/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) CpxIntTrs
(1) Loat Proof [FINISHED, 949 ms]
(2) BOUNDS(INF, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f11(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(f45(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
f37(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(f45(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
f37(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(f45(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
f53(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(f53(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: TRUE
f55(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(f58(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: TRUE
f45(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(f53(A, B, C, 0, X, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: 0 >= X
f45(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(f53(A, B, C, 0, X, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: X >= 1
f37(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(f45(A, B, 2, D + 1, E, F, H, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W)) :|: C >= 2 && C <= 2
f11(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(f45(A, B, C, D, E, F, G, Y, X, Z, A1, D, Y, Y, Y, P, Q, R, S, T, U, V, W)) :|: Y >= 1 && 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) -> Com_1(f37(A, B, B1, D, E, F, G, Y, X, Z, A1, D, Y, Y, Y, Y, R, 0, B1, B1, B1, 0, W)) :|: B >= A + 1 && 0 >= Y && B1 >= 2
f11(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(f37(A, B, B1, D, E, F, G, Y, X, Z, A1, D, Y, Y, Y, Y, R, 0, B1, B1, B1, 0, W)) :|: B >= A + 1 && 0 >= Y && 0 >= B1
f11(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(f11(A + 1, B, 1, D, E, F, G, Y, X, Z, A1, D, Y, Y, Y, Y, R, R, 1, 1, 1, 0, W)) :|: 0 >= Y && 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(f11(A, B, C, D, E, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, 0)) :|: TRUE

The start-symbols are:[f0_23]


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

(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f11 -> f45 : [ A>=B ], cost: 1

      8: f11 -> f45 : H'=free_3, Q'=free_4, J'=free_2, K'=free_5, L'=D, M'=free_3, N'=free_3, O'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      9: f11 -> f37 : C'=free_7, H'=free_9, Q'=free_6, J'=free_10, K'=free_8, L'=D, M'=free_9, N'=free_9, O'=free_9, P'=free_9, Q_1'=R, R'=0, S'=free_7, T'=free_7, U'=free_7, V'=0, [ B>=1+A && 0>=free_9 && free_7>=2 ], cost: 1

     10: f11 -> f37 : C'=free_12, H'=free_14, Q'=free_11, J'=free_15, K'=free_13, L'=D, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, R'=0, S'=free_12, T'=free_12, U'=free_12, V'=0, [ B>=1+A && 0>=free_14 && 0>=free_12 ], cost: 1

     11: f11 -> f11 : A'=1+A, C'=1, H'=free_17, Q'=free_18, J'=free_16, K'=free_19, L'=D, M'=free_17, N'=free_17, O'=free_17, P'=free_17, Q_1'=R, S'=1, T'=1, U'=1, V'=0, [ 0>=free_17 && B>=1+A ], cost: 1

      1: f37 -> f45 : [ C>=3 ], cost: 1

      2: f37 -> f45 : [ 1>=C ], cost: 1

      7: f37 -> f45 : C'=2, D'=1+D, G'=H, [ C==2 ], cost: 1

      3: f53 -> f53 : [], cost: 1

      4: f55 -> f58 : 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: f45 -> f53 : D'=0, E'=free, [ 0>=free ], cost: 1

      6: f45 -> f53 : D'=0, E'=free_1, F'=0, [ free_1>=1 ], cost: 1

     12: f0 -> f11 : F'=0, W'=0, [], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f11 -> f45 : [ A>=B ], cost: 1

      8: f11 -> f45 : H'=free_3, Q'=free_4, J'=free_2, K'=free_5, L'=D, M'=free_3, N'=free_3, O'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      9: f11 -> f37 : C'=free_7, H'=free_9, Q'=free_6, J'=free_10, K'=free_8, L'=D, M'=free_9, N'=free_9, O'=free_9, P'=free_9, Q_1'=R, R'=0, S'=free_7, T'=free_7, U'=free_7, V'=0, [ B>=1+A && 0>=free_9 && free_7>=2 ], cost: 1

     10: f11 -> f37 : C'=free_12, H'=free_14, Q'=free_11, J'=free_15, K'=free_13, L'=D, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, R'=0, S'=free_12, T'=free_12, U'=free_12, V'=0, [ B>=1+A && 0>=free_14 && 0>=free_12 ], cost: 1

