/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1147 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_2, Q'=free_3, J'=free_5, K'=free_4, L'=D, M'=free_2, N'=free_2, O'=free_2, [ free_2>=1 && B>=1+A ], cost: 1

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

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

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



Checking for constant complexity:

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

     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_2, Q'=free_3, J'=free_5, K'=free_4, L'=D, M'=free_2, N'=free_2, O'=free_2, [ free_2>=1 && B>=1+A ], cost: 1

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

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

     11: f11 -> f11 : A'=1+A, C'=1, H'=free_16, Q'=free_17, J'=free_19, K'=free_18, L'=D, M'=free_16, N'=free_16, O'=free_16, P'=free_16, Q_1'=R, S'=1, T'=1, U'=1, V'=0, [ 0>=free_16 && 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_16, Q'=free_17, J'=free_19, K'=free_18, L'=D, M'=free_16, N'=free_16, O'=free_16, P'=free_16, Q_1'=R, S'=1, T'=1, U'=1, V'=0, [ 0>=free_16 && 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_2, Q'=free_3, J'=free_5, K'=free_4, L'=D, M'=free_2, N'=free_2, O'=free_2, [ free_2>=1 && B>=1+A ], cost: 1

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

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

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

      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_2, Q'=free_3, J'=free_5, K'=free_4, L'=D, M'=free_2, N'=free_2, O'=free_2, [ free_2>=1 && B>=1+A ], cost: 1

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

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

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

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

     15: f0 -> f11 : A'=B, C'=1, F'=0, H'=free_16, Q'=free_17, J'=free_19, K'=free_18, L'=D, M'=free_16, N'=free_16, O'=free_16, P'=free_16, Q_1'=R, S'=1, T'=1, U'=1, V'=0, W'=0, [ 0>=free_16 && 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_2, Q'=free_3, J'=free_5, K'=free_4, L'=D, M'=free_2, N'=free_2, O'=free_2, [ free_2>=1 && B>=1+A ], cost: 1

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

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

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

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

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

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

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

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

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

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

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

     23: f0 -> [9] : [ 0>=free_16 && B>=1+A ], cost: 1+B-A



Eliminated locations (on tree-shaped paths):

   Start location: f0

     23: f0 -> [9] : [ 0>=free_16 && B>=1+A ], cost: 1+B-A

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

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

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

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

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

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

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

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

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

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

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

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



Applied pruning (of leafs and parallel rules):

   Start location: f0

     23: f0 -> [9] : [ 0>=free_16 && B>=1+A ], cost: 1+B-A

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

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

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

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

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



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

     23: f0 -> [9] : [ 0>=free_16 && B>=1+A ], cost: 1+B-A

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

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

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

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

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



Computing asymptotic complexity for rule 23

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      B-A (+/+!), 1+B-A (+), 1-free_16 (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {free_16==-n,B==0,A==-n}

      resulting limit problem:

      [solved]



   Solution:

      free_16 / -n

      B / 0

      A / -n

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



Found new complexity Poly(n^1).



Computing asymptotic complexity for rule 27

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



NO


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(2)
BOUNDS(INF, INF)