/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 319 ms]
(2) BOUNDS(INF, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f10(A, B, C, D, E) -> Com_1(f16(A, 0, F, D, E)) :|: 0 >= A && F >= 1
f16(A, B, C, D, E) -> Com_1(f16(A, B, C, D, E)) :|: C >= 1
f25(A, B, C, D, E) -> Com_1(f25(A, B, C, D, E)) :|: TRUE
f27(A, B, C, D, E) -> Com_1(f30(A, B, C, D, E)) :|: TRUE
f16(A, B, C, D, E) -> Com_1(f10(F, B, C, 0, F)) :|: 0 >= C
f10(A, B, C, D, E) -> Com_1(f25(A, B, C, D, E)) :|: A >= 1
f0(A, B, C, D, E) -> Com_1(f10(F, 0, C, 0, F)) :|: TRUE

The start-symbols are:[f0_5]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f10 -> f16 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1

      5: f10 -> f25 : [ A>=1 ], cost: 1

      1: f16 -> f16 : [ C>=1 ], cost: 1

      4: f16 -> f10 : A'=free_1, D'=0, E'=free_1, [ 0>=C ], cost: 1

      2: f25 -> f25 : [], cost: 1

      3: f27 -> f30 : [], cost: 1

      6: f0 -> f10 : A'=free_2, B'=0, D'=0, E'=free_2, [], cost: 1



Checking for constant complexity:

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

      6: f0 -> f10 : A'=free_2, B'=0, D'=0, E'=free_2, [], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f10 -> f16 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1

      5: f10 -> f25 : [ A>=1 ], cost: 1

      1: f16 -> f16 : [ C>=1 ], cost: 1

      4: f16 -> f10 : A'=free_1, D'=0, E'=free_1, [ 0>=C ], cost: 1

      2: f25 -> f25 : [], cost: 1

      6: f0 -> f10 : A'=free_2, B'=0, D'=0, E'=free_2, [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 1.

   Accelerating the following rules:

      1: f16 -> f16 : [ C>=1 ], cost: 1



   Accelerated rule 1 with NONTERM, yielding the new rule 7.

   Removing the simple loops: 1.



Accelerating simple loops of location 2.

   Accelerating the following rules:

      2: f25 -> f25 : [], cost: 1



   Accelerated rule 2 with NONTERM, yielding the new rule 8.

   Removing the simple loops: 2.



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

   Start location: f0

      0: f10 -> f16 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1

      5: f10 -> f25 : [ A>=1 ], cost: 1

      4: f16 -> f10 : A'=free_1, D'=0, E'=free_1, [ 0>=C ], cost: 1

      7: f16 -> [6] : [ C>=1 ], cost: NONTERM

      8: f25 -> [7] : [], cost: NONTERM

      6: f0 -> f10 : A'=free_2, B'=0, D'=0, E'=free_2, [], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f10 -> f16 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1

      5: f10 -> f25 : [ A>=1 ], cost: 1

      9: f10 -> [6] : B'=0, C'=free, [ 0>=A && free>=1 ], cost: NONTERM

     10: f10 -> [7] : [ A>=1 ], cost: NONTERM

      4: f16 -> f10 : A'=free_1, D'=0, E'=free_1, [ 0>=C ], cost: 1

      6: f0 -> f10 : A'=free_2, B'=0, D'=0, E'=free_2, [], cost: 1



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

   Start location: f0

      0: f10 -> f16 : B'=0, C'=free, [ 0>=A && free>=1 ], cost: 1

      9: f10 -> [6] : B'=0, C'=free, [ 0>=A && free>=1 ], cost: NONTERM

     10: f10 -> [7] : [ A>=1 ], cost: NONTERM

      4: f16 -> f10 : A'=free_1, D'=0, E'=free_1, [ 0>=C ], cost: 1

      6: f0 -> f10 : A'=free_2, B'=0, D'=0, E'=free_2, [], cost: 1



Eliminated locations (on linear paths):

   Start location: f0

      9: f10 -> [6] : B'=0, C'=free, [ 0>=A && free>=1 ], cost: NONTERM

     10: f10 -> [7] : [ A>=1 ], cost: NONTERM

      6: f0 -> f10 : A'=free_2, B'=0, D'=0, E'=free_2, [], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: f0

     11: f0 -> [6] : A'=free_2, B'=0, C'=free, D'=0, E'=free_2, [ 0>=free_2 && free>=1 ], cost: NONTERM

     12: f0 -> [7] : A'=free_2, B'=0, D'=0, E'=free_2, [ free_2>=1 ], cost: NONTERM



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

     11: f0 -> [6] : A'=free_2, B'=0, C'=free, D'=0, E'=free_2, [ 0>=free_2 && free>=1 ], cost: NONTERM

     12: f0 -> [7] : A'=free_2, B'=0, D'=0, E'=free_2, [ free_2>=1 ], cost: NONTERM



Computing asymptotic complexity for rule 11

   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:  [ 0>=free_2 && free>=1 ]



NO


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(2)
BOUNDS(INF, INF)