/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 3144 ms]
(2) BOUNDS(INF, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f63(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, B, C, D, E, F, G, H, I, J, K)) :|: A >= 1 + B
f0(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, 10, 20, 1, 20, 0, 0, H, I, J, K)) :|: TRUE
f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, B, C, D, E, F, 1, H, I, J, K)) :|: D >= E && G >= 0 && G <= 0
f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, B, C, D, E, F, 1, H, I, J, K)) :|: D + 1 >= E && E >= 2 + D && G >= 0 && G <= 0
f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, B, C, D, D + 1, F, 1, H, I, J, K)) :|: E >= D + 1 && E <= D + 1 && G >= 0 && G <= 0
f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, B, C, D, D + 1, F, 1, N, I, J, K)) :|: L >= M + 1 && E >= D + 1 && E <= D + 1 && G >= 0 && G <= 0
f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(E, B, C, D, E, F, 0, N, L, D + 1, M)) :|: E >= 2 + D && G >= 0 && G <= 0
f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K)) :|: 0 >= F + 1
f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f59(A, B, C, D, E, F, G, H, I, J, K)) :|: F >= 1
f40(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f43(A, B, C, D, E, 0, G, H, I, J + 1, K)) :|: F >= 0 && F <= 0
f43(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f43(A, B, C, D, E, F, G, H, I, J + 1, K)) :|: K >= N + 1
f48(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f48(A - 1, B, C, D, E, F, G, H, I, J, K)) :|: TRUE
f54(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(A, B, C, D, E, F, G, H, I, J, K)) :|: 0 >= F + 1
f54(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(A, B, C, D, E, F, G, H, I, J, K)) :|: F >= 1
f54(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f40(A, B, C, D, E, 0, G, N, I, J, K)) :|: F >= 0 && F <= 0
f59(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f63(A, B, C, D, E, F, G, H, I, J, K)) :|: B >= A + 1
f59(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f63(A, B, C, D, A - 1, F, G, H, I, J, K)) :|: A >= B
f63(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f11(A, B, C, J, E, F, G, H, I, J, K)) :|: B >= A
f48(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f54(A, B, C, D, E, F, G, H, I, J, K)) :|: A >= J
f48(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f54(A, B, C, D, E, 1, G, H, I, J, K)) :|: J >= A + 1
f43(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f48(A - 1, B, C, D, E, F, G, H, I, J, K)) :|: TRUE
f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f69(A, B, C, D, E, F, G, H, I, J, K)) :|: 0 >= G + 1
f11(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f69(A, B, C, D, E, F, G, H, I, J, K)) :|: G >= 1

The start-symbols are:[f0_11]


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

(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f63 -> f11 : [ A>=1+B ], cost: 1

     17: f63 -> f11 : D'=J, [ B>=A ], cost: 1

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

      2: f11 -> f11 : G'=1, [ D>=E && G==0 ], cost: 1

      3: f11 -> f11 : G'=1, [ 1+D>=E && E>=2+D && G==0 ], cost: 1

      4: f11 -> f11 : E'=1+D, G'=1, [ E==1+D && G==0 ], cost: 1

      5: f11 -> f11 : E'=1+D, G'=1, H'=free_2, [ free>=1+free_1 && E==1+D && G==0 ], cost: 1

      6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1

     21: f11 -> f69 : [ 0>=1+G ], cost: 1

     22: f11 -> f69 : [ G>=1 ], cost: 1

      7: f40 -> f59 : [ 0>=1+F ], cost: 1

      8: f40 -> f59 : [ F>=1 ], cost: 1

      9: f40 -> f43 : F'=0, J'=1+J, [ F==0 ], cost: 1

     10: f43 -> f43 : J'=1+J, [ K>=1+free_6 ], cost: 1

     20: f43 -> f48 : A'=-1+A, [], cost: 1

     11: f48 -> f48 : A'=-1+A, [], cost: 1

     18: f48 -> f54 : [ A>=J ], cost: 1

     19: f48 -> f54 : F'=1, [ J>=1+A ], cost: 1

     12: f54 -> f40 : [ 0>=1+F ], cost: 1

     13: f54 -> f40 : [ F>=1 ], cost: 1

     14: f54 -> f40 : F'=0, H'=free_7, [ F==0 ], cost: 1

     15: f59 -> f63 : [ B>=1+A ], cost: 1

     16: f59 -> f63 : E'=-1+A, [ A>=B ], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f63 -> f11 : [ A>=1+B ], cost: 1

