/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1492 ms]
(2) BOUNDS(INF, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f12(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, B1, C1, D1, E1) -> Com_1(f11(A, B, A, A, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: A >= B + 1
f12(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, B1, C1, D1, E1) -> Com_1(f11(A, B, A, A, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: B >= A + 1
f11(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, B1, C1, D1, E1) -> Com_1(f11(A, B, A, A, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: A >= B + 1
f11(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, B1, C1, D1, E1) -> Com_1(f11(A, B, A, A, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: B >= A + 1
f6(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, B1, C1, D1, E1) -> Com_1(f6(A, B, C, D, H1, F, 1 + G, -(1) + H, 1 + G, -(1) + H, F1, G1, -(1) + H, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: E >= F + 1 && G >= 0 && H >= 1
f6(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, B1, C1, D1, E1) -> Com_1(f6(A, B, C, D, H1, F, 1 + G, -(1) + H, 1 + G, -(1) + H, F1, G1, -(1) + H, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1)) :|: F >= E + 1 && G >= 0 && H >= 1
f26(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, B1, C1, D1, E1) -> Com_1(f6(A, B, C, D, L1, F, 1, 4, 1, 4, K, L, M, F1, 2, 3, G1, H1, 4, J1, 0, K1, M1, M1, M1, M1, N1, O1, P1, 4, E1)) :|: I1 >= F + 1
f26(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, B1, C1, D1, E1) -> Com_1(f6(A, B, C, D, L1, F, 1, 4, 1, 4, K, L, M, F1, 2, 3, G1, H1, 4, J1, 0, K1, M1, M1, M1, M1, N1, O1, P1, 4, E1)) :|: F >= I1 + 1
f6(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, B1, C1, D1, E1) -> Com_1(f12(J1, B, J1, J1, E, E, G, H, I, J, K, L, M, F1, O, P, Q, R, S, T, U, V, W, X, Y, G1, A1, B1, C1, D1, H1)) :|: J1 >= B + 1 && G >= 0 && H >= 1 && E >= F && E <= F
f6(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, B1, C1, D1, E1) -> Com_1(f12(J1, B, J1, J1, E, E, G, H, I, J, K, L, M, F1, O, P, Q, R, S, T, U, V, W, X, Y, G1, A1, B1, C1, D1, H1)) :|: B >= J1 + 1 && G >= 0 && H >= 1 && E >= F && E <= F

The start-symbols are:[f26_31]


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

(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f26

      0: f12 -> f11 : C'=A, D'=A, [ A>=1+B ], cost: 1

      1: f12 -> f11 : C'=A, D'=A, [ B>=1+A ], cost: 1

      2: f11 -> f11 : C'=A, D'=A, [ A>=1+B ], cost: 1

      3: f11 -> f11 : C'=A, D'=A, [ B>=1+A ], cost: 1

      4: f6 -> f6 : E'=free_2, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_1, L'=free, M'=-1+H, [ E>=1+F && G>=0 && H>=1 ], cost: 1

      5: f6 -> f6 : E'=free_5, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_4, L'=free_3, M'=-1+H, [ F>=1+E && G>=0 && H>=1 ], cost: 1

      8: f6 -> f12 : A'=free_31, C'=free_31, D'=free_31, E1'=free_29, F'=E, N'=free_30, Z'=free_28, [ free_31>=1+B && G>=0 && H>=1 && E==F ], cost: 1

      9: f6 -> f12 : A'=free_35, C'=free_35, D'=free_35, E1'=free_33, F'=E, N'=free_34, Z'=free_32, [ B>=1+free_35 && G>=0 && H>=1 && E==F ], cost: 1

      6: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [ free_13>=1+F ], cost: 1

      7: f26 -> f6 : A1'=free_25, B1'=free_21, C1'=free_17, D1'=4, E'=free_26, G'=1, H'=4, Q'=1, J'=4, N'=free_22, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_19, [ F>=1+free_24 ], cost: 1



Checking for constant complexity:

