/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(NON_POLY, ?)
proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).

(0) CpxIntTrs
(1) Loat Proof [FINISHED, 1440 ms]
(2) BOUNDS(INF, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f8(A, B, B, B, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1)) :|: A >= B + 1
f8(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f8(A, B, B, B, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1)) :|: B >= A + 1
f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f2(A, B, C, D, E, B1, -(1) + G, 1 + H, 1 + H, -(1) + G, C1, D1, -(1) + G, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1)) :|: E >= F + 1 && G >= 1 && H >= 0
f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f2(A, B, C, D, E, B1, -(1) + G, 1 + H, 1 + H, -(1) + G, C1, D1, -(1) + G, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1)) :|: F >= E + 1 && G >= 1 && H >= 0
f23(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f2(A, B, C, D, E, B1, 2, 1, 1, 2, K, L, M, 2, C1, D1, F1, G1, G1, G1, G1, H1, I1, 2, J1, 0, A1)) :|: E >= E1 + 1
f23(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f2(A, B, C, D, E, B1, 2, 1, 1, 2, K, L, M, 2, C1, D1, F1, G1, G1, G1, G1, H1, I1, 2, J1, 0, A1)) :|: E1 >= E + 1
f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f8(A, C1, C1, C1, F, F, G, H, I, J, K, L, M, N, O, P, B1, R, S, T, D1, V, W, X, Y, Z, F1)) :|: A >= C1 + 1 && G >= 1 && H >= 0 && F >= E && F <= E
f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1) -> Com_1(f8(A, C1, C1, C1, F, F, G, H, I, J, K, L, M, N, O, P, B1, R, S, T, D1, V, W, X, Y, Z, F1)) :|: C1 >= A + 1 && G >= 1 && H >= 0 && F >= E && F <= E

The start-symbols are:[f23_27]


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

(1) Loat Proof (FINISHED)


### Pre-processing the ITS problem ###



Initial linear ITS problem

   Start location: f23

      0: f8 -> f8 : C'=B, D'=B, [ A>=1+B ], cost: 1

      1: f8 -> f8 : C'=B, D'=B, [ B>=1+A ], cost: 1

      2: f2 -> f2 : F'=free_1, G'=-1+G, H'=1+H, Q'=1+H, J'=-1+G, K'=free, L'=free_2, M'=-1+G, [ E>=1+F && G>=1 && H>=0 ], cost: 1

      3: f2 -> f2 : F'=free_4, G'=-1+G, H'=1+H, Q'=1+H, J'=-1+G, K'=free_3, L'=free_5, M'=-1+G, [ F>=1+E && G>=1 && H>=0 ], cost: 1

      6: f2 -> f8 : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=F, Q_1'=free_24, U'=free_26, [ A>=1+free_25 && G>=1 && H>=0 && F==E ], cost: 1

      7: f2 -> f8 : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=F, Q_1'=free_28, U'=free_30, [ free_29>=1+A && G>=1 && H>=0 && F==E ], cost: 1

      4: f23 -> f2 : F'=free_10, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ E>=1+free_8 ], cost: 1

      5: f23 -> f2 : F'=free_19, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_15, P'=free_21, Q_1'=free_23, R'=free_20, S'=free_20, T'=free_20, U'=free_20, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ free_17>=1+E ], cost: 1



Checking for constant complexity:

   The following rule is satisfiable with cost >= 1, yielding constant complexity:

      4: f23 -> f2 : F'=free_10, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ E>=1+free_8 ], cost: 1



Simplified all rules, resulting in:

   Start location: f23

      0: f8 -> f8 : C'=B, D'=B, [ A>=1+B ], cost: 1

      1: f8 -> f8 : C'=B, D'=B, [ B>=1+A ], cost: 1

      2: f2 -> f2 : F'=free_1, G'=-1+G, H'=1+H, Q'=1+H, J'=-1+G, K'=free, L'=free_2, M'=-1+G, [ E>=1+F && G>=1 && H>=0 ], cost: 1

      3: f2 -> f2 : F'=free_4, G'=-1+G, H'=1+H, Q'=1+H, J'=-1+G, K'=free_3, L'=free_5, M'=-1+G, [ F>=1+E && G>=1 && H>=0 ], cost: 1

      6: f2 -> f8 : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=F, Q_1'=free_24, U'=free_26, [ A>=1+free_25 && G>=1 && H>=0 && F==E ], cost: 1

      7: f2 -> f8 : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=F, Q_1'=free_28, U'=free_30, [ free_29>=1+A && G>=1 && H>=0 && F==E ], cost: 1

      4: f23 -> f2 : F'=free_10, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [], cost: 1

      5: f23 -> f2 : F'=free_19, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_15, P'=free_21, Q_1'=free_23, R'=free_20, S'=free_20, T'=free_20, U'=free_20, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 0.

