/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 633 ms]
(2) BOUNDS(INF, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f6(A, B, C) -> Com_1(f9(A, D, C)) :|: 0 >= A + 1
f6(A, B, C) -> Com_1(f9(A, D, C)) :|: A >= 1
f6(A, B, C) -> Com_1(f17(0, B, C)) :|: A >= 0 && A <= 0
f17(A, B, C) -> Com_1(f24(A, B, C)) :|: 0 >= C
f17(A, B, C) -> Com_1(f24(A, B, C)) :|: C >= 2
f17(A, B, C) -> Com_1(f24(A, B, 0)) :|: C >= 1 && C <= 1
f9(A, B, C) -> Com_1(f17(A, 0, 1)) :|: B >= 0 && B <= 0
f9(A, B, C) -> Com_1(f6(D, B, C)) :|: 0 >= B + 1
f9(A, B, C) -> Com_1(f6(D, B, C)) :|: B >= 1
f0(A, B, C) -> Com_1(f6(D, B, 0)) :|: TRUE

The start-symbols are:[f0_3]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f6 -> f9 : B'=free, [ 0>=1+A ], cost: 1

      1: f6 -> f9 : B'=free_1, [ A>=1 ], cost: 1

      2: f6 -> f17 : A'=0, [ A==0 ], cost: 1

      3: f17 -> f24 : [ 0>=C ], cost: 1

      4: f17 -> f24 : [ C>=2 ], cost: 1

      5: f17 -> f24 : C'=0, [ C==1 ], cost: 1

      6: f9 -> f17 : B'=0, C'=1, [ B==0 ], cost: 1

      7: f9 -> f6 : A'=free_2, [ 0>=1+B ], cost: 1

      8: f9 -> f6 : A'=free_3, [ B>=1 ], cost: 1

      9: f0 -> f6 : A'=free_4, C'=0, [], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f6 -> f9 : B'=free, [ 0>=1+A ], cost: 1

      1: f6 -> f9 : B'=free_1, [ A>=1 ], cost: 1

      7: f9 -> f6 : A'=free_2, [ 0>=1+B ], cost: 1

      8: f9 -> f6 : A'=free_3, [ B>=1 ], cost: 1

      9: f0 -> f6 : A'=free_4, C'=0, [], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on tree-shaped paths):

   Start location: f0

     10: f6 -> f6 : A'=free_2, B'=free, [ 0>=1+A && 0>=1+free ], cost: 2

     11: f6 -> f6 : A'=free_3, B'=free, [ 0>=1+A && free>=1 ], cost: 2

     12: f6 -> f6 : A'=free_2, B'=free_1, [ A>=1 && 0>=1+free_1 ], cost: 2

     13: f6 -> f6 : A'=free_3, B'=free_1, [ A>=1 && free_1>=1 ], cost: 2

      9: f0 -> f6 : A'=free_4, C'=0, [], cost: 1



Accelerating simple loops of location 0.

   Accelerating the following rules:

     10: f6 -> f6 : A'=free_2, B'=free, [ 0>=1+A && 0>=1+free ], cost: 2

     11: f6 -> f6 : A'=free_3, B'=free, [ 0>=1+A && free>=1 ], cost: 2

     12: f6 -> f6 : A'=free_2, B'=free_1, [ A>=1 && 0>=1+free_1 ], cost: 2

     13: f6 -> f6 : A'=free_3, B'=free_1, [ A>=1 && free_1>=1 ], cost: 2



   Accelerated rule 10 with NONTERM (after strengthening guard), yielding the new rule 14.

   Accelerated rule 11 with NONTERM (after strengthening guard), yielding the new rule 15.

   Accelerated rule 12 with NONTERM (after strengthening guard), yielding the new rule 16.

   Accelerated rule 13 with NONTERM (after strengthening guard), yielding the new rule 17.

   Removing the simple loops:.



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

   Start location: f0

     10: f6 -> f6 : A'=free_2, B'=free, [ 0>=1+A && 0>=1+free ], cost: 2

     11: f6 -> f6 : A'=free_3, B'=free, [ 0>=1+A && free>=1 ], cost: 2

     12: f6 -> f6 : A'=free_2, B'=free_1, [ A>=1 && 0>=1+free_1 ], cost: 2

     13: f6 -> f6 : A'=free_3, B'=free_1, [ A>=1 && free_1>=1 ], cost: 2

     14: f6 -> [5] : [ 0>=1+A && 0>=1+free && 0>=1+free_2 ], cost: INF

     15: f6 -> [5] : [ 0>=1+A && free>=1 && 0>=1+free_3 ], cost: INF

     16: f6 -> [5] : [ A>=1 && 0>=1+free_1 && free_2>=1 ], cost: INF

     17: f6 -> [5] : [ A>=1 && free_1>=1 && free_3>=1 ], cost: INF

      9: f0 -> f6 : A'=free_4, C'=0, [], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f0

      9: f0 -> f6 : A'=free_4, C'=0, [], cost: 1

     18: f0 -> f6 : A'=free_2, B'=free, C'=0, [ 0>=1+free ], cost: 3

     19: f0 -> f6 : A'=free_3, B'=free, C'=0, [ free>=1 ], cost: 3

     20: f0 -> f6 : A'=free_2, B'=free_1, C'=0, [ 0>=1+free_1 ], cost: 3

     21: f0 -> f6 : A'=free_3, B'=free_1, C'=0, [ free_1>=1 ], cost: 3

     22: f0 -> [5] : A'=free_4, C'=0, [ 0>=1+free_4 ], cost: INF

     23: f0 -> [5] : A'=free_4, C'=0, [ 0>=1+free_4 ], cost: INF

     24: f0 -> [5] : A'=free_4, C'=0, [ free_4>=1 ], cost: INF

     25: f0 -> [5] : A'=free_4, C'=0, [ free_4>=1 ], cost: INF



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

   Start location: f0

     22: f0 -> [5] : A'=free_4, C'=0, [ 0>=1+free_4 ], cost: INF

     23: f0 -> [5] : A'=free_4, C'=0, [ 0>=1+free_4 ], cost: INF

     24: f0 -> [5] : A'=free_4, C'=0, [ free_4>=1 ], cost: INF

     25: f0 -> [5] : A'=free_4, C'=0, [ free_4>=1 ], cost: INF



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

     23: f0 -> [5] : A'=free_4, C'=0, [ 0>=1+free_4 ], cost: INF

     25: f0 -> [5] : A'=free_4, C'=0, [ free_4>=1 ], cost: INF



Computing asymptotic complexity for rule 23

   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:  [ 0>=1+free_4 ]



NO


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(2)
BOUNDS(INF, INF)