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

      6: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [ free_13>=1+F ], cost: 1



Simplified all rules, resulting in:

   Start location: f26

      0: f12 -> f11 : C'=A, D'=A, [ A>=1+B ], cost: 1

      1: f12 -> f11 : C'=A, D'=A, [ B>=1+A ], cost: 1

      2: f11 -> f11 : C'=A, D'=A, [ A>=1+B ], cost: 1

      3: f11 -> f11 : C'=A, D'=A, [ B>=1+A ], cost: 1

      4: f6 -> f6 : E'=free_2, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_1, L'=free, M'=-1+H, [ E>=1+F && G>=0 && H>=1 ], cost: 1

      5: f6 -> f6 : E'=free_5, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_4, L'=free_3, M'=-1+H, [ F>=1+E && G>=0 && H>=1 ], cost: 1

      8: f6 -> f12 : A'=free_31, C'=free_31, D'=free_31, E1'=free_29, F'=E, N'=free_30, Z'=free_28, [ free_31>=1+B && G>=0 && H>=1 && E==F ], cost: 1

      9: f6 -> f12 : A'=free_35, C'=free_35, D'=free_35, E1'=free_33, F'=E, N'=free_34, Z'=free_32, [ B>=1+free_35 && G>=0 && H>=1 && E==F ], cost: 1

      6: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [], cost: 1

      7: f26 -> f6 : A1'=free_25, B1'=free_21, C1'=free_17, D1'=4, E'=free_26, G'=1, H'=4, Q'=1, J'=4, N'=free_22, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_19, [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 1.

   Accelerating the following rules:

      2: f11 -> f11 : C'=A, D'=A, [ A>=1+B ], cost: 1

      3: f11 -> f11 : C'=A, D'=A, [ B>=1+A ], cost: 1



   Accelerated rule 2 with NONTERM, yielding the new rule 10.

   Accelerated rule 3 with NONTERM, yielding the new rule 11.

   Removing the simple loops: 2 3.



Accelerating simple loops of location 2.

   Accelerating the following rules:

      4: f6 -> f6 : E'=free_2, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_1, L'=free, M'=-1+H, [ E>=1+F && G>=0 && H>=1 ], cost: 1

      5: f6 -> f6 : E'=free_5, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_4, L'=free_3, M'=-1+H, [ F>=1+E && G>=0 && H>=1 ], cost: 1



   Accelerated rule 4 with metering function H (after strengthening guard), yielding the new rule 12.

   Accelerated rule 5 with metering function H (after strengthening guard), yielding the new rule 13.

   Removing the simple loops:.



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

   Start location: f26

      0: f12 -> f11 : C'=A, D'=A, [ A>=1+B ], cost: 1

      1: f12 -> f11 : C'=A, D'=A, [ B>=1+A ], cost: 1

     10: f11 -> [4] : [ A>=1+B ], cost: NONTERM

     11: f11 -> [4] : [ B>=1+A ], cost: NONTERM

      4: f6 -> f6 : E'=free_2, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_1, L'=free, M'=-1+H, [ E>=1+F && G>=0 && H>=1 ], cost: 1

      5: f6 -> f6 : E'=free_5, G'=1+G, H'=-1+H, Q'=1+G, J'=-1+H, K'=free_4, L'=free_3, M'=-1+H, [ F>=1+E && G>=0 && H>=1 ], cost: 1

      8: f6 -> f12 : A'=free_31, C'=free_31, D'=free_31, E1'=free_29, F'=E, N'=free_30, Z'=free_28, [ free_31>=1+B && G>=0 && H>=1 && E==F ], cost: 1

      9: f6 -> f12 : A'=free_35, C'=free_35, D'=free_35, E1'=free_33, F'=E, N'=free_34, Z'=free_32, [ B>=1+free_35 && G>=0 && H>=1 && E==F ], cost: 1

