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


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WORST_CASE(NON_POLY, ?)
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 132 ms]
(2) BOUNDS(INF, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A) -> Com_1(f2(A + 200)) :|: A + 99 >= 0
f0(A) -> Com_1(f2(A + 500)) :|: A >= 1
f2(A) -> Com_1(f2(A + 700)) :|: A + 199 >= 0

The start-symbols are:[f0_1]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f0 -> f2 : A'=200+A, [ 99+A>=0 ], cost: 1

      1: f0 -> f2 : A'=500+A, [ A>=1 ], cost: 1

      2: f2 -> f2 : A'=700+A, [ 199+A>=0 ], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 1.

   Accelerating the following rules:

      2: f2 -> f2 : A'=700+A, [ 199+A>=0 ], cost: 1



   Accelerated rule 2 with NONTERM, yielding the new rule 3.

   Removing the simple loops: 2.



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

   Start location: f0

      0: f0 -> f2 : A'=200+A, [ 99+A>=0 ], cost: 1

      1: f0 -> f2 : A'=500+A, [ A>=1 ], cost: 1

      3: f2 -> [2] : [ 199+A>=0 ], cost: INF



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f0 -> f2 : A'=200+A, [ 99+A>=0 ], cost: 1

      1: f0 -> f2 : A'=500+A, [ A>=1 ], cost: 1

      4: f0 -> [2] : A'=200+A, [ 99+A>=0 ], cost: INF

      5: f0 -> [2] : A'=500+A, [ A>=1 ], cost: INF



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

   Start location: f0

      4: f0 -> [2] : A'=200+A, [ 99+A>=0 ], cost: INF

      5: f0 -> [2] : A'=500+A, [ A>=1 ], cost: INF



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

      4: f0 -> [2] : A'=200+A, [ 99+A>=0 ], cost: INF

      5: f0 -> [2] : A'=500+A, [ A>=1 ], cost: INF



Computing asymptotic complexity for rule 4

   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:  [ 99+A>=0 ]



NO


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(2)
BOUNDS(INF, INF)