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


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


WORST_CASE(NON_POLY, ?)
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 638 ms]
(2) BOUNDS(INF, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f51(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f51(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V)) :|: TRUE
f53(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f56(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V)) :|: TRUE
f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f51(A, B, 0, 0, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V)) :|: 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) -> Com_1(f51(A, B, 0, 0, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V)) :|: E >= 3
f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f51(A, B, 0, 0, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V)) :|: 1 >= E
f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f51(A, B, 0, 0, 2, G, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V)) :|: E >= 2 && E <= 2
f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f51(A, B, 0, 0, E, F, W, X, Y, Z, D, W, W, W, O, P, Q, R, S, T, U, V)) :|: W >= 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) -> Com_1(f37(A, B, C, D, A1, F, W, X, Y, Z, D, W, W, W, W, Q, 0, A1, A1, A1, 0, V)) :|: B >= A + 1 && 0 >= W && A1 >= 2
f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f37(A, B, C, D, A1, F, W, X, Y, Z, D, W, W, W, W, Q, 0, A1, A1, A1, 0, V)) :|: B >= A + 1 && 0 >= W && 0 >= A1
f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V) -> Com_1(f11(A + 1, B, C, D, 1, F, W, X, Y, Z, D, W, W, W, W, Q, Q, 1, 1, 1, 0, V)) :|: 0 >= W && 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) -> Com_1(f11(A, B, 0, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, 0)) :|: TRUE

The start-symbols are:[f0_22]


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

(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f51 -> f51 : [], cost: 1

      1: f53 -> f56 : A1'=B, B'=C, C'=D, D'=E, E'=F, F'=G, G'=H, H'=Q, Q'=J, J'=K, K'=L, L'=M, M'=N, N'=O, O'=P, P'=Q_1, Q_1'=R, R'=S, S'=T, T'=U, U'=V, [], cost: 1

      2: f11 -> f51 : C'=0, D'=0, [ A>=B ], cost: 1

      6: f11 -> f51 : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      7: f11 -> f37 : E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, [ B>=1+A && 0>=free_4 && free_7>=2 ], cost: 1

      8: f11 -> f37 : E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: 1

      9: f11 -> f11 : A'=1+A, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, [ 0>=free_17 && B>=1+A ], cost: 1

      3: f37 -> f51 : C'=0, D'=0, [ E>=3 ], cost: 1

      4: f37 -> f51 : C'=0, D'=0, [ 1>=E ], cost: 1

      5: f37 -> f51 : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: 1

     10: f0 -> f11 : C'=0, V'=0, [], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f51 -> f51 : [], cost: 1

      2: f11 -> f51 : C'=0, D'=0, [ A>=B ], cost: 1

      6: f11 -> f51 : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      7: f11 -> f37 : E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, [ B>=1+A && 0>=free_4 && free_7>=2 ], cost: 1

      8: f11 -> f37 : E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: 1

      9: f11 -> f11 : A'=1+A, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, [ 0>=free_17 && B>=1+A ], cost: 1

      3: f37 -> f51 : C'=0, D'=0, [ E>=3 ], cost: 1

      4: f37 -> f51 : C'=0, D'=0, [ 1>=E ], cost: 1

      5: f37 -> f51 : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: 1

     10: f0 -> f11 : C'=0, V'=0, [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 0.

   Accelerating the following rules:

      0: f51 -> f51 : [], cost: 1



   Accelerated rule 0 with NONTERM, yielding the new rule 11.

   Removing the simple loops: 0.



Accelerating simple loops of location 2.

   Accelerating the following rules:

      9: f11 -> f11 : A'=1+A, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, [ 0>=free_17 && B>=1+A ], cost: 1



   Accelerated rule 9 with metering function B-A, yielding the new rule 12.

   Removing the simple loops: 9.



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

   Start location: f0

     11: f51 -> [6] : [], cost: INF

      2: f11 -> f51 : C'=0, D'=0, [ A>=B ], cost: 1

      6: f11 -> f51 : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      7: f11 -> f37 : E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, [ B>=1+A && 0>=free_4 && free_7>=2 ], cost: 1

      8: f11 -> f37 : E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: 1

     12: f11 -> f11 : A'=B, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, [ 0>=free_17 && B>=1+A ], cost: B-A

      3: f37 -> f51 : C'=0, D'=0, [ E>=3 ], cost: 1

      4: f37 -> f51 : C'=0, D'=0, [ 1>=E ], cost: 1

      5: f37 -> f51 : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: 1

     10: f0 -> f11 : C'=0, V'=0, [], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f0

      2: f11 -> f51 : C'=0, D'=0, [ A>=B ], cost: 1

      6: f11 -> f51 : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      7: f11 -> f37 : E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, [ B>=1+A && 0>=free_4 && free_7>=2 ], cost: 1

      8: f11 -> f37 : E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: 1

     13: f11 -> [6] : C'=0, D'=0, [ A>=B ], cost: INF

     17: f11 -> [6] : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: INF

      3: f37 -> f51 : C'=0, D'=0, [ E>=3 ], cost: 1

      4: f37 -> f51 : C'=0, D'=0, [ 1>=E ], cost: 1

      5: f37 -> f51 : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: 1

     14: f37 -> [6] : C'=0, D'=0, [ E>=3 ], cost: INF

     15: f37 -> [6] : C'=0, D'=0, [ 1>=E ], cost: INF

     16: f37 -> [6] : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: INF

     10: f0 -> f11 : C'=0, V'=0, [], cost: 1

     18: f0 -> f11 : A'=B, C'=0, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, V'=0, [ 0>=free_17 && B>=1+A ], cost: 1+B-A