     17: f63 -> f11 : D'=J, [ B>=A ], cost: 1

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

      2: f11 -> f11 : G'=1, [ D>=E && G==0 ], cost: 1

      3: f11 -> f11 : G'=1, [ 1+D>=E && E>=2+D && G==0 ], cost: 1

      4: f11 -> f11 : E'=1+D, G'=1, [ E==1+D && G==0 ], cost: 1

      5: f11 -> f11 : E'=1+D, G'=1, H'=free_2, [ free>=1+free_1 && E==1+D && G==0 ], cost: 1

      6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1

      7: f40 -> f59 : [ 0>=1+F ], cost: 1

      8: f40 -> f59 : [ F>=1 ], cost: 1

      9: f40 -> f43 : F'=0, J'=1+J, [ F==0 ], cost: 1

     10: f43 -> f43 : J'=1+J, [ K>=1+free_6 ], cost: 1

     20: f43 -> f48 : A'=-1+A, [], cost: 1

     11: f48 -> f48 : A'=-1+A, [], cost: 1

     18: f48 -> f54 : [ A>=J ], cost: 1

     19: f48 -> f54 : F'=1, [ J>=1+A ], cost: 1

     12: f54 -> f40 : [ 0>=1+F ], cost: 1

     13: f54 -> f40 : [ F>=1 ], cost: 1

     14: f54 -> f40 : F'=0, H'=free_7, [ F==0 ], cost: 1

     15: f59 -> f63 : [ B>=1+A ], cost: 1

     16: f59 -> f63 : E'=-1+A, [ A>=B ], cost: 1



Removed rules with unsatisfiable guard:

   Start location: f0

      0: f63 -> f11 : [ A>=1+B ], cost: 1

     17: f63 -> f11 : D'=J, [ B>=A ], cost: 1

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

      2: f11 -> f11 : G'=1, [ D>=E && G==0 ], cost: 1

      4: f11 -> f11 : E'=1+D, G'=1, [ E==1+D && G==0 ], cost: 1

      5: f11 -> f11 : E'=1+D, G'=1, H'=free_2, [ free>=1+free_1 && E==1+D && G==0 ], cost: 1

      6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1

      7: f40 -> f59 : [ 0>=1+F ], cost: 1

      8: f40 -> f59 : [ F>=1 ], cost: 1

      9: f40 -> f43 : F'=0, J'=1+J, [ F==0 ], cost: 1

     10: f43 -> f43 : J'=1+J, [ K>=1+free_6 ], cost: 1

     20: f43 -> f48 : A'=-1+A, [], cost: 1

     11: f48 -> f48 : A'=-1+A, [], cost: 1

     18: f48 -> f54 : [ A>=J ], cost: 1

     19: f48 -> f54 : F'=1, [ J>=1+A ], cost: 1

     12: f54 -> f40 : [ 0>=1+F ], cost: 1

     13: f54 -> f40 : [ F>=1 ], cost: 1

     14: f54 -> f40 : F'=0, H'=free_7, [ F==0 ], cost: 1

     15: f59 -> f63 : [ B>=1+A ], cost: 1

     16: f59 -> f63 : E'=-1+A, [ A>=B ], cost: 1



Simplified all rules, resulting in:

