/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1609 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) -> Com_1(f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: A >= B
f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: C >= 3
f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: 1 >= C
f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f52(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: TRUE
f54(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f57(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: TRUE
f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f52(A, B, C, D, 0, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: D >= 1
f45(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f52(A, B, C, D, 0, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: 0 >= D
f37(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f45(A, B, 2, D, E + 1, F, H, H, I, J, K, L, M, N, O, P, Q, R, S, T, U)) :|: 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) -> Com_1(f45(A, B, C, D, E, F, G, V, W, X, Y, E, V, V, O, P, Q, R, S, T, U)) :|: V >= 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) -> Com_1(f37(A, B, Z, D, E, F, G, V, W, X, Y, E, V, V, V, Q, 0, Z, Z, 0, U)) :|: B >= A + 1 && 0 >= V && Z >= 2
f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f37(A, B, Z, D, E, F, G, V, W, X, Y, E, V, V, V, Q, 0, Z, Z, 0, U)) :|: B >= A + 1 && 0 >= V && 0 >= Z
f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f13(A + 1, B, 1, D, E, F, G, V, W, X, Y, E, V, V, V, Q, Q, 1, 1, 0, U)) :|: 0 >= V && 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) -> Com_1(f13(A, B, C, W, E, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, 0)) :|: 0 >= W
f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U) -> Com_1(f13(A, B, C, W, E, 0, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, 0)) :|: W >= 1

The start-symbols are:[f0_21]


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

(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f13 -> f45 : [ A>=B ], cost: 1

      8: f13 -> f45 : H'=free_3, Q'=free, J'=free_1, K'=free_2, L'=E, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      9: f13 -> f37 : C'=free_8, H'=free_5, Q'=free_6, J'=free_7, K'=free_4, L'=E, M'=free_5, N'=free_5, O'=free_5, P'=Q_1, Q_1'=0, R'=free_8, S'=free_8, T'=0, [ B>=1+A && 0>=free_5 && free_8>=2 ], cost: 1

     10: f13 -> f37 : C'=free_13, H'=free_10, Q'=free_11, J'=free_12, K'=free_9, L'=E, M'=free_10, N'=free_10, O'=free_10, P'=Q_1, Q_1'=0, R'=free_13, S'=free_13, T'=0, [ B>=1+A && 0>=free_10 && 0>=free_13 ], cost: 1

     11: f13 -> f13 : A'=1+A, C'=1, H'=free_17, Q'=free_14, J'=free_15, K'=free_16, L'=E, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=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, E'=1+E, G'=H, [ C==2 ], cost: 1

      3: f52 -> f52 : [], cost: 1

      4: f54 -> f57 : [], cost: 1

      5: f45 -> f52 : E'=0, [ D>=1 ], cost: 1

      6: f45 -> f52 : E'=0, F'=0, [ 0>=D ], cost: 1

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

     13: f0 -> f13 : D'=free_19, F'=0, U'=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, U'=0, [ 0>=free_18 ], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f13 -> f45 : [ A>=B ], cost: 1

      8: f13 -> f45 : H'=free_3, Q'=free, J'=free_1, K'=free_2, L'=E, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      9: f13 -> f37 : C'=free_8, H'=free_5, Q'=free_6, J'=free_7, K'=free_4, L'=E, M'=free_5, N'=free_5, O'=free_5, P'=Q_1, Q_1'=0, R'=free_8, S'=free_8, T'=0, [ B>=1+A && 0>=free_5 && free_8>=2 ], cost: 1

     10: f13 -> f37 : C'=free_13, H'=free_10, Q'=free_11, J'=free_12, K'=free_9, L'=E, M'=free_10, N'=free_10, O'=free_10, P'=Q_1, Q_1'=0, R'=free_13, S'=free_13, T'=0, [ B>=1+A && 0>=free_10 && 0>=free_13 ], cost: 1

     11: f13 -> f13 : A'=1+A, C'=1, H'=free_17, Q'=free_14, J'=free_15, K'=free_16, L'=E, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=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, E'=1+E, G'=H, [ C==2 ], cost: 1

      3: f52 -> f52 : [], cost: 1

      5: f45 -> f52 : E'=0, [ D>=1 ], cost: 1

      6: f45 -> f52 : E'=0, F'=0, [ 0>=D ], cost: 1

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

     13: f0 -> f13 : D'=free_19, F'=0, U'=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_17, Q'=free_14, J'=free_15, K'=free_16, L'=E, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=0, [ 0>=free_17 && B>=1+A ], cost: 1



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

   Removing the simple loops: 11.