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

   Start location: f0

      7: f11 -> f37 : E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, [ B>=1+A && 0>=free_4 && free_7>=2 ], cost: 1

      8: f11 -> f37 : E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: 1

     13: f11 -> [6] : C'=0, D'=0, [ A>=B ], cost: INF

     17: f11 -> [6] : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: INF

     14: f37 -> [6] : C'=0, D'=0, [ E>=3 ], cost: INF

     15: f37 -> [6] : C'=0, D'=0, [ 1>=E ], cost: INF

     16: f37 -> [6] : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: INF

     10: f0 -> f11 : C'=0, V'=0, [], cost: 1

     18: f0 -> f11 : A'=B, C'=0, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, V'=0, [ 0>=free_17 && B>=1+A ], cost: 1+B-A



Eliminated locations (on tree-shaped paths):

   Start location: f0

     14: f37 -> [6] : C'=0, D'=0, [ E>=3 ], cost: INF

     15: f37 -> [6] : C'=0, D'=0, [ 1>=E ], cost: INF

     16: f37 -> [6] : C'=0, D'=0, E'=2, F'=G, [ E==2 ], cost: INF

     19: f0 -> f37 : C'=0, E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, V'=0, [ B>=1+A && 0>=free_4 && free_7>=2 ], cost: 2

     20: f0 -> f37 : C'=0, E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, V'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: 2

     21: f0 -> [6] : C'=0, D'=0, V'=0, [ A>=B ], cost: INF

     22: f0 -> [6] : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, V'=0, [ free_3>=1 && B>=1+A ], cost: INF

     23: f0 -> [6] : A'=B, C'=0, D'=0, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, V'=0, [ 0>=free_17 && B>=1+A ], cost: INF

     24: f0 -> [8] : [ 0>=free_17 && B>=1+A ], cost: 1+B-A



Eliminated locations (on tree-shaped paths):

   Start location: f0

     21: f0 -> [6] : C'=0, D'=0, V'=0, [ A>=B ], cost: INF

     22: f0 -> [6] : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, V'=0, [ free_3>=1 && B>=1+A ], cost: INF

     23: f0 -> [6] : A'=B, C'=0, D'=0, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, V'=0, [ 0>=free_17 && B>=1+A ], cost: INF

     24: f0 -> [8] : [ 0>=free_17 && B>=1+A ], cost: 1+B-A

     25: f0 -> [6] : C'=0, D'=0, E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, V'=0, [ B>=1+A && 0>=free_4 && free_7>=3 ], cost: INF

     26: f0 -> [6] : C'=0, D'=0, E'=2, F'=free_4, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, V'=0, [ B>=1+A && 0>=free_4 && free_7==2 ], cost: INF

     27: f0 -> [6] : C'=0, D'=0, E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, V'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: INF



Applied pruning (of leafs and parallel rules):

   Start location: f0

     21: f0 -> [6] : C'=0, D'=0, V'=0, [ A>=B ], cost: INF

     22: f0 -> [6] : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, V'=0, [ free_3>=1 && B>=1+A ], cost: INF

     23: f0 -> [6] : A'=B, C'=0, D'=0, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, V'=0, [ 0>=free_17 && B>=1+A ], cost: INF

     24: f0 -> [8] : [ 0>=free_17 && B>=1+A ], cost: 1+B-A

     25: f0 -> [6] : C'=0, D'=0, E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, V'=0, [ B>=1+A && 0>=free_4 && free_7>=3 ], cost: INF

     27: f0 -> [6] : C'=0, D'=0, E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, V'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: INF



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

     21: f0 -> [6] : C'=0, D'=0, V'=0, [ A>=B ], cost: INF

     22: f0 -> [6] : C'=0, D'=0, G'=free_3, H'=free, Q'=free_1, J'=free_2, K'=D, L'=free_3, M'=free_3, N'=free_3, V'=0, [ free_3>=1 && B>=1+A ], cost: INF

     23: f0 -> [6] : A'=B, C'=0, D'=0, E'=1, G'=free_17, H'=free_14, Q'=free_15, J'=free_16, K'=D, L'=free_17, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=1, U'=0, V'=0, [ 0>=free_17 && B>=1+A ], cost: INF

     24: f0 -> [8] : [ 0>=free_17 && B>=1+A ], cost: 1+B-A

     25: f0 -> [6] : C'=0, D'=0, E'=free_7, G'=free_4, H'=free_5, Q'=free_6, J'=free_8, K'=D, L'=free_4, M'=free_4, N'=free_4, O'=free_4, P'=Q_1, Q_1'=0, R'=free_7, S'=free_7, T'=free_7, U'=0, V'=0, [ B>=1+A && 0>=free_4 && free_7>=3 ], cost: INF

     27: f0 -> [6] : C'=0, D'=0, E'=free_12, G'=free_9, H'=free_10, Q'=free_11, J'=free_13, K'=D, L'=free_9, M'=free_9, N'=free_9, O'=free_9, P'=Q_1, Q_1'=0, R'=free_12, S'=free_12, T'=free_12, U'=0, V'=0, [ B>=1+A && 0>=free_9 && 0>=free_12 ], cost: INF



Computing asymptotic complexity for rule 21

   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 ]



NO


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

(2)
BOUNDS(INF, INF)