   Start location: f0

      0: f63 -> f11 : [ A>=1+B ], cost: 1

     17: f63 -> f11 : D'=J, [ B>=A ], cost: 1

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

      2: f11 -> f11 : G'=1, [ D>=E && G==0 ], cost: 1

      4: f11 -> f11 : E'=1+D, G'=1, [ E==1+D && G==0 ], cost: 1

      5: f11 -> f11 : E'=1+D, G'=1, H'=free_2, [ E==1+D && G==0 ], cost: 1

      6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1

      7: f40 -> f59 : [ 0>=1+F ], cost: 1

      8: f40 -> f59 : [ F>=1 ], cost: 1

      9: f40 -> f43 : F'=0, J'=1+J, [ F==0 ], cost: 1

     10: f43 -> f43 : J'=1+J, [], cost: 1

     20: f43 -> f48 : A'=-1+A, [], cost: 1

     11: f48 -> f48 : A'=-1+A, [], cost: 1

     18: f48 -> f54 : [ A>=J ], cost: 1

     19: f48 -> f54 : F'=1, [ J>=1+A ], cost: 1

     12: f54 -> f40 : [ 0>=1+F ], cost: 1

     13: f54 -> f40 : [ F>=1 ], cost: 1

     14: f54 -> f40 : F'=0, H'=free_7, [ F==0 ], cost: 1

     15: f59 -> f63 : [ B>=1+A ], cost: 1

     16: f59 -> f63 : E'=-1+A, [ A>=B ], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 2.

   Accelerating the following rules:

      2: f11 -> f11 : G'=1, [ D>=E && G==0 ], cost: 1

      4: f11 -> f11 : E'=1+D, G'=1, [ E==1+D && G==0 ], cost: 1

      5: f11 -> f11 : E'=1+D, G'=1, H'=free_2, [ E==1+D && G==0 ], cost: 1



   Accelerated rule 2 with metering function 1-G, yielding the new rule 23.

   Accelerated rule 4 with metering function 1-G, yielding the new rule 24.

   Accelerated rule 5 with metering function 1-G, yielding the new rule 25.

   Removing the simple loops: 2 4 5.



Accelerating simple loops of location 4.

   Accelerating the following rules:

     10: f43 -> f43 : J'=1+J, [], cost: 1



   Accelerated rule 10 with NONTERM, yielding the new rule 26.

   Removing the simple loops: 10.



Accelerating simple loops of location 5.

   Accelerating the following rules:

     11: f48 -> f48 : A'=-1+A, [], cost: 1



   Accelerated rule 11 with NONTERM, yielding the new rule 27.

   Removing the simple loops: 11.



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

   Start location: f0

      0: f63 -> f11 : [ A>=1+B ], cost: 1

     17: f63 -> f11 : D'=J, [ B>=A ], cost: 1

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

      6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1

     23: f11 -> f11 : G'=1, [ D>=E && G==0 ], cost: 1-G

     24: f11 -> f11 : E'=1+D, G'=1, [ E==1+D && G==0 ], cost: 1-G

     25: f11 -> f11 : E'=1+D, G'=1, H'=free_2, [ E==1+D && G==0 ], cost: 1-G

      7: f40 -> f59 : [ 0>=1+F ], cost: 1

      8: f40 -> f59 : [ F>=1 ], cost: 1

      9: f40 -> f43 : F'=0, J'=1+J, [ F==0 ], cost: 1

     20: f43 -> f48 : A'=-1+A, [], cost: 1

     26: f43 -> [10] : [], cost: INF

     18: f48 -> f54 : [ A>=J ], cost: 1

     19: f48 -> f54 : F'=1, [ J>=1+A ], cost: 1

     27: f48 -> [11] : [], cost: INF

     12: f54 -> f40 : [ 0>=1+F ], cost: 1

     13: f54 -> f40 : [ F>=1 ], cost: 1

     14: f54 -> f40 : F'=0, H'=free_7, [ F==0 ], cost: 1

     15: f59 -> f63 : [ B>=1+A ], cost: 1

     16: f59 -> f63 : E'=-1+A, [ A>=B ], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f63 -> f11 : [ A>=1+B ], cost: 1