     12: f6 -> f6 : E'=free_2, G'=G+H, H'=0, Q'=G+H, J'=0, K'=free_1, L'=free, M'=0, [ E>=1+F && G>=0 && H>=1 && free_2>=1+F ], cost: H

     13: f6 -> f6 : E'=free_5, G'=G+H, H'=0, Q'=G+H, J'=0, K'=free_4, L'=free_3, M'=0, [ F>=1+E && G>=0 && H>=1 && F>=1+free_5 ], cost: H

      6: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [], cost: 1

      7: f26 -> f6 : A1'=free_25, B1'=free_21, C1'=free_17, D1'=4, E'=free_26, G'=1, H'=4, Q'=1, J'=4, N'=free_22, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_19, [], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f26

      0: f12 -> f11 : C'=A, D'=A, [ A>=1+B ], cost: 1

      1: f12 -> f11 : C'=A, D'=A, [ B>=1+A ], cost: 1

     14: f12 -> [4] : C'=A, D'=A, [ A>=1+B ], cost: NONTERM

     15: f12 -> [4] : C'=A, D'=A, [ B>=1+A ], cost: NONTERM

      8: f6 -> f12 : A'=free_31, C'=free_31, D'=free_31, E1'=free_29, F'=E, N'=free_30, Z'=free_28, [ free_31>=1+B && G>=0 && H>=1 && E==F ], cost: 1

      9: f6 -> f12 : A'=free_35, C'=free_35, D'=free_35, E1'=free_33, F'=E, N'=free_34, Z'=free_32, [ B>=1+free_35 && G>=0 && H>=1 && E==F ], cost: 1

      6: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [], cost: 1

      7: f26 -> f6 : A1'=free_25, B1'=free_21, C1'=free_17, D1'=4, E'=free_26, G'=1, H'=4, Q'=1, J'=4, N'=free_22, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_19, [], cost: 1

     16: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [], cost: 2

     17: f26 -> f6 : A1'=free_25, B1'=free_21, C1'=free_17, D1'=4, E'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_22, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_19, [], cost: 2

     18: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_5, G'=2, H'=3, Q'=2, J'=3, K'=free_4, L'=free_3, M'=3, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [], cost: 2

     19: f26 -> f6 : A1'=free_25, B1'=free_21, C1'=free_17, D1'=4, E'=free_5, G'=2, H'=3, Q'=2, J'=3, K'=free_4, L'=free_3, M'=3, N'=free_22, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_19, [], cost: 2

     20: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_2, G'=5, H'=0, Q'=5, J'=0, K'=free_1, L'=free, M'=0, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [ free_2>=1+F ], cost: 5

     21: f26 -> f6 : A1'=free_25, B1'=free_21, C1'=free_17, D1'=4, E'=free_2, G'=5, H'=0, Q'=5, J'=0, K'=free_1, L'=free, M'=0, N'=free_22, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_19, [ free_2>=1+F ], cost: 5

     22: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_5, G'=5, H'=0, Q'=5, J'=0, K'=free_4, L'=free_3, M'=0, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [ F>=1+free_5 ], cost: 5

     23: f26 -> f6 : A1'=free_25, B1'=free_21, C1'=free_17, D1'=4, E'=free_5, G'=5, H'=0, Q'=5, J'=0, K'=free_4, L'=free_3, M'=0, N'=free_22, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_19, [ F>=1+free_5 ], cost: 5



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

   Start location: f26

     14: f12 -> [4] : C'=A, D'=A, [ A>=1+B ], cost: NONTERM

     15: f12 -> [4] : C'=A, D'=A, [ B>=1+A ], cost: NONTERM

      8: f6 -> f12 : A'=free_31, C'=free_31, D'=free_31, E1'=free_29, F'=E, N'=free_30, Z'=free_28, [ free_31>=1+B && G>=0 && H>=1 && E==F ], cost: 1

      9: f6 -> f12 : A'=free_35, C'=free_35, D'=free_35, E1'=free_33, F'=E, N'=free_34, Z'=free_32, [ B>=1+free_35 && G>=0 && H>=1 && E==F ], cost: 1