   Accelerating the following rules:

      0: f8 -> f8 : C'=B, D'=B, [ A>=1+B ], cost: 1

      1: f8 -> f8 : C'=B, D'=B, [ B>=1+A ], cost: 1



   Accelerated rule 0 with NONTERM, yielding the new rule 8.

   Accelerated rule 1 with NONTERM, yielding the new rule 9.

   Removing the simple loops: 0 1.



Accelerating simple loops of location 1.

   Accelerating the following rules:

      2: f2 -> f2 : F'=free_1, G'=-1+G, H'=1+H, Q'=1+H, J'=-1+G, K'=free, L'=free_2, M'=-1+G, [ E>=1+F && G>=1 && H>=0 ], cost: 1

      3: f2 -> f2 : F'=free_4, G'=-1+G, H'=1+H, Q'=1+H, J'=-1+G, K'=free_3, L'=free_5, M'=-1+G, [ F>=1+E && G>=1 && H>=0 ], cost: 1



   Accelerated rule 2 with metering function G (after strengthening guard), yielding the new rule 10.

   Accelerated rule 3 with metering function G (after strengthening guard), yielding the new rule 11.

   Removing the simple loops:.



Accelerated all simple loops using metering functions (where possible):

   Start location: f23

      8: f8 -> [3] : [ A>=1+B ], cost: NONTERM

      9: f8 -> [3] : [ B>=1+A ], cost: NONTERM

      2: f2 -> f2 : F'=free_1, G'=-1+G, H'=1+H, Q'=1+H, J'=-1+G, K'=free, L'=free_2, M'=-1+G, [ E>=1+F && G>=1 && H>=0 ], cost: 1

      3: f2 -> f2 : F'=free_4, G'=-1+G, H'=1+H, Q'=1+H, J'=-1+G, K'=free_3, L'=free_5, M'=-1+G, [ F>=1+E && G>=1 && H>=0 ], cost: 1

      6: f2 -> f8 : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=F, Q_1'=free_24, U'=free_26, [ A>=1+free_25 && G>=1 && H>=0 && F==E ], cost: 1

      7: f2 -> f8 : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=F, Q_1'=free_28, U'=free_30, [ free_29>=1+A && G>=1 && H>=0 && F==E ], cost: 1

     10: f2 -> f2 : F'=free_1, G'=0, H'=G+H, Q'=G+H, J'=0, K'=free, L'=free_2, M'=0, [ E>=1+F && G>=1 && H>=0 && E>=1+free_1 ], cost: G

     11: f2 -> f2 : F'=free_4, G'=0, H'=G+H, Q'=G+H, J'=0, K'=free_3, L'=free_5, M'=0, [ F>=1+E && G>=1 && H>=0 && free_4>=1+E ], cost: G

      4: f23 -> f2 : F'=free_10, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [], cost: 1

      5: f23 -> f2 : F'=free_19, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_15, P'=free_21, Q_1'=free_23, R'=free_20, S'=free_20, T'=free_20, U'=free_20, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f23

      6: f2 -> f8 : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=F, Q_1'=free_24, U'=free_26, [ A>=1+free_25 && G>=1 && H>=0 && F==E ], cost: 1

      7: f2 -> f8 : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=F, Q_1'=free_28, U'=free_30, [ free_29>=1+A && G>=1 && H>=0 && F==E ], cost: 1

     12: f2 -> [3] : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=F, Q_1'=free_24, U'=free_26, [ A>=1+free_25 && G>=1 && H>=0 && F==E ], cost: NONTERM

     13: f2 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=F, Q_1'=free_28, U'=free_30, [ free_29>=1+A && G>=1 && H>=0 && F==E ], cost: NONTERM

      4: f23 -> f2 : F'=free_10, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [], cost: 1