     17: f63 -> f11 : D'=J, [ B>=A ], cost: 1

     28: f63 -> f11 : G'=1, [ A>=1+B && D>=E && G==0 ], cost: 2-G

     29: f63 -> f11 : D'=J, G'=1, [ B>=A && J>=E && G==0 ], cost: 2-G

     30: f63 -> f11 : E'=1+D, G'=1, [ A>=1+B && E==1+D && G==0 ], cost: 2-G

     31: f63 -> f11 : D'=J, E'=1+J, G'=1, [ B>=A && E==1+J && G==0 ], cost: 2-G

     32: f63 -> f11 : E'=1+D, G'=1, H'=free_2, [ A>=1+B && E==1+D && G==0 ], cost: 2-G

     33: f63 -> f11 : D'=J, E'=1+J, G'=1, H'=free_2, [ B>=A && E==1+J && G==0 ], cost: 2-G

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

      6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1

      7: f40 -> f59 : [ 0>=1+F ], cost: 1

      8: f40 -> f59 : [ F>=1 ], cost: 1

      9: f40 -> f43 : F'=0, J'=1+J, [ F==0 ], cost: 1

     34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF

     20: f43 -> f48 : A'=-1+A, [], cost: 1

     35: f43 -> [11] : A'=-1+A, [], cost: INF

     18: f48 -> f54 : [ A>=J ], cost: 1

     19: f48 -> f54 : F'=1, [ J>=1+A ], cost: 1

     12: f54 -> f40 : [ 0>=1+F ], cost: 1

     13: f54 -> f40 : [ F>=1 ], cost: 1

     14: f54 -> f40 : F'=0, H'=free_7, [ F==0 ], cost: 1

     15: f59 -> f63 : [ B>=1+A ], cost: 1

     16: f59 -> f63 : E'=-1+A, [ A>=B ], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: f0

      0: f63 -> f11 : [ A>=1+B ], cost: 1

     17: f63 -> f11 : D'=J, [ B>=A ], cost: 1

     28: f63 -> f11 : G'=1, [ A>=1+B && D>=E && G==0 ], cost: 2-G

     29: f63 -> f11 : D'=J, G'=1, [ B>=A && J>=E && G==0 ], cost: 2-G

     30: f63 -> f11 : E'=1+D, G'=1, [ A>=1+B && E==1+D && G==0 ], cost: 2-G

     31: f63 -> f11 : D'=J, E'=1+J, G'=1, [ B>=A && E==1+J && G==0 ], cost: 2-G

     32: f63 -> f11 : E'=1+D, G'=1, H'=free_2, [ A>=1+B && E==1+D && G==0 ], cost: 2-G

     33: f63 -> f11 : D'=J, E'=1+J, G'=1, H'=free_2, [ B>=A && E==1+J && G==0 ], cost: 2-G

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

      6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1

     34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF

     36: f40 -> f48 : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: 2

     37: f40 -> [11] : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: INF

     38: f40 -> f63 : [ 0>=1+F && B>=1+A ], cost: 2

     39: f40 -> f63 : E'=-1+A, [ 0>=1+F && A>=B ], cost: 2

     40: f40 -> f63 : [ F>=1 && B>=1+A ], cost: 2

     41: f40 -> f63 : E'=-1+A, [ F>=1 && A>=B ], cost: 2

     42: f48 -> f40 : [ A>=J && 0>=1+F ], cost: 2

     43: f48 -> f40 : [ A>=J && F>=1 ], cost: 2

     44: f48 -> f40 : F'=0, H'=free_7, [ A>=J && F==0 ], cost: 2

     45: f48 -> f40 : F'=1, [ J>=1+A ], cost: 2



Applied pruning (of leafs and parallel rules):