      6: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [], cost: 1

      7: f26 -> f6 : A1'=free_25, B1'=free_21, C1'=free_17, D1'=4, E'=free_26, G'=1, H'=4, Q'=1, J'=4, N'=free_22, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_19, [], cost: 1

     16: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [], cost: 2

     17: f26 -> f6 : A1'=free_25, B1'=free_21, C1'=free_17, D1'=4, E'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_22, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_19, [], cost: 2

     18: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_5, G'=2, H'=3, Q'=2, J'=3, K'=free_4, L'=free_3, M'=3, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [], cost: 2

     19: f26 -> f6 : A1'=free_25, B1'=free_21, C1'=free_17, D1'=4, E'=free_5, G'=2, H'=3, Q'=2, J'=3, K'=free_4, L'=free_3, M'=3, N'=free_22, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_19, [], cost: 2

     20: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_2, G'=5, H'=0, Q'=5, J'=0, K'=free_1, L'=free, M'=0, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [ free_2>=1+F ], cost: 5

     21: f26 -> f6 : A1'=free_25, B1'=free_21, C1'=free_17, D1'=4, E'=free_2, G'=5, H'=0, Q'=5, J'=0, K'=free_1, L'=free, M'=0, N'=free_22, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_19, [ free_2>=1+F ], cost: 5

     22: f26 -> f6 : A1'=free_14, B1'=free_10, C1'=free_6, D1'=4, E'=free_5, G'=5, H'=0, Q'=5, J'=0, K'=free_4, L'=free_3, M'=0, N'=free_11, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_8, [ F>=1+free_5 ], cost: 5

     23: f26 -> f6 : A1'=free_25, B1'=free_21, C1'=free_17, D1'=4, E'=free_5, G'=5, H'=0, Q'=5, J'=0, K'=free_4, L'=free_3, M'=0, N'=free_22, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_19, [ F>=1+free_5 ], cost: 5



Eliminated locations (on tree-shaped paths):

   Start location: f26

     14: f12 -> [4] : C'=A, D'=A, [ A>=1+B ], cost: NONTERM

     15: f12 -> [4] : C'=A, D'=A, [ B>=1+A ], cost: NONTERM

     24: f26 -> f12 : A'=free_31, A1'=free_14, B1'=free_10, C'=free_31, C1'=free_6, D'=free_31, D1'=4, E'=free_15, E1'=free_29, F'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_30, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_28, [ free_31>=1+B && free_15==F ], cost: 2

     25: f26 -> f12 : A'=free_35, A1'=free_14, B1'=free_10, C'=free_35, C1'=free_6, D'=free_35, D1'=4, E'=free_15, E1'=free_33, F'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_34, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_32, [ B>=1+free_35 && free_15==F ], cost: 2

     26: f26 -> f12 : A'=free_31, A1'=free_25, B1'=free_21, C'=free_31, C1'=free_17, D'=free_31, D1'=4, E'=free_26, E1'=free_29, F'=free_26, G'=1, H'=4, Q'=1, J'=4, N'=free_30, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_28, [ free_31>=1+B && free_26==F ], cost: 2

     27: f26 -> f12 : A'=free_35, A1'=free_25, B1'=free_21, C'=free_35, C1'=free_17, D'=free_35, D1'=4, E'=free_26, E1'=free_33, F'=free_26, G'=1, H'=4, Q'=1, J'=4, N'=free_34, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_32, [ B>=1+free_35 && free_26==F ], cost: 2

     28: f26 -> f12 : A'=free_31, A1'=free_14, B1'=free_10, C'=free_31, C1'=free_6, D'=free_31, D1'=4, E'=free_2, E1'=free_29, F'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_30, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_28, [ free_31>=1+B && free_2==F ], cost: 3

     29: f26 -> f12 : A'=free_35, A1'=free_14, B1'=free_10, C'=free_35, C1'=free_6, D'=free_35, D1'=4, E'=free_2, E1'=free_33, F'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_34, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_32, [ B>=1+free_35 && free_2==F ], cost: 3