      5: f23 -> f2 : F'=free_19, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_15, P'=free_21, Q_1'=free_23, R'=free_20, S'=free_20, T'=free_20, U'=free_20, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [], cost: 1

     14: f23 -> f2 : F'=free_1, G'=1, H'=2, Q'=2, J'=1, K'=free, L'=free_2, M'=1, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [], cost: 2

     15: f23 -> f2 : F'=free_1, G'=1, H'=2, Q'=2, J'=1, K'=free, L'=free_2, M'=1, N'=2, O'=free_15, P'=free_21, Q_1'=free_23, R'=free_20, S'=free_20, T'=free_20, U'=free_20, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [], cost: 2

     16: f23 -> f2 : F'=free_4, G'=1, H'=2, Q'=2, J'=1, K'=free_3, L'=free_5, M'=1, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [], cost: 2

     17: f23 -> f2 : F'=free_4, G'=1, H'=2, Q'=2, J'=1, K'=free_3, L'=free_5, M'=1, N'=2, O'=free_15, P'=free_21, Q_1'=free_23, R'=free_20, S'=free_20, T'=free_20, U'=free_20, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [], cost: 2

     18: f23 -> f2 : F'=free_1, G'=0, H'=3, Q'=3, J'=0, K'=free, L'=free_2, M'=0, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ E>=1+free_1 ], cost: 3

     19: f23 -> f2 : F'=free_1, G'=0, H'=3, Q'=3, J'=0, K'=free, L'=free_2, M'=0, N'=2, O'=free_15, P'=free_21, Q_1'=free_23, R'=free_20, S'=free_20, T'=free_20, U'=free_20, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ E>=1+free_1 ], cost: 3

     20: f23 -> f2 : F'=free_4, G'=0, H'=3, Q'=3, J'=0, K'=free_3, L'=free_5, M'=0, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ free_4>=1+E ], cost: 3

     21: f23 -> f2 : F'=free_4, G'=0, H'=3, Q'=3, J'=0, K'=free_3, L'=free_5, M'=0, N'=2, O'=free_15, P'=free_21, Q_1'=free_23, R'=free_20, S'=free_20, T'=free_20, U'=free_20, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ free_4>=1+E ], cost: 3



Removed unreachable locations (and leaf rules with constant cost):

   Start location: f23

     12: f2 -> [3] : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=F, Q_1'=free_24, U'=free_26, [ A>=1+free_25 && G>=1 && H>=0 && F==E ], cost: NONTERM

     13: f2 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=F, Q_1'=free_28, U'=free_30, [ free_29>=1+A && G>=1 && H>=0 && F==E ], cost: NONTERM

      4: f23 -> f2 : F'=free_10, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [], cost: 1

      5: f23 -> f2 : F'=free_19, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_15, P'=free_21, Q_1'=free_23, R'=free_20, S'=free_20, T'=free_20, U'=free_20, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [], cost: 1

     14: f23 -> f2 : F'=free_1, G'=1, H'=2, Q'=2, J'=1, K'=free, L'=free_2, M'=1, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [], cost: 2

     15: f23 -> f2 : F'=free_1, G'=1, H'=2, Q'=2, J'=1, K'=free, L'=free_2, M'=1, N'=2, O'=free_15, P'=free_21, Q_1'=free_23, R'=free_20, S'=free_20, T'=free_20, U'=free_20, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [], cost: 2

     16: f23 -> f2 : F'=free_4, G'=1, H'=2, Q'=2, J'=1, K'=free_3, L'=free_5, M'=1, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [], cost: 2

     17: f23 -> f2 : F'=free_4, G'=1, H'=2, Q'=2, J'=1, K'=free_3, L'=free_5, M'=1, N'=2, O'=free_15, P'=free_21, Q_1'=free_23, R'=free_20, S'=free_20, T'=free_20, U'=free_20, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [], cost: 2

     18: f23 -> f2 : F'=free_1, G'=0, H'=3, Q'=3, J'=0, K'=free, L'=free_2, M'=0, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ E>=1+free_1 ], cost: 3

     19: f23 -> f2 : F'=free_1, G'=0, H'=3, Q'=3, J'=0, K'=free, L'=free_2, M'=0, N'=2, O'=free_15, P'=free_21, Q_1'=free_23, R'=free_20, S'=free_20, T'=free_20, U'=free_20, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ E>=1+free_1 ], cost: 3

