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


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WORST_CASE(NON_POLY, ?)
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1598 ms]
(2) BOUNDS(INF, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f47(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: A >= B
f39(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f47(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: C >= 3
f39(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f47(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 1 >= C
f54(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f54(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: TRUE
f56(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: TRUE
f47(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f54(A, B, C, D, 0, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: D >= 1
f47(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f54(A, B, C, D, 0, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 0 >= D
f39(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f47(A, B, 2, D, E + 1, F, H, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: C >= 2 && C <= 2
f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f47(A, B, C, D, E, F, G, X, Y, Z, A1, E, X, X, X, P, Q, R, S, T, U, V, W)) :|: X >= 1 && B >= A + 1
f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f39(A, B, B1, D, E, F, G, X, Y, Z, A1, E, X, X, X, X, R, 0, B1, B1, B1, 0, W)) :|: B >= A + 1 && 0 >= X && B1 >= 2
f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f39(A, B, B1, D, E, F, G, X, Y, Z, A1, E, X, X, X, X, R, 0, B1, B1, B1, 0, W)) :|: B >= A + 1 && 0 >= X && 0 >= B1
f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f13(A + 1, B, 1, D, E, F, G, X, Y, Z, A1, E, X, X, X, X, R, R, 1, 1, 1, 0, W)) :|: 0 >= X && B >= A + 1
f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f13(A, B, C, Y, E, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, 0)) :|: 0 >= Y
f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W) -> Com_1(f13(A, B, C, Y, E, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, 0)) :|: Y >= 1

The start-symbols are:[f0_23]


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

(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f13 -> f47 : [ A>=B ], cost: 1

      8: f13 -> f47 : H'=free, Q'=free_1, J'=free_3, K'=free_2, L'=E, M'=free, N'=free, O'=free, [ free>=1 && B>=1+A ], cost: 1

      9: f13 -> f39 : C'=free_4, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, [ B>=1+A && 0>=free_6 && free_4>=2 ], cost: 1

     10: f13 -> f39 : C'=free_9, H'=free_11, Q'=free_13, J'=free_12, K'=free_10, L'=E, M'=free_11, N'=free_11, O'=free_11, P'=free_11, Q_1'=R, R'=0, S'=free_9, T'=free_9, U'=free_9, V'=0, [ B>=1+A && 0>=free_11 && 0>=free_9 ], cost: 1

     11: f13 -> f13 : A'=1+A, C'=1, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, [ 0>=free_14 && B>=1+A ], cost: 1

      1: f39 -> f47 : [ C>=3 ], cost: 1

      2: f39 -> f47 : [ 1>=C ], cost: 1

      7: f39 -> f47 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1

      3: f54 -> f54 : [], cost: 1

      4: f56 -> f59 : A1'=B, B'=C, B1'=D, C'=E, D'=F, E'=G, F'=H, G'=Q, H'=J, Q'=K, J'=L, K'=M, L'=N, M'=O, N'=P, O'=Q_1, P'=R, Q_1'=S, R'=T, S'=U, T'=V, U'=W, [], cost: 1

      5: f47 -> f54 : E'=0, [ D>=1 ], cost: 1

      6: f47 -> f54 : E'=0, F'=0, [ 0>=D ], cost: 1

     12: f0 -> f13 : D'=free_18, F'=0, W'=0, [ 0>=free_18 ], cost: 1

     13: f0 -> f13 : D'=free_19, F'=0, W'=0, [ free_19>=1 ], cost: 1



Checking for constant complexity:

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

     12: f0 -> f13 : D'=free_18, F'=0, W'=0, [ 0>=free_18 ], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f13 -> f47 : [ A>=B ], cost: 1

      8: f13 -> f47 : H'=free, Q'=free_1, J'=free_3, K'=free_2, L'=E, M'=free, N'=free, O'=free, [ free>=1 && B>=1+A ], cost: 1

      9: f13 -> f39 : C'=free_4, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, [ B>=1+A && 0>=free_6 && free_4>=2 ], cost: 1

     10: f13 -> f39 : C'=free_9, H'=free_11, Q'=free_13, J'=free_12, K'=free_10, L'=E, M'=free_11, N'=free_11, O'=free_11, P'=free_11, Q_1'=R, R'=0, S'=free_9, T'=free_9, U'=free_9, V'=0, [ B>=1+A && 0>=free_11 && 0>=free_9 ], cost: 1

     11: f13 -> f13 : A'=1+A, C'=1, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, [ 0>=free_14 && B>=1+A ], cost: 1

      1: f39 -> f47 : [ C>=3 ], cost: 1

      2: f39 -> f47 : [ 1>=C ], cost: 1

      7: f39 -> f47 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1

      3: f54 -> f54 : [], cost: 1

      5: f47 -> f54 : E'=0, [ D>=1 ], cost: 1

      6: f47 -> f54 : E'=0, F'=0, [ 0>=D ], cost: 1

     12: f0 -> f13 : D'=free_18, F'=0, W'=0, [ 0>=free_18 ], cost: 1

     13: f0 -> f13 : D'=free_19, F'=0, W'=0, [ free_19>=1 ], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 0.