   Start location: f0

      0: f63 -> f11 : [ A>=1+B ], cost: 1

     17: f63 -> f11 : D'=J, [ B>=A ], cost: 1

     29: f63 -> f11 : D'=J, G'=1, [ B>=A && J>=E && G==0 ], cost: 2-G

     30: f63 -> f11 : E'=1+D, G'=1, [ A>=1+B && E==1+D && G==0 ], cost: 2-G

     31: f63 -> f11 : D'=J, E'=1+J, G'=1, [ B>=A && E==1+J && G==0 ], cost: 2-G

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

      6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1

     34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF

     36: f40 -> f48 : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: 2

     37: f40 -> [11] : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: INF

     38: f40 -> f63 : [ 0>=1+F && B>=1+A ], cost: 2

     39: f40 -> f63 : E'=-1+A, [ 0>=1+F && A>=B ], cost: 2

     40: f40 -> f63 : [ F>=1 && B>=1+A ], cost: 2

     41: f40 -> f63 : E'=-1+A, [ F>=1 && A>=B ], cost: 2

     42: f48 -> f40 : [ A>=J && 0>=1+F ], cost: 2

     43: f48 -> f40 : [ A>=J && F>=1 ], cost: 2

     44: f48 -> f40 : F'=0, H'=free_7, [ A>=J && F==0 ], cost: 2

     45: f48 -> f40 : F'=1, [ J>=1+A ], cost: 2



Eliminated locations (on tree-shaped paths):

   Start location: f0

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

      6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1

     34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF

     37: f40 -> [11] : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: INF

     46: f40 -> f11 : D'=J, [ 0>=1+F && B>=1+A ], cost: 3

     47: f40 -> f11 : D'=J, G'=1, [ 0>=1+F && B>=1+A && J>=E && G==0 ], cost: 4-G

     48: f40 -> f11 : D'=J, E'=1+J, G'=1, [ 0>=1+F && B>=1+A && E==1+J && G==0 ], cost: 4-G

     49: f40 -> f11 : E'=-1+A, [ 0>=1+F && A>=1+B ], cost: 3

     50: f40 -> f11 : D'=J, E'=-1+A, [ 0>=1+F && A>=B && B>=A ], cost: 3

     51: f40 -> f11 : D'=J, E'=-1+A, G'=1, [ 0>=1+F && A>=B && B>=A && J>=-1+A && G==0 ], cost: 4-G

     52: f40 -> f11 : E'=1+D, G'=1, [ 0>=1+F && A>=1+B && -1+A==1+D && G==0 ], cost: 4-G

     53: f40 -> f11 : D'=J, E'=1+J, G'=1, [ 0>=1+F && A>=B && B>=A && -1+A==1+J && G==0 ], cost: 4-G

     54: f40 -> f11 : D'=J, [ F>=1 && B>=1+A ], cost: 3

     55: f40 -> f11 : D'=J, G'=1, [ F>=1 && B>=1+A && J>=E && G==0 ], cost: 4-G

     56: f40 -> f11 : D'=J, E'=1+J, G'=1, [ F>=1 && B>=1+A && E==1+J && G==0 ], cost: 4-G

     57: f40 -> f11 : E'=-1+A, [ F>=1 && A>=1+B ], cost: 3

     58: f40 -> f11 : D'=J, E'=-1+A, [ F>=1 && A>=B && B>=A ], cost: 3

     59: f40 -> f11 : D'=J, E'=-1+A, G'=1, [ F>=1 && A>=B && B>=A && J>=-1+A && G==0 ], cost: 4-G

     60: f40 -> f11 : E'=1+D, G'=1, [ F>=1 && A>=1+B && -1+A==1+D && G==0 ], cost: 4-G

     61: f40 -> f11 : D'=J, E'=1+J, G'=1, [ F>=1 && A>=B && B>=A && -1+A==1+J && G==0 ], cost: 4-G

     62: f40 -> f40 : A'=-1+A, F'=0, H'=free_7, J'=1+J, [ F==0 && -1+A>=1+J ], cost: 4

     63: f40 -> f40 : A'=-1+A, F'=1, J'=1+J, [ F==0 && 1+J>=A ], cost: 4



Applied pruning (of leafs and parallel rules):

