/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 227 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) -> Com_1(f1(A, B, J, I, K, F, G, H)) :|: I >= 1 && A >= 1 + B
f1(A, B, C, D, E, F, G, H) -> Com_1(f1(A, B, J, I, K, F, G, H)) :|: 0 >= I + 1 && A >= 1 + B
f1(A, B, C, D, E, F, G, H) -> Com_1(f1(A, B, J, 0, E, F, G, H)) :|: A >= 1 + B
f1(A, B, C, D, E, F, G, H) -> Com_1(f300(A, B, J, D, E, I, G, H)) :|: B >= A
f2(A, B, C, D, E, F, G, H) -> Com_1(f1(A, B, C, D, E, F, J, J)) :|: TRUE

The start-symbols are:[f2_8]


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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_1, D'=free, E'=free_2, [ free>=1 && A>=1+B ], cost: 1

      1: f1 -> f1 : C'=free_4, D'=free_3, E'=free_5, [ 0>=1+free_3 && A>=1+B ], cost: 1

      2: f1 -> f1 : C'=free_6, D'=0, [ A>=1+B ], cost: 1

      3: f1 -> f300 : C'=free_8, F'=free_7, [ B>=A ], cost: 1

      4: f2 -> f1 : G'=free_9, H'=free_9, [], cost: 1



Removed unreachable and leaf rules:

   Start location: f2

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

      1: f1 -> f1 : C'=free_4, D'=free_3, E'=free_5, [ 0>=1+free_3 && A>=1+B ], cost: 1

      2: f1 -> f1 : C'=free_6, D'=0, [ A>=1+B ], cost: 1

      4: f2 -> f1 : G'=free_9, H'=free_9, [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 0.

   Accelerating the following rules:

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

      1: f1 -> f1 : C'=free_4, D'=free_3, E'=free_5, [ 0>=1+free_3 && A>=1+B ], cost: 1

      2: f1 -> f1 : C'=free_6, D'=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 && A>=1+B ], cost: INF

      6: f1 -> [3] : [ 0>=1+free_3 && A>=1+B ], cost: INF

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

      4: f2 -> f1 : G'=free_9, H'=free_9, [], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f2

      4: f2 -> f1 : G'=free_9, H'=free_9, [], cost: 1

      8: f2 -> [3] : G'=free_9, H'=free_9, [ A>=1+B ], cost: INF

      9: f2 -> [3] : G'=free_9, H'=free_9, [ A>=1+B ], cost: INF

     10: f2 -> [3] : G'=free_9, H'=free_9, [ A>=1+B ], cost: INF



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

   Start location: f2

      8: f2 -> [3] : G'=free_9, H'=free_9, [ A>=1+B ], cost: INF

      9: f2 -> [3] : G'=free_9, H'=free_9, [ A>=1+B ], cost: INF

     10: f2 -> [3] : G'=free_9, H'=free_9, [ A>=1+B ], cost: INF



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f2

     10: f2 -> [3] : G'=free_9, H'=free_9, [ A>=1+B ], cost: INF



Computing asymptotic complexity for rule 10

   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:  [ A>=1+B ]



NO


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(2)
BOUNDS(INF, INF)