   Accelerating the following rules:

     11: f13 -> f13 : A'=1+A, C'=1, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, [ 0>=free_14 && B>=1+A ], cost: 1



   Accelerated rule 11 with metering function B-A, yielding the new rule 14.

   Removing the simple loops: 11.



Accelerating simple loops of location 2.

   Accelerating the following rules:

      3: f54 -> f54 : [], cost: 1



   Accelerated rule 3 with NONTERM, yielding the new rule 15.

   Removing the simple loops: 3.



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

   Start location: f0

      0: f13 -> f47 : [ A>=B ], cost: 1

      8: f13 -> f47 : H'=free, Q'=free_1, J'=free_3, K'=free_2, L'=E, M'=free, N'=free, O'=free, [ free>=1 && B>=1+A ], cost: 1

      9: f13 -> f39 : C'=free_4, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, [ B>=1+A && 0>=free_6 && free_4>=2 ], cost: 1

     10: f13 -> f39 : C'=free_9, H'=free_11, Q'=free_13, J'=free_12, K'=free_10, L'=E, M'=free_11, N'=free_11, O'=free_11, P'=free_11, Q_1'=R, R'=0, S'=free_9, T'=free_9, U'=free_9, V'=0, [ B>=1+A && 0>=free_11 && 0>=free_9 ], cost: 1

     14: f13 -> f13 : A'=B, C'=1, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, [ 0>=free_14 && B>=1+A ], cost: B-A

      1: f39 -> f47 : [ C>=3 ], cost: 1

      2: f39 -> f47 : [ 1>=C ], cost: 1

      7: f39 -> f47 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1

     15: f54 -> [8] : [], cost: NONTERM

      5: f47 -> f54 : E'=0, [ D>=1 ], cost: 1

      6: f47 -> f54 : E'=0, F'=0, [ 0>=D ], cost: 1

     12: f0 -> f13 : D'=free_18, F'=0, W'=0, [ 0>=free_18 ], cost: 1

     13: f0 -> f13 : D'=free_19, F'=0, W'=0, [ free_19>=1 ], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f13 -> f47 : [ A>=B ], cost: 1

      8: f13 -> f47 : H'=free, Q'=free_1, J'=free_3, K'=free_2, L'=E, M'=free, N'=free, O'=free, [ free>=1 && B>=1+A ], cost: 1

      9: f13 -> f39 : C'=free_4, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, [ B>=1+A && 0>=free_6 && free_4>=2 ], cost: 1

     10: f13 -> f39 : C'=free_9, H'=free_11, Q'=free_13, J'=free_12, K'=free_10, L'=E, M'=free_11, N'=free_11, O'=free_11, P'=free_11, Q_1'=R, R'=0, S'=free_9, T'=free_9, U'=free_9, V'=0, [ B>=1+A && 0>=free_11 && 0>=free_9 ], cost: 1

      1: f39 -> f47 : [ C>=3 ], cost: 1

      2: f39 -> f47 : [ 1>=C ], cost: 1

      7: f39 -> f47 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1

      5: f47 -> f54 : E'=0, [ D>=1 ], cost: 1

      6: f47 -> f54 : E'=0, F'=0, [ 0>=D ], cost: 1

     18: f47 -> [8] : E'=0, [ D>=1 ], cost: NONTERM

     19: f47 -> [8] : E'=0, F'=0, [ 0>=D ], cost: NONTERM

     12: f0 -> f13 : D'=free_18, F'=0, W'=0, [ 0>=free_18 ], cost: 1

     13: f0 -> f13 : D'=free_19, F'=0, W'=0, [ free_19>=1 ], cost: 1

     16: f0 -> f13 : A'=B, C'=1, D'=free_18, F'=0, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: 1+B-A

     17: f0 -> f13 : A'=B, C'=1, D'=free_19, F'=0, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ free_19>=1 && 0>=free_14 && B>=1+A ], cost: 1+B-A



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

   Start location: f0

      0: f13 -> f47 : [ A>=B ], cost: 1

      8: f13 -> f47 : H'=free, Q'=free_1, J'=free_3, K'=free_2, L'=E, M'=free, N'=free, O'=free, [ free>=1 && B>=1+A ], cost: 1