   Start location: f0

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

      6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1

     34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF

     37: f40 -> [11] : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: INF

     46: f40 -> f11 : D'=J, [ 0>=1+F && B>=1+A ], cost: 3

     47: f40 -> f11 : D'=J, G'=1, [ 0>=1+F && B>=1+A && J>=E && G==0 ], cost: 4-G

     49: f40 -> f11 : E'=-1+A, [ 0>=1+F && A>=1+B ], cost: 3

     53: f40 -> f11 : D'=J, E'=1+J, G'=1, [ 0>=1+F && A>=B && B>=A && -1+A==1+J && G==0 ], cost: 4-G

     55: f40 -> f11 : D'=J, G'=1, [ F>=1 && B>=1+A && J>=E && G==0 ], cost: 4-G

     62: f40 -> f40 : A'=-1+A, F'=0, H'=free_7, J'=1+J, [ F==0 && -1+A>=1+J ], cost: 4

     63: f40 -> f40 : A'=-1+A, F'=1, J'=1+J, [ F==0 && 1+J>=A ], cost: 4



Accelerating simple loops of location 3.

   Accelerating the following rules:

     62: f40 -> f40 : A'=-1+A, F'=0, H'=free_7, J'=1+J, [ F==0 && -1+A>=1+J ], cost: 4

     63: f40 -> f40 : A'=-1+A, F'=1, J'=1+J, [ F==0 && 1+J>=A ], cost: 4



   Accelerated rule 62 with metering function meter (where 2*meter==-1-J+A), yielding the new rule 64.

   Accelerated rule 63 with metering function 1-F, yielding the new rule 65.

   Nested simple loops 63 (outer loop) and 64 (inner loop) with metering function -F, resulting in the new rules: 66.

   Removing the simple loops: 62 63.



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

   Start location: f0

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

      6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1

     34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF

     37: f40 -> [11] : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: INF

     46: f40 -> f11 : D'=J, [ 0>=1+F && B>=1+A ], cost: 3

     47: f40 -> f11 : D'=J, G'=1, [ 0>=1+F && B>=1+A && J>=E && G==0 ], cost: 4-G

     49: f40 -> f11 : E'=-1+A, [ 0>=1+F && A>=1+B ], cost: 3

     53: f40 -> f11 : D'=J, E'=1+J, G'=1, [ 0>=1+F && A>=B && B>=A && -1+A==1+J && G==0 ], cost: 4-G

     55: f40 -> f11 : D'=J, G'=1, [ F>=1 && B>=1+A && J>=E && G==0 ], cost: 4-G

     64: f40 -> f40 : A'=-meter+A, F'=0, H'=free_7, J'=meter+J, [ F==0 && -1+A>=1+J && 2*meter==-1-J+A && meter>=1 ], cost: 4*meter

     65: f40 -> f40 : A'=-1+F+A, F'=1, J'=1-F+J, [ F==0 && 1+J>=A ], cost: 4-4*F

     66: f40 -> f40 : A'=F+F*meter+A, F'=1, H'=free_7, J'=-F+J-F*meter, [ F==0 && -1+A>=1+J && 2*meter==-1-J+A && meter>=1 && -F>=1 ], cost: -4*F-4*F*meter



Chained accelerated rules (with incoming rules):

   Start location: f0

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

      6: f11 -> f40 : A'=E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 ], cost: 1

     67: f11 -> f40 : A'=-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=1+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: 1+4*meter

     68: f11 -> f40 : A'=-1+F+E, F'=1, G'=0, H'=free_5, Q'=free_3, J'=2-F+D, K'=free_4, [ 2+D-E==0 && G==0 && F==0 ], cost: 5-4*F

     34: f40 -> [10] : F'=0, J'=1+J, [ F==0 ], cost: INF

     37: f40 -> [11] : A'=-1+A, F'=0, J'=1+J, [ F==0 ], cost: INF

     46: f40 -> f11 : D'=J, [ 0>=1+F && B>=1+A ], cost: 3

     47: f40 -> f11 : D'=J, G'=1, [ 0>=1+F && B>=1+A && J>=E && G==0 ], cost: 4-G

     49: f40 -> f11 : E'=-1+A, [ 0>=1+F && A>=1+B ], cost: 3

     53: f40 -> f11 : D'=J, E'=1+J, G'=1, [ 0>=1+F && A>=B && B>=A && -1+A==1+J && G==0 ], cost: 4-G

