/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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)


----------------------------------------

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f2(A, B, C) -> Com_1(f2(A + 1, B, C)) :|: TRUE
f3(A, B, C) -> Com_1(f3(A, B - 1, C)) :|: B >= 1
f5(A, B, C) -> Com_1(f5(A, B, 1)) :|: TRUE
f0(A, B, C) -> Com_1(f2(0, B, C)) :|: C >= 1
f0(A, B, C) -> Com_1(f3(0, B, C)) :|: 0 >= C
f3(A, B, C) -> Com_1(f5(0, B, C)) :|: 0 >= B

The start-symbols are:[f0_3]


----------------------------------------

(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f2 -> f2 : A'=1+A, [], cost: 1

      1: f3 -> f3 : B'=-1+B, [ B>=1 ], cost: 1

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

      2: f5 -> f5 : C'=1, [], cost: 1

      3: f0 -> f2 : A'=0, [ C>=1 ], cost: 1

      4: f0 -> f3 : A'=0, [ 0>=C ], cost: 1



Checking for constant complexity:

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

      3: f0 -> f2 : A'=0, [ C>=1 ], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 0.

   Accelerating the following rules:

      0: f2 -> f2 : A'=1+A, [], cost: 1



   Accelerated rule 0 with NONTERM, yielding the new rule 6.

   Removing the simple loops: 0.



Accelerating simple loops of location 1.

   Accelerating the following rules:

      1: f3 -> f3 : B'=-1+B, [ B>=1 ], cost: 1



   Accelerated rule 1 with metering function B, yielding the new rule 7.

   Removing the simple loops: 1.



Accelerating simple loops of location 2.

   Accelerating the following rules:

      2: f5 -> f5 : C'=1, [], 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

      6: f2 -> [4] : [], cost: NONTERM

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

      7: f3 -> f3 : B'=0, [ B>=1 ], cost: B

      8: f5 -> [6] : [], cost: NONTERM

      3: f0 -> f2 : A'=0, [ C>=1 ], cost: 1

      4: f0 -> f3 : A'=0, [ 0>=C ], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f0

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

     11: f3 -> [6] : A'=0, [ 0>=B ], cost: NONTERM

      3: f0 -> f2 : A'=0, [ C>=1 ], cost: 1

      4: f0 -> f3 : A'=0, [ 0>=C ], cost: 1

      9: f0 -> [4] : A'=0, [ C>=1 ], cost: NONTERM

     10: f0 -> f3 : A'=0, B'=0, [ 0>=C && B>=1 ], cost: 1+B



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

   Start location: f0

     11: f3 -> [6] : A'=0, [ 0>=B ], cost: NONTERM

      4: f0 -> f3 : A'=0, [ 0>=C ], cost: 1

      9: f0 -> [4] : A'=0, [ C>=1 ], cost: NONTERM

     10: f0 -> f3 : A'=0, B'=0, [ 0>=C && B>=1 ], cost: 1+B



Eliminated locations (on tree-shaped paths):

   Start location: f0

      9: f0 -> [4] : A'=0, [ C>=1 ], cost: NONTERM

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

     13: f0 -> [6] : A'=0, B'=0, [ 0>=C && B>=1 ], cost: NONTERM



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

      9: f0 -> [4] : A'=0, [ C>=1 ], cost: NONTERM

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

     13: f0 -> [6] : A'=0, B'=0, [ 0>=C && B>=1 ], cost: NONTERM



Computing asymptotic complexity for rule 9

   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:  [ C>=1 ]



NO


----------------------------------------

(2)
BOUNDS(INF, INF)