/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, B) -> Com_1(f1(A, A)) :|: A >= B && A <= B
f1(A, B) -> Com_1(f1(A + 1, B + 1)) :|: TRUE
f1(A, B) -> Com_1(f2(A, B)) :|: TRUE
f1(A, B) -> Com_1(f10000(A, B)) :|: A >= B + 1

The start-symbols are:[f0_2]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

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

      1: f1 -> f1 : A'=1+A, B'=1+B, [], cost: 1

      2: f1 -> f2 : [], cost: 1

      3: f1 -> f10000 : [ A>=1+B ], cost: 1



Checking for constant complexity:

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

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



Removed unreachable and leaf rules:

   Start location: f0

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

      1: f1 -> f1 : A'=1+A, B'=1+B, [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 1.

   Accelerating the following rules:

      1: f1 -> f1 : A'=1+A, B'=1+B, [], cost: 1



   Accelerated rule 1 with NONTERM, yielding the new rule 4.

   Removing the simple loops: 1.



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

   Start location: f0

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

      4: f1 -> [4] : [], cost: NONTERM



Chained accelerated rules (with incoming rules):

   Start location: f0

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

      5: f0 -> [4] : B'=A, [ A==B ], cost: NONTERM



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

   Start location: f0

      5: f0 -> [4] : B'=A, [ A==B ], cost: NONTERM



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

      5: f0 -> [4] : B'=A, [ A==B ], cost: NONTERM



Computing asymptotic complexity for rule 5

   Guard is satisfiable, yielding nontermination

   Resulting cost NONTERM 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: NONTERM

   Rule cost:   NONTERM

   Rule guard:  [ A==B ]



NO


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(2)
BOUNDS(INF, INF)