/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).

(0) CpxIntTrs
(1) Loat Proof [FINISHED, 425 ms]
(2) BOUNDS(INF, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A, B, C, D, E) -> Com_1(f9(F, F, F, 0, E)) :|: TRUE
f9(A, B, C, D, E) -> Com_1(f9(A, B, C, D + 1, F)) :|: C >= D + 1
f24(A, B, C, D, E) -> Com_1(f24(A, B, C, D, E)) :|: 0 >= F + 1
f24(A, B, C, D, E) -> Com_1(f24(A, B, C, D, E)) :|: TRUE
f37(A, B, C, D, E) -> Com_1(f37(A, B, C, D, E)) :|: F >= G + 1
f37(A, B, C, D, E) -> Com_1(f37(A, B, C, D, E)) :|: TRUE
f37(A, B, C, D, E) -> Com_1(f48(A, B, C, D, E)) :|: TRUE
f24(A, B, C, D, E) -> Com_1(f37(A, B, C, D, E)) :|: TRUE
f9(A, B, C, D, E) -> Com_1(f24(A, B, C, D, E)) :|: D >= C

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: f0 -> f9 : A'=free, B'=free, C'=free, D'=0, [], cost: 1

      1: f9 -> f9 : D'=1+D, E'=free_1, [ C>=1+D ], cost: 1

      8: f9 -> f24 : [ D>=C ], cost: 1

      2: f24 -> f24 : [ 0>=1+free_2 ], cost: 1

      3: f24 -> f24 : [], cost: 1

      7: f24 -> f37 : [], cost: 1

      4: f37 -> f37 : [ free_3>=1+free_4 ], cost: 1

      5: f37 -> f37 : [], cost: 1

      6: f37 -> f48 : [], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f0 -> f9 : A'=free, B'=free, C'=free, D'=0, [], cost: 1

      1: f9 -> f9 : D'=1+D, E'=free_1, [ C>=1+D ], cost: 1

      8: f9 -> f24 : [ D>=C ], cost: 1

      2: f24 -> f24 : [ 0>=1+free_2 ], cost: 1

      3: f24 -> f24 : [], cost: 1

      7: f24 -> f37 : [], cost: 1

      4: f37 -> f37 : [ free_3>=1+free_4 ], cost: 1

      5: f37 -> f37 : [], cost: 1



Simplified all rules, resulting in:

   Start location: f0

      0: f0 -> f9 : A'=free, B'=free, C'=free, D'=0, [], cost: 1

      1: f9 -> f9 : D'=1+D, E'=free_1, [ C>=1+D ], cost: 1

      8: f9 -> f24 : [ D>=C ], cost: 1

      3: f24 -> f24 : [], cost: 1

      7: f24 -> f37 : [], cost: 1

      5: f37 -> f37 : [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 1.

   Accelerating the following rules:

      1: f9 -> f9 : D'=1+D, E'=free_1, [ C>=1+D ], cost: 1



   Accelerated rule 1 with metering function C-D, yielding the new rule 9.

   Removing the simple loops: 1.



Accelerating simple loops of location 2.

   Accelerating the following rules:

      3: f24 -> f24 : [], cost: 1



   Accelerated rule 3 with NONTERM, yielding the new rule 10.

   Removing the simple loops: 3.



Accelerating simple loops of location 3.

   Accelerating the following rules:

      5: f37 -> f37 : [], cost: 1



   Accelerated rule 5 with NONTERM, yielding the new rule 11.

   Removing the simple loops: 5.



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

   Start location: f0

      0: f0 -> f9 : A'=free, B'=free, C'=free, D'=0, [], cost: 1

      8: f9 -> f24 : [ D>=C ], cost: 1

      9: f9 -> f9 : D'=C, E'=free_1, [ C>=1+D ], cost: C-D

      7: f24 -> f37 : [], cost: 1

     10: f24 -> [6] : [], cost: INF

     11: f37 -> [7] : [], cost: INF



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f0 -> f9 : A'=free, B'=free, C'=free, D'=0, [], cost: 1

     12: f0 -> f9 : A'=free, B'=free, C'=free, D'=free, E'=free_1, [ free>=1 ], cost: 1+free

      8: f9 -> f24 : [ D>=C ], cost: 1

     13: f9 -> [6] : [ D>=C ], cost: INF

      7: f24 -> f37 : [], cost: 1

     14: f24 -> [7] : [], cost: INF



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

   Start location: f0

      0: f0 -> f9 : A'=free, B'=free, C'=free, D'=0, [], cost: 1

     12: f0 -> f9 : A'=free, B'=free, C'=free, D'=free, E'=free_1, [ free>=1 ], cost: 1+free

      8: f9 -> f24 : [ D>=C ], cost: 1

     13: f9 -> [6] : [ D>=C ], cost: INF

     14: f24 -> [7] : [], cost: INF



Eliminated locations (on linear paths):

   Start location: f0

      0: f0 -> f9 : A'=free, B'=free, C'=free, D'=0, [], cost: 1

     12: f0 -> f9 : A'=free, B'=free, C'=free, D'=free, E'=free_1, [ free>=1 ], cost: 1+free

     13: f9 -> [6] : [ D>=C ], cost: INF

     15: f9 -> [7] : [ D>=C ], cost: INF



Eliminated locations (on tree-shaped paths):

   Start location: f0

     16: f0 -> [6] : A'=free, B'=free, C'=free, D'=0, [ 0>=free ], cost: INF

     17: f0 -> [7] : A'=free, B'=free, C'=free, D'=0, [ 0>=free ], cost: INF

     18: f0 -> [6] : A'=free, B'=free, C'=free, D'=free, E'=free_1, [ free>=1 ], cost: INF

     19: f0 -> [7] : A'=free, B'=free, C'=free, D'=free, E'=free_1, [ free>=1 ], cost: INF



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

     17: f0 -> [7] : A'=free, B'=free, C'=free, D'=0, [ 0>=free ], cost: INF

     19: f0 -> [7] : A'=free, B'=free, C'=free, D'=free, E'=free_1, [ free>=1 ], cost: INF



Computing asymptotic complexity for rule 17

   Resulting cost INF 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: INF

   Rule cost:   INF

   Rule guard:  [ 0>=free ]



NO


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(2)
BOUNDS(INF, INF)