     20: f23 -> f2 : F'=free_4, G'=0, H'=3, Q'=3, J'=0, K'=free_3, L'=free_5, M'=0, N'=2, O'=free_6, P'=free_12, Q_1'=free_14, R'=free_11, S'=free_11, T'=free_11, U'=free_11, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ free_4>=1+E ], cost: 3

     21: f23 -> f2 : F'=free_4, G'=0, H'=3, Q'=3, J'=0, K'=free_3, L'=free_5, M'=0, N'=2, O'=free_15, P'=free_21, Q_1'=free_23, R'=free_20, S'=free_20, T'=free_20, U'=free_20, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ free_4>=1+E ], cost: 3



Eliminated locations (on tree-shaped paths):

   Start location: f23

     22: f23 -> [3] : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=free_10, F'=free_10, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_6, P'=free_12, Q_1'=free_24, R'=free_11, S'=free_11, T'=free_11, U'=free_26, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ A>=1+free_25 && free_10==E ], cost: NONTERM

     23: f23 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=free_10, F'=free_10, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_6, P'=free_12, Q_1'=free_28, R'=free_11, S'=free_11, T'=free_11, U'=free_30, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ free_29>=1+A && free_10==E ], cost: NONTERM

     24: f23 -> [3] : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=free_19, F'=free_19, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_15, P'=free_21, Q_1'=free_24, R'=free_20, S'=free_20, T'=free_20, U'=free_26, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ A>=1+free_25 && free_19==E ], cost: NONTERM

     25: f23 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=free_19, F'=free_19, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_15, P'=free_21, Q_1'=free_28, R'=free_20, S'=free_20, T'=free_20, U'=free_30, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ free_29>=1+A && free_19==E ], cost: NONTERM

     26: f23 -> [3] : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=free_1, F'=free_1, G'=1, H'=2, Q'=2, J'=1, K'=free, L'=free_2, M'=1, N'=2, O'=free_6, P'=free_12, Q_1'=free_24, R'=free_11, S'=free_11, T'=free_11, U'=free_26, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ A>=1+free_25 && free_1==E ], cost: NONTERM

     27: f23 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=free_1, F'=free_1, G'=1, H'=2, Q'=2, J'=1, K'=free, L'=free_2, M'=1, N'=2, O'=free_6, P'=free_12, Q_1'=free_28, R'=free_11, S'=free_11, T'=free_11, U'=free_30, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ free_29>=1+A && free_1==E ], cost: NONTERM

     28: f23 -> [3] : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=free_1, F'=free_1, G'=1, H'=2, Q'=2, J'=1, K'=free, L'=free_2, M'=1, N'=2, O'=free_15, P'=free_21, Q_1'=free_24, R'=free_20, S'=free_20, T'=free_20, U'=free_26, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ A>=1+free_25 && free_1==E ], cost: NONTERM

     29: f23 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=free_1, F'=free_1, G'=1, H'=2, Q'=2, J'=1, K'=free, L'=free_2, M'=1, N'=2, O'=free_15, P'=free_21, Q_1'=free_28, R'=free_20, S'=free_20, T'=free_20, U'=free_30, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ free_29>=1+A && free_1==E ], cost: NONTERM

     30: f23 -> [3] : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=free_4, F'=free_4, G'=1, H'=2, Q'=2, J'=1, K'=free_3, L'=free_5, M'=1, N'=2, O'=free_6, P'=free_12, Q_1'=free_24, R'=free_11, S'=free_11, T'=free_11, U'=free_26, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ A>=1+free_25 && free_4==E ], cost: NONTERM

     31: f23 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=free_4, F'=free_4, G'=1, H'=2, Q'=2, J'=1, K'=free_3, L'=free_5, M'=1, N'=2, O'=free_6, P'=free_12, Q_1'=free_28, R'=free_11, S'=free_11, T'=free_11, U'=free_30, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ free_29>=1+A && free_4==E ], cost: NONTERM

     32: f23 -> [3] : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=free_4, F'=free_4, G'=1, H'=2, Q'=2, J'=1, K'=free_3, L'=free_5, M'=1, N'=2, O'=free_15, P'=free_21, Q_1'=free_24, R'=free_20, S'=free_20, T'=free_20, U'=free_26, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ A>=1+free_25 && free_4==E ], cost: NONTERM