     11: f11 -> f11 : A'=1+A, C'=1, H'=free_17, Q'=free_18, J'=free_16, K'=free_19, L'=D, M'=free_17, N'=free_17, O'=free_17, P'=free_17, Q_1'=R, S'=1, T'=1, U'=1, V'=0, [ 0>=free_17 && B>=1+A ], cost: 1

      1: f37 -> f45 : [ C>=3 ], cost: 1

      2: f37 -> f45 : [ 1>=C ], cost: 1

      7: f37 -> f45 : C'=2, D'=1+D, G'=H, [ C==2 ], cost: 1

      3: f53 -> f53 : [], cost: 1

      5: f45 -> f53 : D'=0, E'=free, [ 0>=free ], cost: 1

      6: f45 -> f53 : D'=0, E'=free_1, F'=0, [ free_1>=1 ], cost: 1

     12: f0 -> f11 : F'=0, W'=0, [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 0.

   Accelerating the following rules:

     11: f11 -> f11 : A'=1+A, C'=1, H'=free_17, Q'=free_18, J'=free_16, K'=free_19, L'=D, M'=free_17, N'=free_17, O'=free_17, P'=free_17, Q_1'=R, S'=1, T'=1, U'=1, V'=0, [ 0>=free_17 && B>=1+A ], cost: 1



   Accelerated rule 11 with metering function B-A, yielding the new rule 13.

   Removing the simple loops: 11.



Accelerating simple loops of location 2.

   Accelerating the following rules:

      3: f53 -> f53 : [], cost: 1



   Accelerated rule 3 with NONTERM, yielding the new rule 14.

   Removing the simple loops: 3.



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

   Start location: f0

      0: f11 -> f45 : [ A>=B ], cost: 1

      8: f11 -> f45 : H'=free_3, Q'=free_4, J'=free_2, K'=free_5, L'=D, M'=free_3, N'=free_3, O'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      9: f11 -> f37 : C'=free_7, H'=free_9, Q'=free_6, J'=free_10, K'=free_8, L'=D, M'=free_9, N'=free_9, O'=free_9, P'=free_9, Q_1'=R, R'=0, S'=free_7, T'=free_7, U'=free_7, V'=0, [ B>=1+A && 0>=free_9 && free_7>=2 ], cost: 1

     10: f11 -> f37 : C'=free_12, H'=free_14, Q'=free_11, J'=free_15, K'=free_13, L'=D, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, R'=0, S'=free_12, T'=free_12, U'=free_12, V'=0, [ B>=1+A && 0>=free_14 && 0>=free_12 ], cost: 1

     13: f11 -> f11 : A'=B, C'=1, H'=free_17, Q'=free_18, J'=free_16, K'=free_19, L'=D, M'=free_17, N'=free_17, O'=free_17, P'=free_17, Q_1'=R, S'=1, T'=1, U'=1, V'=0, [ 0>=free_17 && B>=1+A ], cost: B-A

      1: f37 -> f45 : [ C>=3 ], cost: 1

      2: f37 -> f45 : [ 1>=C ], cost: 1

      7: f37 -> f45 : C'=2, D'=1+D, G'=H, [ C==2 ], cost: 1

     14: f53 -> [8] : [], cost: INF

      5: f45 -> f53 : D'=0, E'=free, [ 0>=free ], cost: 1

      6: f45 -> f53 : D'=0, E'=free_1, F'=0, [ free_1>=1 ], cost: 1

     12: f0 -> f11 : F'=0, W'=0, [], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f11 -> f45 : [ A>=B ], cost: 1

      8: f11 -> f45 : H'=free_3, Q'=free_4, J'=free_2, K'=free_5, L'=D, M'=free_3, N'=free_3, O'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      9: f11 -> f37 : C'=free_7, H'=free_9, Q'=free_6, J'=free_10, K'=free_8, L'=D, M'=free_9, N'=free_9, O'=free_9, P'=free_9, Q_1'=R, R'=0, S'=free_7, T'=free_7, U'=free_7, V'=0, [ B>=1+A && 0>=free_9 && free_7>=2 ], cost: 1

     10: f11 -> f37 : C'=free_12, H'=free_14, Q'=free_11, J'=free_15, K'=free_13, L'=D, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, R'=0, S'=free_12, T'=free_12, U'=free_12, V'=0, [ B>=1+A && 0>=free_14 && 0>=free_12 ], cost: 1

