/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 217 ms]
(2) BOUNDS(INF, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A, B, C) -> Com_1(f15(2, B, C)) :|: TRUE
f15(A, B, C) -> Com_1(f18(A, A, C)) :|: 10 >= A
f18(A, B, C) -> Com_1(f18(A, B - 1, F)) :|: D >= E + 1
f18(A, B, C) -> Com_1(f15(A + 1, B, C)) :|: TRUE
f15(A, B, C) -> Com_1(f28(A, B, C)) :|: A >= 11

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: f0 -> f15 : A'=2, [], cost: 1

      1: f15 -> f18 : B'=A, [ 10>=A ], cost: 1

      4: f15 -> f28 : [ A>=11 ], cost: 1

      2: f18 -> f18 : B'=-1+B, C'=free, [ free_1>=1+free_2 ], cost: 1

      3: f18 -> f15 : A'=1+A, [], cost: 1



Checking for constant complexity:

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

      0: f0 -> f15 : A'=2, [], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f0 -> f15 : A'=2, [], cost: 1

      1: f15 -> f18 : B'=A, [ 10>=A ], cost: 1

      2: f18 -> f18 : B'=-1+B, C'=free, [ free_1>=1+free_2 ], cost: 1

      3: f18 -> f15 : A'=1+A, [], cost: 1



Simplified all rules, resulting in:

   Start location: f0

      0: f0 -> f15 : A'=2, [], cost: 1

      1: f15 -> f18 : B'=A, [ 10>=A ], cost: 1

      2: f18 -> f18 : B'=-1+B, C'=free, [], cost: 1

      3: f18 -> f15 : A'=1+A, [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 2.

   Accelerating the following rules:

      2: f18 -> f18 : B'=-1+B, C'=free, [], cost: 1



   Accelerated rule 2 with NONTERM, yielding the new rule 5.

   Removing the simple loops: 2.



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

   Start location: f0

      0: f0 -> f15 : A'=2, [], cost: 1

      1: f15 -> f18 : B'=A, [ 10>=A ], cost: 1

      3: f18 -> f15 : A'=1+A, [], cost: 1

      5: f18 -> [4] : [], cost: NONTERM



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f0 -> f15 : A'=2, [], cost: 1

      1: f15 -> f18 : B'=A, [ 10>=A ], cost: 1

      6: f15 -> [4] : B'=A, [ 10>=A ], cost: NONTERM

      3: f18 -> f15 : A'=1+A, [], cost: 1



Eliminated locations (on linear paths):

   Start location: f0

      0: f0 -> f15 : A'=2, [], cost: 1

      6: f15 -> [4] : B'=A, [ 10>=A ], cost: NONTERM

      7: f15 -> f15 : A'=1+A, B'=A, [ 10>=A ], cost: 2



Accelerating simple loops of location 1.

   Accelerating the following rules:

      7: f15 -> f15 : A'=1+A, B'=A, [ 10>=A ], cost: 2



   Accelerated rule 7 with metering function 11-A, yielding the new rule 8.

   Removing the simple loops: 7.



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

   Start location: f0

      0: f0 -> f15 : A'=2, [], cost: 1

      6: f15 -> [4] : B'=A, [ 10>=A ], cost: NONTERM

      8: f15 -> f15 : A'=11, B'=10, [ 10>=A ], cost: 22-2*A



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f0 -> f15 : A'=2, [], cost: 1

      9: f0 -> f15 : A'=11, B'=10, [], cost: 19

      6: f15 -> [4] : B'=A, [ 10>=A ], cost: NONTERM



Eliminated locations (on tree-shaped paths):

   Start location: f0

     10: f0 -> [4] : A'=2, B'=2, [], cost: NONTERM



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

     10: f0 -> [4] : A'=2, B'=2, [], 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)