      9: f13 -> f39 : C'=free_4, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, [ B>=1+A && 0>=free_6 && free_4>=2 ], cost: 1

     10: f13 -> f39 : C'=free_9, H'=free_11, Q'=free_13, J'=free_12, K'=free_10, L'=E, M'=free_11, N'=free_11, O'=free_11, P'=free_11, Q_1'=R, R'=0, S'=free_9, T'=free_9, U'=free_9, V'=0, [ B>=1+A && 0>=free_11 && 0>=free_9 ], cost: 1

      1: f39 -> f47 : [ C>=3 ], cost: 1

      2: f39 -> f47 : [ 1>=C ], cost: 1

      7: f39 -> f47 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1

     18: f47 -> [8] : E'=0, [ D>=1 ], cost: NONTERM

     19: f47 -> [8] : E'=0, F'=0, [ 0>=D ], cost: NONTERM

     12: f0 -> f13 : D'=free_18, F'=0, W'=0, [ 0>=free_18 ], cost: 1

     13: f0 -> f13 : D'=free_19, F'=0, W'=0, [ free_19>=1 ], cost: 1

     16: f0 -> f13 : A'=B, C'=1, D'=free_18, F'=0, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: 1+B-A

     17: f0 -> f13 : A'=B, C'=1, D'=free_19, F'=0, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ free_19>=1 && 0>=free_14 && B>=1+A ], cost: 1+B-A



Eliminated locations (on tree-shaped paths):

   Start location: f0

      1: f39 -> f47 : [ C>=3 ], cost: 1

      2: f39 -> f47 : [ 1>=C ], cost: 1

      7: f39 -> f47 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1

     18: f47 -> [8] : E'=0, [ D>=1 ], cost: NONTERM

     19: f47 -> [8] : E'=0, F'=0, [ 0>=D ], cost: NONTERM

     20: f0 -> f47 : D'=free_18, F'=0, W'=0, [ 0>=free_18 && A>=B ], cost: 2

     21: f0 -> f47 : D'=free_18, F'=0, H'=free, Q'=free_1, J'=free_3, K'=free_2, L'=E, M'=free, N'=free, O'=free, W'=0, [ 0>=free_18 && free>=1 && B>=1+A ], cost: 2

     22: f0 -> f39 : C'=free_4, D'=free_18, F'=0, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, W'=0, [ 0>=free_18 && B>=1+A && 0>=free_6 && free_4>=2 ], cost: 2

     23: f0 -> f39 : C'=free_9, D'=free_18, F'=0, H'=free_11, Q'=free_13, J'=free_12, K'=free_10, L'=E, M'=free_11, N'=free_11, O'=free_11, P'=free_11, Q_1'=R, R'=0, S'=free_9, T'=free_9, U'=free_9, V'=0, W'=0, [ 0>=free_18 && B>=1+A && 0>=free_11 && 0>=free_9 ], cost: 2

     24: f0 -> f47 : D'=free_19, F'=0, W'=0, [ free_19>=1 && A>=B ], cost: 2

     25: f0 -> f47 : D'=free_19, F'=0, H'=free, Q'=free_1, J'=free_3, K'=free_2, L'=E, M'=free, N'=free, O'=free, W'=0, [ free_19>=1 && free>=1 && B>=1+A ], cost: 2

     26: f0 -> f39 : C'=free_4, D'=free_19, F'=0, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, W'=0, [ free_19>=1 && B>=1+A && 0>=free_6 && free_4>=2 ], cost: 2

     27: f0 -> f39 : C'=free_9, D'=free_19, F'=0, H'=free_11, Q'=free_13, J'=free_12, K'=free_10, L'=E, M'=free_11, N'=free_11, O'=free_11, P'=free_11, Q_1'=R, R'=0, S'=free_9, T'=free_9, U'=free_9, V'=0, W'=0, [ free_19>=1 && B>=1+A && 0>=free_11 && 0>=free_9 ], cost: 2

     28: f0 -> f47 : A'=B, C'=1, D'=free_18, F'=0, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: 2+B-A

     29: f0 -> f47 : A'=B, C'=1, D'=free_19, F'=0, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ free_19>=1 && 0>=free_14 && B>=1+A ], cost: 2+B-A

     30: f0 -> [9] : [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: 1+B-A

     31: f0 -> [9] : [ free_19>=1 && 0>=free_14 && B>=1+A ], cost: 1+B-A



Applied pruning (of leafs and parallel rules):

