/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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:
f2(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f2(A, B, M, N, L, O, G, H, I, J, K)) :|: L >= 1 && B >= 1 + A
f2(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f2(A, B, M, N, L, O, G, H, I, J, K)) :|: 0 >= L + 1 && B >= 1 + A
f2(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f2(A, B, M, N, 0, F, G, H, I, J, K)) :|: B >= 1 + A
f2(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f300(A, B, M, N, E, F, L, H, I, J, K)) :|: A >= B
f1(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f2(A, B, C, D, E, F, G, M, N, N, M)) :|: TRUE

The start-symbols are:[f1_11]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f1

      0: f2 -> f2 : C'=free, D'=free_1, E'=free_3, F'=free_2, [ free_3>=1 && A>=1+B ], cost: 1

      1: f2 -> f2 : C'=free_4, D'=free_5, E'=free_7, F'=free_6, [ 0>=1+free_7 && A>=1+B ], cost: 1

      2: f2 -> f2 : C'=free_8, D'=free_9, E'=0, [ A>=1+B ], cost: 1

      3: f2 -> f300 : C'=free_10, D'=free_11, G'=free_12, [ B>=A ], cost: 1

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



Checking for constant complexity:

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

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



Removed unreachable and leaf rules:

   Start location: f1

      0: f2 -> f2 : C'=free, D'=free_1, E'=free_3, F'=free_2, [ free_3>=1 && A>=1+B ], cost: 1

      1: f2 -> f2 : C'=free_4, D'=free_5, E'=free_7, F'=free_6, [ 0>=1+free_7 && A>=1+B ], cost: 1

      2: f2 -> f2 : C'=free_8, D'=free_9, E'=0, [ A>=1+B ], cost: 1

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



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 0.

   Accelerating the following rules:

      0: f2 -> f2 : C'=free, D'=free_1, E'=free_3, F'=free_2, [ free_3>=1 && A>=1+B ], cost: 1

      1: f2 -> f2 : C'=free_4, D'=free_5, E'=free_7, F'=free_6, [ 0>=1+free_7 && A>=1+B ], cost: 1

      2: f2 -> f2 : 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: f1

      5: f2 -> [3] : [ free_3>=1 && A>=1+B ], cost: NONTERM

      6: f2 -> [3] : [ 0>=1+free_7 && A>=1+B ], cost: NONTERM

      7: f2 -> [3] : [ A>=1+B ], cost: NONTERM

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



Chained accelerated rules (with incoming rules):

   Start location: f1

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

      8: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ A>=1+B ], cost: NONTERM

      9: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ A>=1+B ], cost: NONTERM

     10: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ A>=1+B ], cost: NONTERM



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

   Start location: f1

      8: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ A>=1+B ], cost: NONTERM

      9: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ A>=1+B ], cost: NONTERM

     10: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ A>=1+B ], cost: NONTERM



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f1

     10: f1 -> [3] : H'=free_13, Q'=free_14, J'=free_14, K'=free_13, [ 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)