/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1020 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_1, [ C>=B && A>=1+free ], cost: 1

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

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



Checking for constant complexity:

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

      0: f0 -> f6 : A'=8, B'=0, C'=14, D'=-1, [], 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_1, [ C>=B && A>=1+free ], cost: 1

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

      3: f6 -> f6 : C'=-1+B, D'=free_4, E'=free_3, [ 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_1, [ C>=B ], cost: 1

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

      3: f6 -> f6 : C'=-1+B, D'=free_4, E'=free_3, [ 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_4, E'=free_3, [ 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_1, [ C>=B ], cost: 1

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

      3: f6 -> f6 : C'=-1+B, D'=free_4, E'=free_3, [ 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_4, E'=free_3, [], cost: 2

      1: f6 -> f12 : E'=free_1, [ 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_4, E'=free_3, [ -1+E>=B ], cost: 2

      9: f12 -> f6 : B'=1+E, C'=E, D'=free_4, E'=free_3, [ 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_4, E'=free_3, [], cost: 2

     10: f6 -> f6 : C'=-1+free_1, E'=free_1, [ C>=B ], cost: 2

     11: f6 -> f6 : B'=1+free_1, E'=free_1, [ C>=B ], cost: 2

     12: f6 -> f6 : C'=-1+B, D'=free_4, E'=free_3, [ C>=B && -1+free_1>=B ], cost: 3

     13: f6 -> f6 : B'=1+free_1, C'=free_1, D'=free_4, E'=free_3, [ C>=B && C>=1+free_1 ], 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_4, E'=free_3, [ C>=B && -1+free_2>=B ], cost: 3

     17: f6 -> f6 : B'=1+free_2, C'=free_2, D'=free_4, E'=free_3, [ 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_4, E'=free_3, [], cost: 2

     10: f6 -> f6 : C'=-1+free_1, E'=free_1, [ C>=B ], cost: 2

     11: f6 -> f6 : B'=1+free_1, E'=free_1, [ C>=B ], cost: 2

     13: f6 -> f6 : B'=1+free_1, C'=free_1, D'=free_4, E'=free_3, [ C>=B && C>=1+free_1 ], 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_1, E'=free_1, [ C>=B ], cost: 2

     11: f6 -> f6 : B'=1+free_1, E'=free_1, [ C>=B ], cost: 2

     13: f6 -> f6 : B'=1+free_1, C'=free_1, D'=free_4, E'=free_3, [ C>=B && C>=1+free_1 ], 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_4, E'=free_3, [], cost: 2

     10: f6 -> f6 : C'=-1+free_1, E'=free_1, [ C>=B ], cost: 2

     11: f6 -> f6 : B'=1+free_1, E'=free_1, [ C>=B ], cost: 2

     13: f6 -> f6 : B'=1+free_1, C'=free_1, D'=free_4, E'=free_3, [ C>=B && C>=1+free_1 ], 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_1>=B ], cost: NONTERM

     19: f6 -> [5] : [ C>=B && C>=1+free_1 ], cost: NONTERM

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

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



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_4, E'=free_3, [], cost: 2

     22: f0 -> f6 : A'=8, B'=0, C'=-1+free_1, D'=-1, E'=free_1, [], cost: 3

     23: f0 -> f6 : A'=8, B'=1+free_1, C'=14, D'=-1, E'=free_1, [], cost: 3

     24: f0 -> f6 : A'=8, B'=1+free_1, C'=free_1, D'=free_4, E'=free_3, [ 14>=1+free_1 ], 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: NONTERM

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

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

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



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

   Start location: f0

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

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

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

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



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

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



Computing asymptotic complexity for rule 30

   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:  []



NO


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(2)
BOUNDS(INF, INF)