   Start location: f0

      1: f39 -> f47 : [ C>=3 ], cost: 1

      2: f39 -> f47 : [ 1>=C ], cost: 1

      7: f39 -> f47 : C'=2, E'=1+E, G'=H, [ C==2 ], cost: 1

     18: f47 -> [8] : E'=0, [ D>=1 ], cost: NONTERM

     19: f47 -> [8] : E'=0, F'=0, [ 0>=D ], cost: NONTERM

     21: f0 -> f47 : D'=free_18, F'=0, H'=free, Q'=free_1, J'=free_3, K'=free_2, L'=E, M'=free, N'=free, O'=free, W'=0, [ 0>=free_18 && free>=1 && B>=1+A ], cost: 2

     22: f0 -> f39 : C'=free_4, D'=free_18, F'=0, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, W'=0, [ 0>=free_18 && B>=1+A && 0>=free_6 && free_4>=2 ], cost: 2

     23: f0 -> f39 : C'=free_9, D'=free_18, F'=0, H'=free_11, Q'=free_13, J'=free_12, K'=free_10, L'=E, M'=free_11, N'=free_11, O'=free_11, P'=free_11, Q_1'=R, R'=0, S'=free_9, T'=free_9, U'=free_9, V'=0, W'=0, [ 0>=free_18 && B>=1+A && 0>=free_11 && 0>=free_9 ], cost: 2

     24: f0 -> f47 : D'=free_19, F'=0, W'=0, [ free_19>=1 && A>=B ], cost: 2

     25: f0 -> f47 : D'=free_19, F'=0, H'=free, Q'=free_1, J'=free_3, K'=free_2, L'=E, M'=free, N'=free, O'=free, W'=0, [ free_19>=1 && free>=1 && B>=1+A ], cost: 2

     26: f0 -> f39 : C'=free_4, D'=free_19, F'=0, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, W'=0, [ free_19>=1 && B>=1+A && 0>=free_6 && free_4>=2 ], cost: 2

     27: f0 -> f39 : C'=free_9, D'=free_19, F'=0, H'=free_11, Q'=free_13, J'=free_12, K'=free_10, L'=E, M'=free_11, N'=free_11, O'=free_11, P'=free_11, Q_1'=R, R'=0, S'=free_9, T'=free_9, U'=free_9, V'=0, W'=0, [ free_19>=1 && B>=1+A && 0>=free_11 && 0>=free_9 ], cost: 2

     28: f0 -> f47 : A'=B, C'=1, D'=free_18, F'=0, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: 2+B-A

     29: f0 -> f47 : A'=B, C'=1, D'=free_19, F'=0, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ free_19>=1 && 0>=free_14 && B>=1+A ], cost: 2+B-A

     30: f0 -> [9] : [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: 1+B-A

     31: f0 -> [9] : [ free_19>=1 && 0>=free_14 && B>=1+A ], cost: 1+B-A



Eliminated locations (on tree-shaped paths):

   Start location: f0

     30: f0 -> [9] : [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: 1+B-A

     31: f0 -> [9] : [ free_19>=1 && 0>=free_14 && B>=1+A ], cost: 1+B-A

     38: f0 -> [8] : D'=free_18, E'=0, F'=0, H'=free, Q'=free_1, J'=free_3, K'=free_2, L'=E, M'=free, N'=free, O'=free, W'=0, [ 0>=free_18 && free>=1 && B>=1+A ], cost: NONTERM

     39: f0 -> [8] : D'=free_19, E'=0, F'=0, W'=0, [ free_19>=1 && A>=B ], cost: NONTERM

     40: f0 -> [8] : D'=free_19, E'=0, F'=0, H'=free, Q'=free_1, J'=free_3, K'=free_2, L'=E, M'=free, N'=free, O'=free, W'=0, [ free_19>=1 && free>=1 && B>=1+A ], cost: NONTERM

     41: f0 -> [8] : A'=B, C'=1, D'=free_18, E'=0, F'=0, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: NONTERM

     42: f0 -> [8] : A'=B, C'=1, D'=free_19, E'=0, F'=0, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ free_19>=1 && 0>=free_14 && B>=1+A ], cost: NONTERM

     43: f0 -> [8] : C'=free_4, D'=free_18, E'=0, F'=0, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, W'=0, [ 0>=free_18 && B>=1+A && 0>=free_6 && free_4>=3 ], cost: NONTERM

     44: f0 -> [8] : C'=2, D'=free_18, E'=0, F'=0, G'=free_6, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, W'=0, [ 0>=free_18 && B>=1+A && 0>=free_6 && free_4==2 ], cost: NONTERM