Accelerating simple loops of location 2.

   Accelerating the following rules:

      3: f52 -> f52 : [], 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 -> f45 : [ A>=B ], cost: 1

      8: f13 -> f45 : H'=free_3, Q'=free, J'=free_1, K'=free_2, L'=E, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      9: f13 -> f37 : C'=free_8, H'=free_5, Q'=free_6, J'=free_7, K'=free_4, L'=E, M'=free_5, N'=free_5, O'=free_5, P'=Q_1, Q_1'=0, R'=free_8, S'=free_8, T'=0, [ B>=1+A && 0>=free_5 && free_8>=2 ], cost: 1

     10: f13 -> f37 : C'=free_13, H'=free_10, Q'=free_11, J'=free_12, K'=free_9, L'=E, M'=free_10, N'=free_10, O'=free_10, P'=Q_1, Q_1'=0, R'=free_13, S'=free_13, T'=0, [ B>=1+A && 0>=free_10 && 0>=free_13 ], cost: 1

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

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

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

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

     15: f52 -> [8] : [], cost: NONTERM

      5: f45 -> f52 : E'=0, [ D>=1 ], cost: 1

      6: f45 -> f52 : E'=0, F'=0, [ 0>=D ], cost: 1

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

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



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f13 -> f45 : [ A>=B ], cost: 1

      8: f13 -> f45 : H'=free_3, Q'=free, J'=free_1, K'=free_2, L'=E, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      9: f13 -> f37 : C'=free_8, H'=free_5, Q'=free_6, J'=free_7, K'=free_4, L'=E, M'=free_5, N'=free_5, O'=free_5, P'=Q_1, Q_1'=0, R'=free_8, S'=free_8, T'=0, [ B>=1+A && 0>=free_5 && free_8>=2 ], cost: 1

     10: f13 -> f37 : C'=free_13, H'=free_10, Q'=free_11, J'=free_12, K'=free_9, L'=E, M'=free_10, N'=free_10, O'=free_10, P'=Q_1, Q_1'=0, R'=free_13, S'=free_13, T'=0, [ B>=1+A && 0>=free_10 && 0>=free_13 ], cost: 1

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

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

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

      5: f45 -> f52 : E'=0, [ D>=1 ], cost: 1

      6: f45 -> f52 : E'=0, F'=0, [ 0>=D ], cost: 1

     18: f45 -> [8] : E'=0, [ D>=1 ], cost: NONTERM

     19: f45 -> [8] : E'=0, F'=0, [ 0>=D ], cost: NONTERM

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

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

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

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



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

   Start location: f0

      0: f13 -> f45 : [ A>=B ], cost: 1

      8: f13 -> f45 : H'=free_3, Q'=free, J'=free_1, K'=free_2, L'=E, M'=free_3, N'=free_3, [ free_3>=1 && B>=1+A ], cost: 1

      9: f13 -> f37 : C'=free_8, H'=free_5, Q'=free_6, J'=free_7, K'=free_4, L'=E, M'=free_5, N'=free_5, O'=free_5, P'=Q_1, Q_1'=0, R'=free_8, S'=free_8, T'=0, [ B>=1+A && 0>=free_5 && free_8>=2 ], cost: 1

     10: f13 -> f37 : C'=free_13, H'=free_10, Q'=free_11, J'=free_12, K'=free_9, L'=E, M'=free_10, N'=free_10, O'=free_10, P'=Q_1, Q_1'=0, R'=free_13, S'=free_13, T'=0, [ B>=1+A && 0>=free_10 && 0>=free_13 ], cost: 1

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

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

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

     18: f45 -> [8] : E'=0, [ D>=1 ], cost: NONTERM

     19: f45 -> [8] : E'=0, F'=0, [ 0>=D ], cost: NONTERM

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

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

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

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



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, E'=1+E, G'=H, [ C==2 ], cost: 1

