/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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MAYBE
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(1, INF).

(0) CpxIntTrs
(1) Loat Proof [FINISHED, 530 ms]
(2) BOUNDS(1, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A, B, C, D, E, F) -> Com_1(f0(-(A), B + A, C + A, D, E, F)) :|: 0 >= A + 1
f0(A, B, C, D, E, F) -> Com_1(f0(A + B, -(B), C, D + B, E, F)) :|: 0 >= B + 1
f0(A, B, C, D, E, F) -> Com_1(f0(A, B + D, C, -(D), E + D, F)) :|: 0 >= D + 1
f0(A, B, C, D, E, F) -> Com_1(f0(A, B, C + E, D + E, -(E), F)) :|: 0 >= E + 1
f0(A, B, C, D, E, F) -> Com_1(f0(A + C, B, -(C), D, E + C, F)) :|: 0 >= C + 1
f1(A, B, C, D, E, F) -> Com_1(f0(G, H, K, I, J, G + H + I + J + K)) :|: G + H + I + J + K >= 1

The start-symbols are:[f1_6]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f1

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

      1: f0 -> f0 : A'=A+B, B'=-B, D'=D+B, [ 0>=1+B ], cost: 1

      2: f0 -> f0 : B'=D+B, D'=-D, E'=D+E, [ 0>=1+D ], cost: 1

      3: f0 -> f0 : C'=C+E, D'=D+E, E'=-E, [ 0>=1+E ], cost: 1

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

      5: f1 -> f0 : A'=free_2, B'=free_4, C'=free_3, D'=free, E'=free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 ], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 0.

   Accelerating the following rules:

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

      1: f0 -> f0 : A'=A+B, B'=-B, D'=D+B, [ 0>=1+B ], cost: 1

      2: f0 -> f0 : B'=D+B, D'=-D, E'=D+E, [ 0>=1+D ], cost: 1

      3: f0 -> f0 : C'=C+E, D'=D+E, E'=-E, [ 0>=1+E ], cost: 1

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



   Found no metering function for rule 0.

   Found no metering function for rule 1.

   Found no metering function for rule 2.

   Found no metering function for rule 3.

   Found no metering function for rule 4.

   Removing the simple loops:.



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

   Start location: f1

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

      1: f0 -> f0 : A'=A+B, B'=-B, D'=D+B, [ 0>=1+B ], cost: 1

      2: f0 -> f0 : B'=D+B, D'=-D, E'=D+E, [ 0>=1+D ], cost: 1

      3: f0 -> f0 : C'=C+E, D'=D+E, E'=-E, [ 0>=1+E ], cost: 1

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

      5: f1 -> f0 : A'=free_2, B'=free_4, C'=free_3, D'=free, E'=free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 ], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f1

      5: f1 -> f0 : A'=free_2, B'=free_4, C'=free_3, D'=free, E'=free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 ], cost: 1

      6: f1 -> f0 : A'=-free_2, B'=free_4+free_2, C'=free_2+free_3, D'=free, E'=free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 && 0>=1+free_2 ], cost: 2

      7: f1 -> f0 : A'=free_4+free_2, B'=-free_4, C'=free_3, D'=free+free_4, E'=free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 && 0>=1+free_4 ], cost: 2

      8: f1 -> f0 : A'=free_2, B'=free+free_4, C'=free_3, D'=-free, E'=free+free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 && 0>=1+free ], cost: 2

      9: f1 -> f0 : A'=free_2, B'=free_4, C'=free_1+free_3, D'=free+free_1, E'=-free_1, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 && 0>=1+free_1 ], cost: 2

     10: f1 -> f0 : A'=free_2+free_3, B'=free_4, C'=-free_3, D'=free, E'=free_1+free_3, F'=free+free_4+free_1+free_2+free_3, [ free+free_4+free_1+free_2+free_3>=1 && 0>=1+free_3 ], cost: 2



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

   Start location: f1



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f1



Obtained the following overall complexity (w.r.t. the length of the input n):

   Complexity:  Unknown

   Cpx degree:  ?

   Solved cost: 0

   Rule cost:   0

   Rule guard:  []



WORST_CASE(Omega(0),?)


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(2)
BOUNDS(1, INF)