     45: f0 -> [8] : C'=free_9, D'=free_18, E'=0, F'=0, H'=free_11, Q'=free_13, J'=free_12, K'=free_10, L'=E, M'=free_11, N'=free_11, O'=free_11, P'=free_11, Q_1'=R, R'=0, S'=free_9, T'=free_9, U'=free_9, V'=0, W'=0, [ 0>=free_18 && B>=1+A && 0>=free_11 && 0>=free_9 ], cost: NONTERM

     46: f0 -> [8] : C'=free_4, D'=free_19, E'=0, F'=0, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, W'=0, [ free_19>=1 && B>=1+A && 0>=free_6 && free_4>=3 ], cost: NONTERM

     47: f0 -> [8] : C'=2, D'=free_19, E'=0, F'=0, G'=free_6, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, W'=0, [ free_19>=1 && B>=1+A && 0>=free_6 && free_4==2 ], cost: NONTERM

     48: f0 -> [8] : C'=free_9, D'=free_19, E'=0, F'=0, H'=free_11, Q'=free_13, J'=free_12, K'=free_10, L'=E, M'=free_11, N'=free_11, O'=free_11, P'=free_11, Q_1'=R, R'=0, S'=free_9, T'=free_9, U'=free_9, V'=0, W'=0, [ free_19>=1 && B>=1+A && 0>=free_11 && 0>=free_9 ], cost: NONTERM

     49: f0 -> [10] : [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: 2+B-A

     50: f0 -> [10] : [ free_19>=1 && 0>=free_14 && B>=1+A ], cost: 2+B-A



Applied pruning (of leafs and parallel rules):

   Start location: f0

     30: f0 -> [9] : [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: 1+B-A

     31: f0 -> [9] : [ free_19>=1 && 0>=free_14 && B>=1+A ], cost: 1+B-A

     38: f0 -> [8] : D'=free_18, E'=0, F'=0, H'=free, Q'=free_1, J'=free_3, K'=free_2, L'=E, M'=free, N'=free, O'=free, W'=0, [ 0>=free_18 && free>=1 && B>=1+A ], cost: NONTERM

     39: f0 -> [8] : D'=free_19, E'=0, F'=0, W'=0, [ free_19>=1 && A>=B ], cost: NONTERM

     41: f0 -> [8] : A'=B, C'=1, D'=free_18, E'=0, F'=0, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: NONTERM

     43: f0 -> [8] : C'=free_4, D'=free_18, E'=0, F'=0, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, W'=0, [ 0>=free_18 && B>=1+A && 0>=free_6 && free_4>=3 ], cost: NONTERM

     44: f0 -> [8] : C'=2, D'=free_18, E'=0, F'=0, G'=free_6, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, W'=0, [ 0>=free_18 && B>=1+A && 0>=free_6 && free_4==2 ], cost: NONTERM

     49: f0 -> [10] : [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: 2+B-A

     50: f0 -> [10] : [ free_19>=1 && 0>=free_14 && B>=1+A ], cost: 2+B-A



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

     38: f0 -> [8] : D'=free_18, E'=0, F'=0, H'=free, Q'=free_1, J'=free_3, K'=free_2, L'=E, M'=free, N'=free, O'=free, W'=0, [ 0>=free_18 && free>=1 && B>=1+A ], cost: NONTERM

     39: f0 -> [8] : D'=free_19, E'=0, F'=0, W'=0, [ free_19>=1 && A>=B ], cost: NONTERM

     41: f0 -> [8] : A'=B, C'=1, D'=free_18, E'=0, F'=0, H'=free_14, Q'=free_15, J'=free_17, K'=free_16, L'=E, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: NONTERM

     43: f0 -> [8] : C'=free_4, D'=free_18, E'=0, F'=0, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, W'=0, [ 0>=free_18 && B>=1+A && 0>=free_6 && free_4>=3 ], cost: NONTERM

     44: f0 -> [8] : C'=2, D'=free_18, E'=0, F'=0, G'=free_6, H'=free_6, Q'=free_8, J'=free_7, K'=free_5, L'=E, M'=free_6, N'=free_6, O'=free_6, P'=free_6, Q_1'=R, R'=0, S'=free_4, T'=free_4, U'=free_4, V'=0, W'=0, [ 0>=free_18 && B>=1+A && 0>=free_6 && free_4==2 ], cost: NONTERM

     49: f0 -> [10] : [ 0>=free_18 && 0>=free_14 && B>=1+A ], cost: 2+B-A

     50: f0 -> [10] : [ free_19>=1 && 0>=free_14 && B>=1+A ], cost: 2+B-A



Computing asymptotic complexity for rule 38

   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:  [ 0>=free_18 && free>=1 && B>=1+A ]



NO


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(2)
BOUNDS(INF, INF)