     18: f45 -> [8] : E'=0, [ D>=1 ], cost: NONTERM

     19: f45 -> [8] : E'=0, F'=0, [ 0>=D ], cost: NONTERM

     20: f0 -> f45 : D'=free_18, F'=0, U'=0, [ 0>=free_18 && A>=B ], cost: 2

     21: f0 -> f45 : D'=free_18, F'=0, H'=free_3, Q'=free, J'=free_1, K'=free_2, L'=E, M'=free_3, N'=free_3, U'=0, [ 0>=free_18 && free_3>=1 && B>=1+A ], cost: 2

     22: f0 -> f37 : C'=free_8, D'=free_18, F'=0, H'=free_5, Q'=free_6, J'=free_7, K'=free_4, L'=E, M'=free_5, N'=free_5, O'=free_5, P'=Q_1, Q_1'=0, R'=free_8, S'=free_8, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_5 && free_8>=2 ], cost: 2

     23: f0 -> f37 : C'=free_13, D'=free_18, F'=0, H'=free_10, Q'=free_11, J'=free_12, K'=free_9, L'=E, M'=free_10, N'=free_10, O'=free_10, P'=Q_1, Q_1'=0, R'=free_13, S'=free_13, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_10 && 0>=free_13 ], cost: 2

     24: f0 -> f45 : D'=free_19, F'=0, U'=0, [ free_19>=1 && A>=B ], cost: 2

     25: f0 -> f45 : D'=free_19, F'=0, H'=free_3, Q'=free, J'=free_1, K'=free_2, L'=E, M'=free_3, N'=free_3, U'=0, [ free_19>=1 && free_3>=1 && B>=1+A ], cost: 2

     26: f0 -> f37 : C'=free_8, D'=free_19, F'=0, H'=free_5, Q'=free_6, J'=free_7, K'=free_4, L'=E, M'=free_5, N'=free_5, O'=free_5, P'=Q_1, Q_1'=0, R'=free_8, S'=free_8, T'=0, U'=0, [ free_19>=1 && B>=1+A && 0>=free_5 && free_8>=2 ], cost: 2

     27: f0 -> f37 : C'=free_13, D'=free_19, F'=0, H'=free_10, Q'=free_11, J'=free_12, K'=free_9, L'=E, M'=free_10, N'=free_10, O'=free_10, P'=Q_1, Q_1'=0, R'=free_13, S'=free_13, T'=0, U'=0, [ free_19>=1 && B>=1+A && 0>=free_10 && 0>=free_13 ], cost: 2

     28: f0 -> f45 : A'=B, C'=1, D'=free_18, F'=0, H'=free_17, Q'=free_14, J'=free_15, K'=free_16, L'=E, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ 0>=free_18 && 0>=free_17 && B>=1+A ], cost: 2-A+B

     29: f0 -> f45 : A'=B, C'=1, D'=free_19, F'=0, H'=free_17, Q'=free_14, J'=free_15, K'=free_16, L'=E, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ free_19>=1 && 0>=free_17 && B>=1+A ], cost: 2-A+B

     30: f0 -> [9] : [ 0>=free_18 && 0>=free_17 && B>=1+A ], cost: 1-A+B

     31: f0 -> [9] : [ free_19>=1 && 0>=free_17 && B>=1+A ], cost: 1-A+B



Applied pruning (of leafs and parallel rules):

   Start location: f0

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

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

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

     18: f45 -> [8] : E'=0, [ D>=1 ], cost: NONTERM

     19: f45 -> [8] : E'=0, F'=0, [ 0>=D ], cost: NONTERM

     21: f0 -> f45 : D'=free_18, F'=0, H'=free_3, Q'=free, J'=free_1, K'=free_2, L'=E, M'=free_3, N'=free_3, U'=0, [ 0>=free_18 && free_3>=1 && B>=1+A ], cost: 2

     22: f0 -> f37 : C'=free_8, D'=free_18, F'=0, H'=free_5, Q'=free_6, J'=free_7, K'=free_4, L'=E, M'=free_5, N'=free_5, O'=free_5, P'=Q_1, Q_1'=0, R'=free_8, S'=free_8, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_5 && free_8>=2 ], cost: 2

