/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1031 ms]
(2) BOUNDS(INF, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A, B, C, D, E, F, G) -> Com_1(f6(8, 0, 14, -(1), E, F, G)) :|: TRUE
f6(A, B, C, D, E, F, G) -> Com_1(f12(A, B, C, D, I, F, G)) :|: C >= B && A >= H + 1
f6(A, B, C, D, E, F, G) -> Com_1(f12(A, B, C, D, I, F, G)) :|: C >= B
f6(A, B, C, D, E, F, G) -> Com_1(f6(A, B, B - 1, I, H, F, G)) :|: C >= B
f12(A, B, C, D, E, F, G) -> Com_1(f6(A, B, E - 1, D, E, F, G)) :|: TRUE
f12(A, B, C, D, E, F, G) -> Com_1(f6(A, E + 1, C, D, E, F, G)) :|: TRUE
f6(A, B, C, D, E, F, G) -> Com_1(f20(A, B, C, D, E, D, D)) :|: B >= 1 + C

The start-symbols are:[f0_7]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1

      1: f6 -> f12 : E'=free, [ C>=B && A>=1+free_1 ], cost: 1

      2: f6 -> f12 : E'=free_2, [ C>=B ], cost: 1

      3: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B ], cost: 1

      6: f6 -> f20 : F'=D, G'=D, [ B>=1+C ], cost: 1

      4: f12 -> f6 : C'=-1+E, [], cost: 1

      5: f12 -> f6 : B'=1+E, [], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1

      1: f6 -> f12 : E'=free, [ C>=B && A>=1+free_1 ], cost: 1

      2: f6 -> f12 : E'=free_2, [ C>=B ], cost: 1

      3: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B ], cost: 1

      4: f12 -> f6 : C'=-1+E, [], cost: 1

      5: f12 -> f6 : B'=1+E, [], cost: 1



Simplified all rules, resulting in:

   Start location: f0

      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1

      1: f6 -> f12 : E'=free, [ C>=B ], cost: 1

      2: f6 -> f12 : E'=free_2, [ C>=B ], cost: 1

      3: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B ], cost: 1

      4: f12 -> f6 : C'=-1+E, [], cost: 1

      5: f12 -> f6 : B'=1+E, [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 1.

   Accelerating the following rules:

      3: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B ], cost: 1



   Found no metering function for rule 3.

   Removing the simple loops:.



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

   Start location: f0

      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1

      1: f6 -> f12 : E'=free, [ C>=B ], cost: 1

      2: f6 -> f12 : E'=free_2, [ C>=B ], cost: 1

      3: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B ], cost: 1

      4: f12 -> f6 : C'=-1+E, [], cost: 1

      5: f12 -> f6 : B'=1+E, [], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1

      7: f0 -> f6 : A'=8, B'=0, C'=-1, D'=free_3, E'=free_4, [], cost: 2

      1: f6 -> f12 : E'=free, [ C>=B ], cost: 1

      2: f6 -> f12 : E'=free_2, [ C>=B ], cost: 1

      4: f12 -> f6 : C'=-1+E, [], cost: 1

      5: f12 -> f6 : B'=1+E, [], cost: 1

      8: f12 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ -1+E>=B ], cost: 2

      9: f12 -> f6 : B'=1+E, C'=E, D'=free_3, E'=free_4, [ C>=1+E ], cost: 2



Eliminated locations (on tree-shaped paths):

   Start location: f0

      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1

      7: f0 -> f6 : A'=8, B'=0, C'=-1, D'=free_3, E'=free_4, [], cost: 2

     10: f6 -> f6 : C'=-1+free, E'=free, [ C>=B ], cost: 2

     11: f6 -> f6 : B'=1+free, E'=free, [ C>=B ], cost: 2

     12: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B && -1+free>=B ], cost: 3

     13: f6 -> f6 : B'=1+free, C'=free, D'=free_3, E'=free_4, [ C>=B && C>=1+free ], cost: 3

     14: f6 -> f6 : C'=-1+free_2, E'=free_2, [ C>=B ], cost: 2

     15: f6 -> f6 : B'=1+free_2, E'=free_2, [ C>=B ], cost: 2

     16: f6 -> f6 : C'=-1+B, D'=free_3, E'=free_4, [ C>=B && -1+free_2>=B ], cost: 3

     17: f6 -> f6 : B'=1+free_2, C'=free_2, D'=free_3, E'=free_4, [ C>=B && C>=1+free_2 ], cost: 3



