/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 335 ms]
(2) BOUNDS(INF, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f4(A, B, C, D, E) -> Com_1(f5(A, 1, C, D, E)) :|: A >= 2
f4(A, B, C, D, E) -> Com_1(f5(A, 0, C, D, E)) :|: 1 >= A
f30(A, B, C, D, E) -> Com_1(f4(2, B, 2, F, E)) :|: TRUE
f5(A, B, C, D, E) -> Com_1(f4(A - 1, B, C, F, E)) :|: 0 >= F && F >= 1
f5(A, B, C, D, E) -> Com_1(f4(A + 1, B, C, F, E)) :|: F >= 1
f5(A, B, C, D, E) -> Com_1(f3(A, B, C, D, 0)) :|: 0 >= B

The start-symbols are:[f30_5]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f30

      0: f4 -> f5 : B'=1, [ A>=2 ], cost: 1

      1: f4 -> f5 : B'=0, [ 1>=A ], cost: 1

      2: f30 -> f4 : A'=2, C'=2, D'=free, [], cost: 1

      3: f5 -> f4 : A'=-1+A, D'=free_1, [ 0>=free_1 && free_1>=1 ], cost: 1

      4: f5 -> f4 : A'=1+A, D'=free_2, [ free_2>=1 ], cost: 1

      5: f5 -> f3 : E'=0, [ 0>=B ], cost: 1



Checking for constant complexity:

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

      2: f30 -> f4 : A'=2, C'=2, D'=free, [], cost: 1



Removed unreachable and leaf rules:

   Start location: f30

      0: f4 -> f5 : B'=1, [ A>=2 ], cost: 1

      1: f4 -> f5 : B'=0, [ 1>=A ], cost: 1

      2: f30 -> f4 : A'=2, C'=2, D'=free, [], cost: 1

      3: f5 -> f4 : A'=-1+A, D'=free_1, [ 0>=free_1 && free_1>=1 ], cost: 1

      4: f5 -> f4 : A'=1+A, D'=free_2, [ free_2>=1 ], cost: 1



Removed rules with unsatisfiable guard:

   Start location: f30

      0: f4 -> f5 : B'=1, [ A>=2 ], cost: 1

      1: f4 -> f5 : B'=0, [ 1>=A ], cost: 1

      2: f30 -> f4 : A'=2, C'=2, D'=free, [], cost: 1

      4: f5 -> f4 : A'=1+A, D'=free_2, [ free_2>=1 ], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on tree-shaped paths):

   Start location: f30

      6: f4 -> f4 : A'=1+A, B'=1, D'=free_2, [ A>=2 && free_2>=1 ], cost: 2

      7: f4 -> f4 : A'=1+A, B'=0, D'=free_2, [ 1>=A && free_2>=1 ], cost: 2

      2: f30 -> f4 : A'=2, C'=2, D'=free, [], cost: 1



Accelerating simple loops of location 0.

   Accelerating the following rules:

      6: f4 -> f4 : A'=1+A, B'=1, D'=free_2, [ A>=2 && free_2>=1 ], cost: 2

      7: f4 -> f4 : A'=1+A, B'=0, D'=free_2, [ 1>=A && free_2>=1 ], cost: 2



   Accelerated rule 6 with NONTERM, yielding the new rule 8.

   Accelerated rule 7 with metering function 2-A, yielding the new rule 9.

   Removing the simple loops: 6 7.



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

   Start location: f30

      8: f4 -> [4] : [ A>=2 && free_2>=1 ], cost: NONTERM

      9: f4 -> f4 : A'=2, B'=0, D'=free_2, [ 1>=A && free_2>=1 ], cost: 4-2*A

      2: f30 -> f4 : A'=2, C'=2, D'=free, [], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f30

      2: f30 -> f4 : A'=2, C'=2, D'=free, [], cost: 1

     10: f30 -> [4] : A'=2, C'=2, D'=free, [], cost: NONTERM



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

   Start location: f30

     10: f30 -> [4] : A'=2, C'=2, D'=free, [], cost: NONTERM



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f30

     10: f30 -> [4] : A'=2, C'=2, D'=free, [], 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:  []



NO


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(2)
BOUNDS(INF, INF)