     30: f26 -> f12 : A'=free_31, A1'=free_25, B1'=free_21, C'=free_31, C1'=free_17, D'=free_31, D1'=4, E'=free_2, E1'=free_29, F'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_30, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_28, [ free_31>=1+B && free_2==F ], cost: 3

     31: f26 -> f12 : A'=free_35, A1'=free_25, B1'=free_21, C'=free_35, C1'=free_17, D'=free_35, D1'=4, E'=free_2, E1'=free_33, F'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_34, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_32, [ B>=1+free_35 && free_2==F ], cost: 3

     32: f26 -> f12 : A'=free_31, A1'=free_14, B1'=free_10, C'=free_31, C1'=free_6, D'=free_31, D1'=4, E'=free_5, E1'=free_29, F'=free_5, G'=2, H'=3, Q'=2, J'=3, K'=free_4, L'=free_3, M'=3, N'=free_30, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_28, [ free_31>=1+B && free_5==F ], cost: 3

     33: f26 -> f12 : A'=free_35, A1'=free_14, B1'=free_10, C'=free_35, C1'=free_6, D'=free_35, D1'=4, E'=free_5, E1'=free_33, F'=free_5, G'=2, H'=3, Q'=2, J'=3, K'=free_4, L'=free_3, M'=3, N'=free_34, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_32, [ B>=1+free_35 && free_5==F ], cost: 3

     34: f26 -> f12 : A'=free_31, A1'=free_25, B1'=free_21, C'=free_31, C1'=free_17, D'=free_31, D1'=4, E'=free_5, E1'=free_29, F'=free_5, G'=2, H'=3, Q'=2, J'=3, K'=free_4, L'=free_3, M'=3, N'=free_30, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_28, [ free_31>=1+B && free_5==F ], cost: 3

     35: f26 -> f12 : A'=free_35, A1'=free_25, B1'=free_21, C'=free_35, C1'=free_17, D'=free_35, D1'=4, E'=free_5, E1'=free_33, F'=free_5, G'=2, H'=3, Q'=2, J'=3, K'=free_4, L'=free_3, M'=3, N'=free_34, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_32, [ B>=1+free_35 && free_5==F ], cost: 3



Applied pruning (of leafs and parallel rules):

   Start location: f26

     14: f12 -> [4] : C'=A, D'=A, [ A>=1+B ], cost: NONTERM

     15: f12 -> [4] : C'=A, D'=A, [ B>=1+A ], cost: NONTERM

     24: f26 -> f12 : A'=free_31, A1'=free_14, B1'=free_10, C'=free_31, C1'=free_6, D'=free_31, D1'=4, E'=free_15, E1'=free_29, F'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_30, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_28, [ free_31>=1+B && free_15==F ], cost: 2

     25: f26 -> f12 : A'=free_35, A1'=free_14, B1'=free_10, C'=free_35, C1'=free_6, D'=free_35, D1'=4, E'=free_15, E1'=free_33, F'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_34, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_32, [ B>=1+free_35 && free_15==F ], cost: 2

     27: f26 -> f12 : A'=free_35, A1'=free_25, B1'=free_21, C'=free_35, C1'=free_17, D'=free_35, D1'=4, E'=free_26, E1'=free_33, F'=free_26, G'=1, H'=4, Q'=1, J'=4, N'=free_34, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_32, [ B>=1+free_35 && free_26==F ], cost: 2

     29: f26 -> f12 : A'=free_35, A1'=free_14, B1'=free_10, C'=free_35, C1'=free_6, D'=free_35, D1'=4, E'=free_2, E1'=free_33, F'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_34, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_32, [ B>=1+free_35 && free_2==F ], cost: 3

     30: f26 -> f12 : A'=free_31, A1'=free_25, B1'=free_21, C'=free_31, C1'=free_17, D'=free_31, D1'=4, E'=free_2, E1'=free_29, F'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_30, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_28, [ free_31>=1+B && free_2==F ], cost: 3