     33: f23 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=free_4, F'=free_4, G'=1, H'=2, Q'=2, J'=1, K'=free_3, L'=free_5, M'=1, N'=2, O'=free_15, P'=free_21, Q_1'=free_28, R'=free_20, S'=free_20, T'=free_20, U'=free_30, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ free_29>=1+A && free_4==E ], cost: NONTERM



Applied pruning (of leafs and parallel rules):

   Start location: f23

     22: f23 -> [3] : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=free_10, F'=free_10, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_6, P'=free_12, Q_1'=free_24, R'=free_11, S'=free_11, T'=free_11, U'=free_26, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ A>=1+free_25 && free_10==E ], cost: NONTERM

     23: f23 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=free_10, F'=free_10, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_6, P'=free_12, Q_1'=free_28, R'=free_11, S'=free_11, T'=free_11, U'=free_30, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ free_29>=1+A && free_10==E ], cost: NONTERM

     25: f23 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=free_19, F'=free_19, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_15, P'=free_21, Q_1'=free_28, R'=free_20, S'=free_20, T'=free_20, U'=free_30, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ free_29>=1+A && free_19==E ], cost: NONTERM

     27: f23 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=free_1, F'=free_1, G'=1, H'=2, Q'=2, J'=1, K'=free, L'=free_2, M'=1, N'=2, O'=free_6, P'=free_12, Q_1'=free_28, R'=free_11, S'=free_11, T'=free_11, U'=free_30, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ free_29>=1+A && free_1==E ], cost: NONTERM

     28: f23 -> [3] : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=free_1, F'=free_1, G'=1, H'=2, Q'=2, J'=1, K'=free, L'=free_2, M'=1, N'=2, O'=free_15, P'=free_21, Q_1'=free_24, R'=free_20, S'=free_20, T'=free_20, U'=free_26, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ A>=1+free_25 && free_1==E ], cost: NONTERM



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f23

     22: f23 -> [3] : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=free_10, F'=free_10, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_6, P'=free_12, Q_1'=free_24, R'=free_11, S'=free_11, T'=free_11, U'=free_26, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ A>=1+free_25 && free_10==E ], cost: NONTERM

     23: f23 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=free_10, F'=free_10, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_6, P'=free_12, Q_1'=free_28, R'=free_11, S'=free_11, T'=free_11, U'=free_30, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ free_29>=1+A && free_10==E ], cost: NONTERM

     25: f23 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=free_19, F'=free_19, G'=2, H'=1, Q'=1, J'=2, N'=2, O'=free_15, P'=free_21, Q_1'=free_28, R'=free_20, S'=free_20, T'=free_20, U'=free_30, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ free_29>=1+A && free_19==E ], cost: NONTERM

     27: f23 -> [3] : A1'=free_31, B'=free_29, C'=free_29, D'=free_29, E'=free_1, F'=free_1, G'=1, H'=2, Q'=2, J'=1, K'=free, L'=free_2, M'=1, N'=2, O'=free_6, P'=free_12, Q_1'=free_28, R'=free_11, S'=free_11, T'=free_11, U'=free_30, V'=free_7, W'=free_13, X'=2, Y'=free_9, Z'=0, [ free_29>=1+A && free_1==E ], cost: NONTERM

     28: f23 -> [3] : A1'=free_27, B'=free_25, C'=free_25, D'=free_25, E'=free_1, F'=free_1, G'=1, H'=2, Q'=2, J'=1, K'=free, L'=free_2, M'=1, N'=2, O'=free_15, P'=free_21, Q_1'=free_24, R'=free_20, S'=free_20, T'=free_20, U'=free_26, V'=free_16, W'=free_22, X'=2, Y'=free_18, Z'=0, [ A>=1+free_25 && free_1==E ], cost: NONTERM



Computing asymptotic complexity for rule 22

   Guard is satisfiable, yielding nontermination

   Resulting cost NONTERM has complexity: Nonterm



Found new complexity Nonterm.



Obtained the following overall complexity (w.r.t. the length of the input n):

   Complexity:  Nonterm

   Cpx degree:  Nonterm

   Solved cost: NONTERM

   Rule cost:   NONTERM

   Rule guard:  [ A>=1+free_25 && free_10==E ]



NO


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(2)
BOUNDS(INF, INF)