/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 222 ms]
(2) BOUNDS(INF, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A, B, C, D) -> Com_1(f14(E, E, 0, D)) :|: 0 >= E
f0(A, B, C, D) -> Com_1(f14(E, E, 0, D)) :|: E >= 1024
f0(A, B, C, D) -> Com_1(f14(E, E, 0, F)) :|: 1023 >= E && E >= 1
f14(A, B, C, D) -> Com_1(f14(A, B, C + 1, D)) :|: E >= C + 1
f14(A, B, C, D) -> Com_1(f22(A, B, C, D)) :|: C >= E

The start-symbols are:[f0_4]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f0 -> f14 : A'=free, B'=free, C'=0, [ 0>=free ], cost: 1

      1: f0 -> f14 : A'=free_1, B'=free_1, C'=0, [ free_1>=1024 ], cost: 1

      2: f0 -> f14 : A'=free_3, B'=free_3, C'=0, D'=free_2, [ 1023>=free_3 && free_3>=1 ], cost: 1

      3: f14 -> f14 : C'=1+C, [ free_4>=1+C ], cost: 1

      4: f14 -> f22 : [ C>=free_5 ], cost: 1



Checking for constant complexity:

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

      0: f0 -> f14 : A'=free, B'=free, C'=0, [ 0>=free ], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f0 -> f14 : A'=free, B'=free, C'=0, [ 0>=free ], cost: 1

      1: f0 -> f14 : A'=free_1, B'=free_1, C'=0, [ free_1>=1024 ], cost: 1

      2: f0 -> f14 : A'=free_3, B'=free_3, C'=0, D'=free_2, [ 1023>=free_3 && free_3>=1 ], cost: 1

      3: f14 -> f14 : C'=1+C, [ free_4>=1+C ], cost: 1



Simplified all rules, resulting in:

   Start location: f0

      0: f0 -> f14 : A'=free, B'=free, C'=0, [ 0>=free ], cost: 1

      1: f0 -> f14 : A'=free_1, B'=free_1, C'=0, [ free_1>=1024 ], cost: 1

      2: f0 -> f14 : A'=free_3, B'=free_3, C'=0, D'=free_2, [ 1023>=free_3 && free_3>=1 ], cost: 1

      3: f14 -> f14 : C'=1+C, [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 1.

   Accelerating the following rules:

      3: f14 -> f14 : C'=1+C, [], cost: 1



   Accelerated rule 3 with NONTERM, yielding the new rule 5.

   Removing the simple loops: 3.



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

   Start location: f0

      0: f0 -> f14 : A'=free, B'=free, C'=0, [ 0>=free ], cost: 1

      1: f0 -> f14 : A'=free_1, B'=free_1, C'=0, [ free_1>=1024 ], cost: 1

      2: f0 -> f14 : A'=free_3, B'=free_3, C'=0, D'=free_2, [ 1023>=free_3 && free_3>=1 ], cost: 1

      5: f14 -> [3] : [], cost: NONTERM



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f0 -> f14 : A'=free, B'=free, C'=0, [ 0>=free ], cost: 1

      1: f0 -> f14 : A'=free_1, B'=free_1, C'=0, [ free_1>=1024 ], cost: 1

      2: f0 -> f14 : A'=free_3, B'=free_3, C'=0, D'=free_2, [ 1023>=free_3 && free_3>=1 ], cost: 1

      6: f0 -> [3] : A'=free, B'=free, C'=0, [ 0>=free ], cost: NONTERM

      7: f0 -> [3] : A'=free_1, B'=free_1, C'=0, [ free_1>=1024 ], cost: NONTERM

      8: f0 -> [3] : A'=free_3, B'=free_3, C'=0, D'=free_2, [ 1023>=free_3 && free_3>=1 ], cost: NONTERM



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

   Start location: f0

      6: f0 -> [3] : A'=free, B'=free, C'=0, [ 0>=free ], cost: NONTERM

      7: f0 -> [3] : A'=free_1, B'=free_1, C'=0, [ free_1>=1024 ], cost: NONTERM

      8: f0 -> [3] : A'=free_3, B'=free_3, C'=0, D'=free_2, [ 1023>=free_3 && free_3>=1 ], cost: NONTERM



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

      6: f0 -> [3] : A'=free, B'=free, C'=0, [ 0>=free ], cost: NONTERM

      7: f0 -> [3] : A'=free_1, B'=free_1, C'=0, [ free_1>=1024 ], cost: NONTERM

      8: f0 -> [3] : A'=free_3, B'=free_3, C'=0, D'=free_2, [ 1023>=free_3 && free_3>=1 ], cost: NONTERM



Computing asymptotic complexity for rule 6

   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 ]



NO


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(2)
BOUNDS(INF, INF)