/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 115 ms]
(2) BOUNDS(INF, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A) -> Com_1(f1(B)) :|: B >= 2
f1(A) -> Com_1(f1(B)) :|: 1 >= B && B + 1 >= 0 && C >= 2

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 -> f1 : A'=free, [ free>=2 ], cost: 1

      1: f1 -> f1 : A'=free_2, [ 1>=free_2 && 1+free_2>=0 && free_1>=2 ], cost: 1



Simplified all rules, resulting in:

   Start location: f0

      0: f0 -> f1 : A'=free, [ free>=2 ], cost: 1

      1: f1 -> f1 : A'=free_2, [ 1>=free_2 && 1+free_2>=0 ], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 1.

   Accelerating the following rules:

      1: f1 -> f1 : A'=free_2, [ 1>=free_2 && 1+free_2>=0 ], cost: 1



   Accelerated rule 1 with NONTERM, yielding the new rule 2.

   Removing the simple loops: 1.



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

   Start location: f0

      0: f0 -> f1 : A'=free, [ free>=2 ], cost: 1

      2: f1 -> [2] : [ 1>=free_2 && 1+free_2>=0 ], cost: INF



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f0 -> f1 : A'=free, [ free>=2 ], cost: 1

      3: f0 -> [2] : A'=free, [ free>=2 ], cost: INF



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

   Start location: f0

      3: f0 -> [2] : A'=free, [ free>=2 ], cost: INF



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

      3: f0 -> [2] : A'=free, [ free>=2 ], cost: INF



Computing asymptotic complexity for rule 3

   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:  [ free>=2 ]



NO


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(2)
BOUNDS(INF, INF)