/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 326 ms]
(2) BOUNDS(INF, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f1(A, B, C, D, E, F, G, H, I) -> Com_1(f1(A, B, K, L, J, M, G, H, I)) :|: J >= 1 && B >= 1 + A
f1(A, B, C, D, E, F, G, H, I) -> Com_1(f1(A, B, K, L, J, M, G, H, I)) :|: 0 >= J + 1 && B >= 1 + A
f1(A, B, C, D, E, F, G, H, I) -> Com_1(f1(A, B, K, L, 0, F, G, H, I)) :|: B >= 1 + A
f1(A, B, C, D, E, F, G, H, I) -> Com_1(f300(A, B, K, L, E, F, J, H, I)) :|: A >= B
f2(A, B, C, D, E, F, G, H, I) -> Com_1(f1(A, B, C, D, E, F, G, K, L)) :|: TRUE

The start-symbols are:[f2_9]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f2

      0: f1 -> f1 : C'=free_2, D'=free_3, E'=free_1, F'=free, [ free_1>=1 && A>=1+B ], cost: 1

      1: f1 -> f1 : C'=free_6, D'=free_7, E'=free_5, F'=free_4, [ 0>=1+free_5 && A>=1+B ], cost: 1

      2: f1 -> f1 : C'=free_8, D'=free_9, E'=0, [ A>=1+B ], cost: 1

      3: f1 -> f300 : C'=free_11, D'=free_12, G'=free_10, [ B>=A ], cost: 1

      4: f2 -> f1 : H'=free_13, Q'=free_14, [], cost: 1



Checking for constant complexity:

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

      4: f2 -> f1 : H'=free_13, Q'=free_14, [], cost: 1



Removed unreachable and leaf rules:

   Start location: f2

      0: f1 -> f1 : C'=free_2, D'=free_3, E'=free_1, F'=free, [ free_1>=1 && A>=1+B ], cost: 1

      1: f1 -> f1 : C'=free_6, D'=free_7, E'=free_5, F'=free_4, [ 0>=1+free_5 && A>=1+B ], cost: 1

      2: f1 -> f1 : C'=free_8, D'=free_9, E'=0, [ A>=1+B ], cost: 1

      4: f2 -> f1 : H'=free_13, Q'=free_14, [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 0.

   Accelerating the following rules:

      0: f1 -> f1 : C'=free_2, D'=free_3, E'=free_1, F'=free, [ free_1>=1 && A>=1+B ], cost: 1

      1: f1 -> f1 : C'=free_6, D'=free_7, E'=free_5, F'=free_4, [ 0>=1+free_5 && A>=1+B ], cost: 1

      2: f1 -> f1 : C'=free_8, D'=free_9, E'=0, [ A>=1+B ], cost: 1



   Accelerated rule 0 with NONTERM, yielding the new rule 5.

   Accelerated rule 1 with NONTERM, yielding the new rule 6.

   Accelerated rule 2 with NONTERM, yielding the new rule 7.

   Removing the simple loops: 0 1 2.



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

   Start location: f2

      5: f1 -> [3] : [ free_1>=1 && A>=1+B ], cost: NONTERM

      6: f1 -> [3] : [ 0>=1+free_5 && A>=1+B ], cost: NONTERM

      7: f1 -> [3] : [ A>=1+B ], cost: NONTERM

      4: f2 -> f1 : H'=free_13, Q'=free_14, [], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f2

      4: f2 -> f1 : H'=free_13, Q'=free_14, [], cost: 1

      8: f2 -> [3] : H'=free_13, Q'=free_14, [ A>=1+B ], cost: NONTERM

      9: f2 -> [3] : H'=free_13, Q'=free_14, [ A>=1+B ], cost: NONTERM

     10: f2 -> [3] : H'=free_13, Q'=free_14, [ A>=1+B ], cost: NONTERM



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

   Start location: f2

      8: f2 -> [3] : H'=free_13, Q'=free_14, [ A>=1+B ], cost: NONTERM

      9: f2 -> [3] : H'=free_13, Q'=free_14, [ A>=1+B ], cost: NONTERM

     10: f2 -> [3] : H'=free_13, Q'=free_14, [ A>=1+B ], cost: NONTERM



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f2

     10: f2 -> [3] : H'=free_13, Q'=free_14, [ A>=1+B ], cost: NONTERM



Computing asymptotic complexity for rule 10

   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>=1+B ]



NO


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(2)
BOUNDS(INF, INF)