     55: f40 -> f11 : D'=J, G'=1, [ F>=1 && B>=1+A && J>=E && G==0 ], cost: 4-G



Eliminated locations (on tree-shaped paths):

   Start location: f0

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

     69: f11 -> [10] : A'=E, F'=0, G'=0, H'=free_5, Q'=free_3, J'=2+D, K'=free_4, [ E>=2+D && G==0 && F==0 ], cost: INF

     70: f11 -> [11] : A'=-1+E, F'=0, G'=0, H'=free_5, Q'=free_3, J'=2+D, K'=free_4, [ E>=2+D && G==0 && F==0 ], cost: INF

     71: f11 -> f11 : A'=E, D'=1+D, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && B>=1+E ], cost: 4

     72: f11 -> f11 : A'=E, E'=-1+E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && E>=1+B ], cost: 4

     73: f11 -> f11 : A'=E, D'=1+D, E'=2+D, G'=1, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ G==0 && 0>=1+F && E>=B && B>=E && -1+E==2+D ], cost: 5

     74: f11 -> [10] : A'=-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=2+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: INF

     75: f11 -> [11] : A'=-1-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=2+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: INF

     76: f11 -> f11 : A'=-1+F+E, D'=2-F+D, F'=1, G'=1, H'=free_5, Q'=free_3, J'=2-F+D, K'=free_4, [ 2+D-E==0 && G==0 && F==0 && B>=F+E && 2-F+D>=E ], cost: 9-4*F

     77: f11 -> [13] : [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: 1+4*meter

     78: f11 -> [13] : [ 2+D-E==0 && G==0 && F==0 ], cost: 5-4*F



Accelerating simple loops of location 2.

   Simplified some of the simple loops (and removed duplicate rules).

   Accelerating the following rules:

     71: f11 -> f11 : A'=E, D'=1+D, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && B>=1+E ], cost: 4

     72: f11 -> f11 : A'=E, E'=-1+E, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && E>=1+B ], cost: 4

     73: f11 -> f11 : A'=E, D'=1+D, E'=2+D, G'=1, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ G==0 && 0>=1+F && -E+B==0 && -1+E==2+D ], cost: 5

     76: f11 -> f11 : A'=-1+F+E, D'=2-F+D, F'=1, G'=1, H'=free_5, Q'=free_3, J'=2-F+D, K'=free_4, [ 2+D-E==0 && G==0 && F==0 && B>=F+E && 2-F+D>=E ], cost: 9-4*F



   Accelerated rule 71 with metering function -1-D+E, yielding the new rule 79.

   Accelerated rule 72 with backward acceleration, yielding the new rule 80.

   Accelerated rule 72 with backward acceleration, yielding the new rule 81.

   Accelerated rule 73 with metering function meter_2 (where 4*meter_2==-3-G-D+2*E-B), yielding the new rule 82.

   Accelerated rule 76 with metering function meter_3 (where 4*meter_3==-2-F-G-D+E), yielding the new rule 83.

   Nested simple loops 73 (outer loop) and 81 (inner loop) with metering function meter_4 (where 2*meter_4==-3-G-D+B), resulting in the new rules: 84.

   Removing the simple loops: 71 72 73 76.



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

   Start location: f0

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

     69: f11 -> [10] : A'=E, F'=0, G'=0, H'=free_5, Q'=free_3, J'=2+D, K'=free_4, [ E>=2+D && G==0 && F==0 ], cost: INF

     70: f11 -> [11] : A'=-1+E, F'=0, G'=0, H'=free_5, Q'=free_3, J'=2+D, K'=free_4, [ E>=2+D && G==0 && F==0 ], cost: INF

     74: f11 -> [10] : A'=-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=2+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: INF

     75: f11 -> [11] : A'=-1-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=2+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: INF