      1: f37 -> f45 : [ C>=3 ], cost: 1

      2: f37 -> f45 : [ 1>=C ], cost: 1

      7: f37 -> f45 : C'=2, D'=1+D, G'=H, [ C==2 ], cost: 1

      5: f45 -> f53 : D'=0, E'=free, [ 0>=free ], cost: 1

      6: f45 -> f53 : D'=0, E'=free_1, F'=0, [ free_1>=1 ], cost: 1

     16: f45 -> [8] : D'=0, E'=free, [ 0>=free ], cost: INF

     17: f45 -> [8] : D'=0, E'=free_1, F'=0, [ free_1>=1 ], cost: INF

     12: f0 -> f11 : F'=0, W'=0, [], cost: 1

     15: f0 -> f11 : A'=B, C'=1, F'=0, H'=free_17, Q'=free_18, J'=free_16, K'=free_19, L'=D, M'=free_17, N'=free_17, O'=free_17, P'=free_17, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_17 && B>=1+A ], cost: 1+B-A



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

   Start location: f0

      0: f11 -> f45 : [ A>=B ], cost: 1

      8: f11 -> f45 : H'=free_3, Q'=free_4, J'=free_2, K'=free_5, L'=D, M'=free_3, N'=free_3, O'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      9: f11 -> f37 : C'=free_7, H'=free_9, Q'=free_6, J'=free_10, K'=free_8, L'=D, M'=free_9, N'=free_9, O'=free_9, P'=free_9, Q_1'=R, R'=0, S'=free_7, T'=free_7, U'=free_7, V'=0, [ B>=1+A && 0>=free_9 && free_7>=2 ], cost: 1

     10: f11 -> f37 : C'=free_12, H'=free_14, Q'=free_11, J'=free_15, K'=free_13, L'=D, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, R'=0, S'=free_12, T'=free_12, U'=free_12, V'=0, [ B>=1+A && 0>=free_14 && 0>=free_12 ], cost: 1

      1: f37 -> f45 : [ C>=3 ], cost: 1

      2: f37 -> f45 : [ 1>=C ], cost: 1

      7: f37 -> f45 : C'=2, D'=1+D, G'=H, [ C==2 ], cost: 1

     16: f45 -> [8] : D'=0, E'=free, [ 0>=free ], cost: INF

     17: f45 -> [8] : D'=0, E'=free_1, F'=0, [ free_1>=1 ], cost: INF

     12: f0 -> f11 : F'=0, W'=0, [], cost: 1

     15: f0 -> f11 : A'=B, C'=1, F'=0, H'=free_17, Q'=free_18, J'=free_16, K'=free_19, L'=D, M'=free_17, N'=free_17, O'=free_17, P'=free_17, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_17 && B>=1+A ], cost: 1+B-A



Eliminated locations (on tree-shaped paths):

   Start location: f0

      1: f37 -> f45 : [ C>=3 ], cost: 1

      2: f37 -> f45 : [ 1>=C ], cost: 1

      7: f37 -> f45 : C'=2, D'=1+D, G'=H, [ C==2 ], cost: 1

     16: f45 -> [8] : D'=0, E'=free, [ 0>=free ], cost: INF

     17: f45 -> [8] : D'=0, E'=free_1, F'=0, [ free_1>=1 ], cost: INF

     18: f0 -> f45 : F'=0, W'=0, [ A>=B ], cost: 2

     19: f0 -> f45 : F'=0, H'=free_3, Q'=free_4, J'=free_2, K'=free_5, L'=D, M'=free_3, N'=free_3, O'=free_3, W'=0, [ free_3>=1 && B>=1+A ], cost: 2

     20: f0 -> f37 : C'=free_7, F'=0, H'=free_9, Q'=free_6, J'=free_10, K'=free_8, L'=D, M'=free_9, N'=free_9, O'=free_9, P'=free_9, Q_1'=R, R'=0, S'=free_7, T'=free_7, U'=free_7, V'=0, W'=0, [ B>=1+A && 0>=free_9 && free_7>=2 ], cost: 2