Applied pruning (of leafs and parallel rules):

   Start location: f0

      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1

      7: f0 -> f6 : A'=8, B'=0, C'=-1, D'=free_3, E'=free_4, [], cost: 2

     10: f6 -> f6 : C'=-1+free, E'=free, [ C>=B ], cost: 2

     11: f6 -> f6 : B'=1+free, E'=free, [ C>=B ], cost: 2

     13: f6 -> f6 : B'=1+free, C'=free, D'=free_3, E'=free_4, [ C>=B && C>=1+free ], cost: 3

     14: f6 -> f6 : C'=-1+free_2, E'=free_2, [ C>=B ], cost: 2

     15: f6 -> f6 : B'=1+free_2, E'=free_2, [ C>=B ], cost: 2



Accelerating simple loops of location 1.

   Accelerating the following rules:

     10: f6 -> f6 : C'=-1+free, E'=free, [ C>=B ], cost: 2

     11: f6 -> f6 : B'=1+free, E'=free, [ C>=B ], cost: 2

     13: f6 -> f6 : B'=1+free, C'=free, D'=free_3, E'=free_4, [ C>=B && C>=1+free ], cost: 3

     14: f6 -> f6 : C'=-1+free_2, E'=free_2, [ C>=B ], cost: 2

     15: f6 -> f6 : B'=1+free_2, E'=free_2, [ C>=B ], cost: 2



   Accelerated rule 10 with NONTERM (after strengthening guard), yielding the new rule 18.

   Accelerated rule 11 with NONTERM (after strengthening guard), yielding the new rule 19.

   Found no metering function for rule 13.

   Accelerated rule 14 with NONTERM (after strengthening guard), yielding the new rule 20.

   Accelerated rule 15 with NONTERM (after strengthening guard), yielding the new rule 21.

   Removing the simple loops:.



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

   Start location: f0

      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1

      7: f0 -> f6 : A'=8, B'=0, C'=-1, D'=free_3, E'=free_4, [], cost: 2

     10: f6 -> f6 : C'=-1+free, E'=free, [ C>=B ], cost: 2

     11: f6 -> f6 : B'=1+free, E'=free, [ C>=B ], cost: 2

     13: f6 -> f6 : B'=1+free, C'=free, D'=free_3, E'=free_4, [ C>=B && C>=1+free ], cost: 3

     14: f6 -> f6 : C'=-1+free_2, E'=free_2, [ C>=B ], cost: 2

     15: f6 -> f6 : B'=1+free_2, E'=free_2, [ C>=B ], cost: 2

     18: f6 -> [5] : [ C>=B && -1+free>=B ], cost: INF

     19: f6 -> [5] : [ C>=B && C>=1+free ], cost: INF

     20: f6 -> [5] : [ C>=B && -1+free_2>=B ], cost: INF

     21: f6 -> [5] : [ C>=B && C>=1+free_2 ], cost: INF



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], cost: 1

      7: f0 -> f6 : A'=8, B'=0, C'=-1, D'=free_3, E'=free_4, [], cost: 2

     22: f0 -> f6 : A'=8, B'=0, C'=-1+free, D'=-1, E'=free, [], cost: 3

     23: f0 -> f6 : A'=8, B'=1+free, C'=14, D'=-1, E'=free, [], cost: 3

     24: f0 -> f6 : A'=8, B'=1+free, C'=free, D'=free_3, E'=free_4, [ 14>=1+free ], cost: 4

     25: f0 -> f6 : A'=8, B'=0, C'=-1+free_2, D'=-1, E'=free_2, [], cost: 3

     26: f0 -> f6 : A'=8, B'=1+free_2, C'=14, D'=-1, E'=free_2, [], cost: 3

     27: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF

     28: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF

     29: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF

     30: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF



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

   Start location: f0

     27: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF

     28: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF

     29: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF

     30: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

     30: f0 -> [5] : A'=8, B'=0, C'=14, D'=-1, [], cost: INF



Computing asymptotic complexity for rule 30

   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


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(2)
BOUNDS(INF, INF)