     23: f0 -> f37 : C'=free_13, D'=free_18, F'=0, H'=free_10, Q'=free_11, J'=free_12, K'=free_9, L'=E, M'=free_10, N'=free_10, O'=free_10, P'=Q_1, Q_1'=0, R'=free_13, S'=free_13, T'=0, U'=0, [ 0>=free_18 && B>=1+A && 0>=free_10 && 0>=free_13 ], cost: 2

     24: f0 -> f45 : D'=free_19, F'=0, U'=0, [ free_19>=1 && A>=B ], cost: 2

     25: f0 -> f45 : D'=free_19, F'=0, H'=free_3, Q'=free, J'=free_1, K'=free_2, L'=E, M'=free_3, N'=free_3, U'=0, [ free_19>=1 && free_3>=1 && B>=1+A ], cost: 2

     26: f0 -> f37 : C'=free_8, D'=free_19, F'=0, H'=free_5, Q'=free_6, J'=free_7, K'=free_4, L'=E, M'=free_5, N'=free_5, O'=free_5, P'=Q_1, Q_1'=0, R'=free_8, S'=free_8, T'=0, U'=0, [ free_19>=1 && B>=1+A && 0>=free_5 && free_8>=2 ], cost: 2

     27: f0 -> f37 : C'=free_13, D'=free_19, F'=0, H'=free_10, Q'=free_11, J'=free_12, K'=free_9, L'=E, M'=free_10, N'=free_10, O'=free_10, P'=Q_1, Q_1'=0, R'=free_13, S'=free_13, T'=0, U'=0, [ free_19>=1 && B>=1+A && 0>=free_10 && 0>=free_13 ], cost: 2

     28: f0 -> f45 : A'=B, C'=1, D'=free_18, F'=0, H'=free_17, Q'=free_14, J'=free_15, K'=free_16, L'=E, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ 0>=free_18 && 0>=free_17 && B>=1+A ], cost: 2-A+B

     29: f0 -> f45 : A'=B, C'=1, D'=free_19, F'=0, H'=free_17, Q'=free_14, J'=free_15, K'=free_16, L'=E, M'=free_17, N'=free_17, O'=free_17, P'=Q_1, R'=1, S'=1, T'=0, U'=0, [ free_19>=1 && 0>=free_17 && B>=1+A ], cost: 2-A+B

     30: f0 -> [9] : [ 0>=free_18 && 0>=free_17 && B>=1+A ], cost: 1-A+B

     31: f0 -> [9] : [ free_19>=1 && 0>=free_17 && B>=1+A ], cost: 1-A+B



Eliminated locations (on tree-shaped paths):

   Start location: f0

     30: f0 -> [9] : [ 0>=free_18 && 0>=free_17 && B>=1+A ], cost: 1-A+B

     31: f0 -> [9] : [ free_19>=1 && 0>=free_17 && B>=1+A ], cost: 1-A+B

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

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

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

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

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

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

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

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

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

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

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

     49: f0 -> [10] : [ 0>=free_18 && 0>=free_17 && B>=1+A ], cost: 2-A+B

     50: f0 -> [10] : [ free_19>=1 && 0>=free_17 && B>=1+A ], cost: 2-A+B



Applied pruning (of leafs and parallel rules):

   Start location: f0

     30: f0 -> [9] : [ 0>=free_18 && 0>=free_17 && B>=1+A ], cost: 1-A+B

     31: f0 -> [9] : [ free_19>=1 && 0>=free_17 && B>=1+A ], cost: 1-A+B

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

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

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

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

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

     49: f0 -> [10] : [ 0>=free_18 && 0>=free_17 && B>=1+A ], cost: 2-A+B

     50: f0 -> [10] : [ free_19>=1 && 0>=free_17 && B>=1+A ], cost: 2-A+B



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

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

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

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

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

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

     49: f0 -> [10] : [ 0>=free_18 && 0>=free_17 && B>=1+A ], cost: 2-A+B

     50: f0 -> [10] : [ free_19>=1 && 0>=free_17 && B>=1+A ], cost: 2-A+B



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_3>=1 && B>=1+A ]



NO


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(2)
BOUNDS(INF, INF)