     21: f0 -> f37 : C'=free_12, F'=0, H'=free_14, Q'=free_11, J'=free_15, K'=free_13, L'=D, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, R'=0, S'=free_12, T'=free_12, U'=free_12, V'=0, W'=0, [ B>=1+A && 0>=free_14 && 0>=free_12 ], cost: 2

     22: f0 -> f45 : A'=B, C'=1, F'=0, H'=free_17, Q'=free_18, J'=free_16, K'=free_19, L'=D, M'=free_17, N'=free_17, O'=free_17, P'=free_17, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_17 && B>=1+A ], cost: 2+B-A

     23: f0 -> [9] : [ 0>=free_17 && B>=1+A ], cost: 1+B-A



Eliminated locations (on tree-shaped paths):

   Start location: f0

     23: f0 -> [9] : [ 0>=free_17 && B>=1+A ], cost: 1+B-A

     27: f0 -> [8] : D'=0, E'=free, F'=0, W'=0, [ A>=B && 0>=free ], cost: INF

     28: f0 -> [8] : D'=0, E'=free_1, F'=0, W'=0, [ A>=B && free_1>=1 ], cost: INF

     29: f0 -> [8] : D'=0, E'=free, F'=0, H'=free_3, Q'=free_4, J'=free_2, K'=free_5, L'=D, M'=free_3, N'=free_3, O'=free_3, W'=0, [ free_3>=1 && B>=1+A && 0>=free ], cost: INF

     30: f0 -> [8] : D'=0, E'=free_1, F'=0, H'=free_3, Q'=free_4, J'=free_2, K'=free_5, L'=D, M'=free_3, N'=free_3, O'=free_3, W'=0, [ free_3>=1 && B>=1+A && free_1>=1 ], cost: INF

     31: f0 -> [8] : A'=B, C'=1, D'=0, E'=free, F'=0, H'=free_17, Q'=free_18, J'=free_16, K'=free_19, L'=D, M'=free_17, N'=free_17, O'=free_17, P'=free_17, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_17 && B>=1+A && 0>=free ], cost: INF

     32: f0 -> [8] : A'=B, C'=1, D'=0, E'=free_1, F'=0, H'=free_17, Q'=free_18, J'=free_16, K'=free_19, L'=D, M'=free_17, N'=free_17, O'=free_17, P'=free_17, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_17 && B>=1+A && free_1>=1 ], cost: INF

     33: f0 -> [8] : C'=free_7, D'=0, E'=free, F'=0, H'=free_9, Q'=free_6, J'=free_10, K'=free_8, L'=D, M'=free_9, N'=free_9, O'=free_9, P'=free_9, Q_1'=R, R'=0, S'=free_7, T'=free_7, U'=free_7, V'=0, W'=0, [ B>=1+A && 0>=free_9 && free_7>=3 && 0>=free ], cost: INF

     34: f0 -> [8] : C'=free_7, D'=0, E'=free_1, F'=0, H'=free_9, Q'=free_6, J'=free_10, K'=free_8, L'=D, M'=free_9, N'=free_9, O'=free_9, P'=free_9, Q_1'=R, R'=0, S'=free_7, T'=free_7, U'=free_7, V'=0, W'=0, [ B>=1+A && 0>=free_9 && free_7>=3 && free_1>=1 ], cost: INF

     35: f0 -> [8] : C'=2, D'=0, E'=free, F'=0, G'=free_9, H'=free_9, Q'=free_6, J'=free_10, K'=free_8, L'=D, M'=free_9, N'=free_9, O'=free_9, P'=free_9, Q_1'=R, R'=0, S'=free_7, T'=free_7, U'=free_7, V'=0, W'=0, [ B>=1+A && 0>=free_9 && free_7==2 && 0>=free ], cost: INF

     36: f0 -> [8] : C'=2, D'=0, E'=free_1, F'=0, G'=free_9, H'=free_9, Q'=free_6, J'=free_10, K'=free_8, L'=D, M'=free_9, N'=free_9, O'=free_9, P'=free_9, Q_1'=R, R'=0, S'=free_7, T'=free_7, U'=free_7, V'=0, W'=0, [ B>=1+A && 0>=free_9 && free_7==2 && free_1>=1 ], cost: INF