     77: f11 -> [13] : [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: 1+4*meter

     78: f11 -> [13] : [ 2+D-E==0 && G==0 && F==0 ], cost: 5-4*F

     79: f11 -> f11 : A'=E, D'=-1+E, G'=0, H'=free_5, Q'=free_3, J'=-1+E, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && B>=1+E ], cost: -4-4*D+4*E

     80: f11 -> f11 : A'=2+D, E'=1+D, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && E>=1+B && 2+D>=1+B ], cost: -4-4*D+4*E

     81: f11 -> f11 : A'=1+B, E'=B, G'=0, H'=free_5, Q'=free_3, J'=1+D, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && E>=1+B && 1+B>=2+D ], cost: 4*E-4*B

     82: f11 -> f11 : A'=D+meter_2, D'=D+meter_2, E'=1+D+meter_2, G'=1, H'=free_5, Q'=free_3, J'=D+meter_2, K'=free_4, [ G==0 && 0>=1+F && -E+B==0 && -1+E==2+D && 4*meter_2==-3-G-D+2*E-B && meter_2>=1 ], cost: 5*meter_2

     83: f11 -> f11 : A'=E, D'=D+meter_3, F'=1, G'=1, H'=free_5, Q'=free_3, J'=D+meter_3, K'=free_4, [ 2+D-E==0 && G==0 && F==0 && B>=F+E && 2-F+D>=E && 4*meter_3==-2-F-G-D+E && meter_3>=1 ], cost: 5*meter_3

     84: f11 -> f11 : A'=B, D'=D+meter_4, E'=1+D+meter_4, G'=1, H'=free_5, Q'=free_3, J'=D+meter_4, K'=free_4, [ E>=2+D && G==0 && 0>=1+F && E>=1+B && -1+B==2+D && 2*meter_4==-3-G-D+B && meter_4>=1 ], cost: -4*meter_4*B+7*meter_4+2*meter_4^2+4*D*meter_4



Chained accelerated rules (with incoming rules):

   Start location: f0

      1: f0 -> f11 : B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, [], cost: 1

     69: f11 -> [10] : A'=E, F'=0, G'=0, H'=free_5, Q'=free_3, J'=2+D, K'=free_4, [ E>=2+D && G==0 && F==0 ], cost: INF

     70: f11 -> [11] : A'=-1+E, F'=0, G'=0, H'=free_5, Q'=free_3, J'=2+D, K'=free_4, [ E>=2+D && G==0 && F==0 ], cost: INF

     74: f11 -> [10] : A'=-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=2+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: INF

     75: f11 -> [11] : A'=-1-meter+E, F'=0, G'=0, H'=free_7, Q'=free_3, J'=2+meter+D, K'=free_4, [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: INF

     77: f11 -> [13] : [ G==0 && F==0 && -1+E>=2+D && 2*meter==-2-D+E && meter>=1 ], cost: 1+4*meter

     78: f11 -> [13] : [ 2+D-E==0 && G==0 && F==0 ], cost: 5-4*F



Eliminated locations (on tree-shaped paths):

   Start location: f0

     85: f0 -> [10] : A'=20, B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, H'=free_5, Q'=free_3, J'=3, K'=free_4, [], cost: INF

     86: f0 -> [11] : A'=19, B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, H'=free_5, Q'=free_3, J'=3, K'=free_4, [], cost: INF



Applied pruning (of leafs and parallel rules):

   Start location: f0

     85: f0 -> [10] : A'=20, B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, H'=free_5, Q'=free_3, J'=3, K'=free_4, [], cost: INF

     86: f0 -> [11] : A'=19, B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, H'=free_5, Q'=free_3, J'=3, K'=free_4, [], cost: INF



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

     86: f0 -> [11] : A'=19, B'=10, C'=20, D'=1, E'=20, F'=0, G'=0, H'=free_5, Q'=free_3, J'=3, K'=free_4, [], cost: INF



Computing asymptotic complexity for rule 86

   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:  []



NO


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

(2)
BOUNDS(INF, INF)