1)
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
K tuples:none
Defined Rule Symbols:   cons_2

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(93) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   cons(z0, z1) -> n__cons(z0, z1)

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH1(z0) -> c4(LENGTH(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(95) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH1(z0) -> c4(LENGTH(z0)) by 
   LENGTH1(n__cons(y0, y1)) -> c4(LENGTH(n__cons(y0, y1)))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
S tuples:
   LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(99) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0)) by 
   LENGTH(n__cons(z0, n__cons(y0, y1))) -> c3(LENGTH1(n__cons(y0, y1)))
   LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(103) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1))) by 
   LENGTH1(n__cons(z0, n__from(y1))) -> c4(LENGTH(n__cons(z0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(z0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__nil))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__nil))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__nil))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__nil))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__nil))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__nil))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(105) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH1(n__cons(y0, y1)) -> c4(LENGTH(n__cons(y0, y1))) by 
   LENGTH1(n__cons(z0, n__from(y1))) -> c4(LENGTH(n__cons(z0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(z0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__nil))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__nil))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__nil))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__nil))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__nil))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__nil))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__nil))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__nil))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__nil))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__nil))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(109) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1))) by 
   LENGTH(n__cons(z0, n__cons(z1, n__from(y1)))) -> c3(LENGTH1(n__cons(z1, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(n__cons(z0, z1)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__nil))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__nil))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__nil))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__nil))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(111) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH(n__cons(z0, n__cons(y0, y1))) -> c3(LENGTH1(n__cons(y0, y1))) by 
   LENGTH(n__cons(z0, n__cons(z1, n__from(y1)))) -> c3(LENGTH1(n__cons(z1, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__nil))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__nil))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__nil))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__nil))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   LENGTH1(n__cons(z0, n__cons(y1, n__nil))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__nil))))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(115) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2)))) by 
   LENGTH1(n__cons(z0, n__cons(z1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(117) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH1(n__cons(z0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(z0, n__cons(y1, y2)))) by 
   LENGTH1(n__cons(z0, n__cons(z1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH1(n__cons(z0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(z0, n__cons(y1, y2)))) by 
   LENGTH1(n__cons(z0, n__cons(z1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__nil)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__nil))))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2)))) by 
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(125) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, y2)))) by 
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(127) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, y2)))) by 
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(129) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__nil)))))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(131) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3))))) by 
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, y4))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(133) CdtRuleRemovalProof (UPPER BOUND(ADD(n^2)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
We considered the (Usable) Rules:none
And the Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))))
The order we found is given by the following interpretation:

Matrix interpretation [MATRO]:

Non-tuple symbols: 
<<<
 M( s_1(x_1) ) =  	[[2], [0]] 	+ 	[[1, 2], [0, 0]] 	* 	x_1
>>>

<<<
 M( n__nil ) =  	[[0], [1]]
>>>

<<<
 M( n__from_1(x_1) ) =  	[[1], [0]] 	+ 	[[0, 0], [0, 0]] 	* 	x_1
>>>

<<<
 M( n__cons_2(x_1, x_2) ) =  	[[1], [1]] 	+ 	[[0, 0], [0, 0]] 	* 	x_1 	+ 	[[0, 2], [0, 1]] 	* 	x_2
>>>

Tuple symbols: 
<<<
 M( LENGTH_1(x_1) ) =  	[[0], [0]] 	+ 	[[0, 2], [0, 0]] 	* 	x_1
>>>

<<<
 M( LENGTH1_1(x_1) ) =  	[[1], [4]] 	+ 	[[1, 0], [0, 0]] 	* 	x_1
>>>

<<<
 M( c3_1(x_1) ) =  	[[0], [0]] 	+ 	[[1, 0], [0, 0]] 	* 	x_1
>>>

<<<
 M( c4_1(x_1) ) =  	[[0], [0]] 	+ 	[[1, 0], [0, 0]] 	* 	x_1
>>>



Matrix type: 

We used a basic matrix type which is not further parametrizeable.





As matrix orders are CE-compatible, we used usable rules w.r.t. argument filtering in the order.
----------------------------------------

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))))
K tuples:
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1


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

(135) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, y4))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(z1, n__from(y1)))) -> c3(LENGTH1(n__cons(z1, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(z1, n__from(y1)))) -> c3(LENGTH1(n__cons(z1, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(y1, n__cons(y2, y3)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))))
S tuples:
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__from(z0)))
   LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__from(z0)) -> c4(LENGTH(n__cons(z0, n__from(s(z0)))))
   LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))))
K tuples:
   LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__from(y2))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__from(y2)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(y1, n__cons(y2, y3))))) -> c3(LENGTH1(n__cons(z1, n__cons(y1, n__cons(y2, y3)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__from(y3))))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__nil))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__nil)))))
   LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4)))))) -> c3(LENGTH1(n__cons(z1, n__cons(z2, n__cons(y2, n__cons(y3, y4))))))
   LENGTH1(n__cons(z0, n__cons(y1, n__from(y2)))) -> c4(LENGTH(n__cons(z0, n__cons(y1, n__from(y2)))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__from(y3))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(y2, n__cons(y3, y4))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__from(y4)))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__nil))))))
   LENGTH1(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))) -> c4(LENGTH(n__cons(z0, n__cons(z1, n__cons(z2, n__cons(y3, n__cons(y4, y5)))))))
Defined Rule Symbols:none

Defined Pair Symbols:   LENGTH_1, LENGTH1_1

Compound Symbols:   c3_1, c4_1