     37: f0 -> [8] : C'=free_12, D'=0, E'=free, F'=0, H'=free_14, Q'=free_11, J'=free_15, K'=free_13, L'=D, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, R'=0, S'=free_12, T'=free_12, U'=free_12, V'=0, W'=0, [ B>=1+A && 0>=free_14 && 0>=free_12 && 0>=free ], cost: INF

     38: f0 -> [8] : C'=free_12, D'=0, E'=free_1, F'=0, H'=free_14, Q'=free_11, J'=free_15, K'=free_13, L'=D, M'=free_14, N'=free_14, O'=free_14, P'=free_14, Q_1'=R, R'=0, S'=free_12, T'=free_12, U'=free_12, V'=0, W'=0, [ B>=1+A && 0>=free_14 && 0>=free_12 && free_1>=1 ], cost: INF



Applied pruning (of leafs and parallel rules):

   Start location: f0

     23: f0 -> [9] : [ 0>=free_17 && B>=1+A ], cost: 1+B-A

     27: f0 -> [8] : D'=0, E'=free, F'=0, W'=0, [ A>=B && 0>=free ], cost: INF

     28: f0 -> [8] : D'=0, E'=free_1, F'=0, W'=0, [ A>=B && free_1>=1 ], cost: INF

     30: f0 -> [8] : D'=0, E'=free_1, F'=0, H'=free_3, Q'=free_4, J'=free_2, K'=free_5, L'=D, M'=free_3, N'=free_3, O'=free_3, W'=0, [ free_3>=1 && B>=1+A && free_1>=1 ], cost: INF

     32: f0 -> [8] : A'=B, C'=1, D'=0, E'=free_1, F'=0, H'=free_17, Q'=free_18, J'=free_16, K'=free_19, L'=D, M'=free_17, N'=free_17, O'=free_17, P'=free_17, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_17 && B>=1+A && free_1>=1 ], cost: INF

     33: f0 -> [8] : C'=free_7, D'=0, E'=free, F'=0, H'=free_9, Q'=free_6, J'=free_10, K'=free_8, L'=D, M'=free_9, N'=free_9, O'=free_9, P'=free_9, Q_1'=R, R'=0, S'=free_7, T'=free_7, U'=free_7, V'=0, W'=0, [ B>=1+A && 0>=free_9 && free_7>=3 && 0>=free ], cost: INF



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

     23: f0 -> [9] : [ 0>=free_17 && B>=1+A ], cost: 1+B-A

     27: f0 -> [8] : D'=0, E'=free, F'=0, W'=0, [ A>=B && 0>=free ], cost: INF

     28: f0 -> [8] : D'=0, E'=free_1, F'=0, W'=0, [ A>=B && free_1>=1 ], cost: INF

     30: f0 -> [8] : D'=0, E'=free_1, F'=0, H'=free_3, Q'=free_4, J'=free_2, K'=free_5, L'=D, M'=free_3, N'=free_3, O'=free_3, W'=0, [ free_3>=1 && B>=1+A && free_1>=1 ], cost: INF

     32: f0 -> [8] : A'=B, C'=1, D'=0, E'=free_1, F'=0, H'=free_17, Q'=free_18, J'=free_16, K'=free_19, L'=D, M'=free_17, N'=free_17, O'=free_17, P'=free_17, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_17 && B>=1+A && free_1>=1 ], cost: INF

     33: f0 -> [8] : C'=free_7, D'=0, E'=free, F'=0, H'=free_9, Q'=free_6, J'=free_10, K'=free_8, L'=D, M'=free_9, N'=free_9, O'=free_9, P'=free_9, Q_1'=R, R'=0, S'=free_7, T'=free_7, U'=free_7, V'=0, W'=0, [ B>=1+A && 0>=free_9 && free_7>=3 && 0>=free ], cost: INF



Computing asymptotic complexity for rule 23

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      1+B-A (+), B-A (+/+!), 1-free_17 (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {B==0,A==-n,free_17==-n}

      resulting limit problem:

      [solved]



   Solution:

      B / 0

      A / -n

      free_17 / -n

   Resulting cost 1+n has complexity: Poly(n^1)



Found new complexity Poly(n^1).



Computing asymptotic complexity for rule 27

   Resulting cost INF 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: INF

   Rule cost:   INF

   Rule guard:  [ A>=B && 0>=free ]



NO


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

(2)
BOUNDS(INF, INF)