Eliminated locations (on tree-shaped paths):

   Start location: f26

     36: f26 -> [4] : A'=free_31, A1'=free_14, B1'=free_10, C'=free_31, C1'=free_6, D'=free_31, D1'=4, E'=free_15, E1'=free_29, F'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_30, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_28, [ free_31>=1+B && free_15==F ], cost: NONTERM

     37: f26 -> [4] : A'=free_35, A1'=free_14, B1'=free_10, C'=free_35, C1'=free_6, D'=free_35, D1'=4, E'=free_15, E1'=free_33, F'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_34, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_32, [ B>=1+free_35 && free_15==F ], cost: NONTERM

     38: f26 -> [4] : A'=free_35, A1'=free_25, B1'=free_21, C'=free_35, C1'=free_17, D'=free_35, D1'=4, E'=free_26, E1'=free_33, F'=free_26, G'=1, H'=4, Q'=1, J'=4, N'=free_34, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_32, [ B>=1+free_35 && free_26==F ], cost: NONTERM

     39: f26 -> [4] : A'=free_35, A1'=free_14, B1'=free_10, C'=free_35, C1'=free_6, D'=free_35, D1'=4, E'=free_2, E1'=free_33, F'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_34, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_32, [ B>=1+free_35 && free_2==F ], cost: NONTERM

     40: f26 -> [4] : A'=free_31, A1'=free_25, B1'=free_21, C'=free_31, C1'=free_17, D'=free_31, D1'=4, E'=free_2, E1'=free_29, F'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_30, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_28, [ free_31>=1+B && free_2==F ], cost: NONTERM



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f26

     36: f26 -> [4] : A'=free_31, A1'=free_14, B1'=free_10, C'=free_31, C1'=free_6, D'=free_31, D1'=4, E'=free_15, E1'=free_29, F'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_30, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_28, [ free_31>=1+B && free_15==F ], cost: NONTERM

     37: f26 -> [4] : A'=free_35, A1'=free_14, B1'=free_10, C'=free_35, C1'=free_6, D'=free_35, D1'=4, E'=free_15, E1'=free_33, F'=free_15, G'=1, H'=4, Q'=1, J'=4, N'=free_34, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_32, [ B>=1+free_35 && free_15==F ], cost: NONTERM

     38: f26 -> [4] : A'=free_35, A1'=free_25, B1'=free_21, C'=free_35, C1'=free_17, D'=free_35, D1'=4, E'=free_26, E1'=free_33, F'=free_26, G'=1, H'=4, Q'=1, J'=4, N'=free_34, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_32, [ B>=1+free_35 && free_26==F ], cost: NONTERM

     39: f26 -> [4] : A'=free_35, A1'=free_14, B1'=free_10, C'=free_35, C1'=free_6, D'=free_35, D1'=4, E'=free_2, E1'=free_33, F'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_34, O'=2, P'=3, Q_1'=free_7, R'=free_9, S'=4, T'=free_16, U'=0, V'=free_12, W'=free_8, X'=free_8, Y'=free_8, Z'=free_32, [ B>=1+free_35 && free_2==F ], cost: NONTERM

     40: f26 -> [4] : A'=free_31, A1'=free_25, B1'=free_21, C'=free_31, C1'=free_17, D'=free_31, D1'=4, E'=free_2, E1'=free_29, F'=free_2, G'=2, H'=3, Q'=2, J'=3, K'=free_1, L'=free, M'=3, N'=free_30, O'=2, P'=3, Q_1'=free_18, R'=free_20, S'=4, T'=free_27, U'=0, V'=free_23, W'=free_19, X'=free_19, Y'=free_19, Z'=free_28, [ free_31>=1+B && free_2==F ], cost: NONTERM



Computing asymptotic complexity for rule 36

   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:  [ free_31>=1+B && free_15==F ]



NO


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(2)
BOUNDS(INF, INF)