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


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MAYBE
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(1, INF).

(0) CpxIntTrs
(1) Loat Proof [FINISHED, 214 ms]
(2) BOUNDS(1, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f4(A, B, C, D, E, F, G) -> Com_1(f4(A - B, B, C, D, E, F, G)) :|: A >= 0
f4(A, B, C, D, E, F, G) -> Com_1(f6(A, B, 0, 0, 0, 0, 0)) :|: 0 >= A + 1
f5(A, B, C, D, E, F, G) -> Com_1(f4(A, B, C, D, E, F, G)) :|: 0 >= B + 1
f5(A, B, C, D, E, F, G) -> Com_1(f6(A, B, 0, 0, 0, 0, 0)) :|: B >= 0

The start-symbols are:[f5_7]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f5

      0: f4 -> f4 : A'=A-B, [ A>=0 ], cost: 1

      1: f4 -> f6 : C'=0, D'=0, E'=0, F'=0, G'=0, [ 0>=1+A ], cost: 1

      2: f5 -> f4 : [ 0>=1+B ], cost: 1

      3: f5 -> f6 : C'=0, D'=0, E'=0, F'=0, G'=0, [ B>=0 ], cost: 1



Checking for constant complexity:

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

      2: f5 -> f4 : [ 0>=1+B ], cost: 1



Removed unreachable and leaf rules:

   Start location: f5

      0: f4 -> f4 : A'=A-B, [ A>=0 ], cost: 1

      2: f5 -> f4 : [ 0>=1+B ], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 0.

   Accelerating the following rules:

      0: f4 -> f4 : A'=A-B, [ A>=0 ], cost: 1



   Found no metering function for rule 0.

   Removing the simple loops:.



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

   Start location: f5

      0: f4 -> f4 : A'=A-B, [ A>=0 ], cost: 1

      2: f5 -> f4 : [ 0>=1+B ], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f5

      2: f5 -> f4 : [ 0>=1+B ], cost: 1

      4: f5 -> f4 : A'=A-B, [ 0>=1+B && A>=0 ], cost: 2



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

   Start location: f5

     <empty>



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f5

     <empty>



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

   Complexity:  Constant

   Cpx degree:  0

   Solved cost: 1

   Rule cost:   1

   Rule guard:  [ 0>=1+B ]



WORST_CASE(Omega(1),?)


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(2)
BOUNDS(1, INF)