/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 437 ms]
(2) BOUNDS(1, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
evalgcdstart(A, B) -> Com_1(evalgcdentryin(A, B)) :|: TRUE
evalgcdentryin(A, B) -> Com_1(evalgcdreturnin(A, B)) :|: 0 >= A
evalgcdentryin(A, B) -> Com_1(evalgcdreturnin(A, B)) :|: 0 >= B
evalgcdentryin(A, B) -> Com_1(evalgcdbb7in(B, A)) :|: A >= 1 && B >= 1
evalgcdbb7in(A, B) -> Com_1(evalgcdbb4in(A, B)) :|: A >= B + 1
evalgcdbb7in(A, B) -> Com_1(evalgcdbb4in(A, B)) :|: B >= A + 1
evalgcdbb7in(A, B) -> Com_1(evalgcdreturnin(A, B)) :|: B >= A && B <= A
evalgcdbb4in(A, B) -> Com_1(evalgcdbb5in(A, B)) :|: A >= B + 1
evalgcdbb4in(A, B) -> Com_1(evalgcdbb6in(A, B)) :|: B >= A
evalgcdbb5in(A, B) -> Com_1(evalgcdbb7in(A - B, B)) :|: TRUE
evalgcdbb6in(A, B) -> Com_1(evalgcdbb7in(A, B - A)) :|: TRUE
evalgcdreturnin(A, B) -> Com_1(evalgcdstop(A, B)) :|: TRUE

The start-symbols are:[evalgcdstart_2]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: evalgcdstart

      0: evalgcdstart -> evalgcdentryin : [], cost: 1

      1: evalgcdentryin -> evalgcdreturnin : [ 0>=A ], cost: 1

      2: evalgcdentryin -> evalgcdreturnin : [ 0>=B ], cost: 1

      3: evalgcdentryin -> evalgcdbb7in : A'=B, B'=A, [ A>=1 && B>=1 ], cost: 1

      4: evalgcdbb7in -> evalgcdbb4in : [ A>=1+B ], cost: 1

      5: evalgcdbb7in -> evalgcdbb4in : [ B>=1+A ], cost: 1

      6: evalgcdbb7in -> evalgcdreturnin : [ B==A ], cost: 1

      7: evalgcdbb4in -> evalgcdbb5in : [ A>=1+B ], cost: 1

      8: evalgcdbb4in -> evalgcdbb6in : [ B>=A ], cost: 1

      9: evalgcdbb5in -> evalgcdbb7in : A'=A-B, [], cost: 1

     10: evalgcdbb6in -> evalgcdbb7in : B'=-A+B, [], cost: 1

     11: evalgcdreturnin -> evalgcdstop : [], cost: 1



Checking for constant complexity:

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

      0: evalgcdstart -> evalgcdentryin : [], cost: 1



Removed unreachable and leaf rules:

   Start location: evalgcdstart

      0: evalgcdstart -> evalgcdentryin : [], cost: 1

      3: evalgcdentryin -> evalgcdbb7in : A'=B, B'=A, [ A>=1 && B>=1 ], cost: 1

      4: evalgcdbb7in -> evalgcdbb4in : [ A>=1+B ], cost: 1

      5: evalgcdbb7in -> evalgcdbb4in : [ B>=1+A ], cost: 1

      7: evalgcdbb4in -> evalgcdbb5in : [ A>=1+B ], cost: 1

      8: evalgcdbb4in -> evalgcdbb6in : [ B>=A ], cost: 1

      9: evalgcdbb5in -> evalgcdbb7in : A'=A-B, [], cost: 1

     10: evalgcdbb6in -> evalgcdbb7in : B'=-A+B, [], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on linear paths):

   Start location: evalgcdstart

     12: evalgcdstart -> evalgcdbb7in : A'=B, B'=A, [ A>=1 && B>=1 ], cost: 2

      4: evalgcdbb7in -> evalgcdbb4in : [ A>=1+B ], cost: 1

      5: evalgcdbb7in -> evalgcdbb4in : [ B>=1+A ], cost: 1

     13: evalgcdbb4in -> evalgcdbb7in : A'=A-B, [ A>=1+B ], cost: 2

     14: evalgcdbb4in -> evalgcdbb7in : B'=-A+B, [ B>=A ], cost: 2



Eliminated locations (on tree-shaped paths):

   Start location: evalgcdstart

     12: evalgcdstart -> evalgcdbb7in : A'=B, B'=A, [ A>=1 && B>=1 ], cost: 2

     15: evalgcdbb7in -> evalgcdbb7in : A'=A-B, [ A>=1+B ], cost: 3

     16: evalgcdbb7in -> evalgcdbb7in : B'=-A+B, [ B>=1+A ], cost: 3



Accelerating simple loops of location 2.

   Accelerating the following rules:

     15: evalgcdbb7in -> evalgcdbb7in : A'=A-B, [ A>=1+B ], cost: 3

     16: evalgcdbb7in -> evalgcdbb7in : B'=-A+B, [ B>=1+A ], cost: 3



   Found no metering function for rule 15.

   Found no metering function for rule 16.

   Removing the simple loops:.



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

   Start location: evalgcdstart

     12: evalgcdstart -> evalgcdbb7in : A'=B, B'=A, [ A>=1 && B>=1 ], cost: 2

     15: evalgcdbb7in -> evalgcdbb7in : A'=A-B, [ A>=1+B ], cost: 3

     16: evalgcdbb7in -> evalgcdbb7in : B'=-A+B, [ B>=1+A ], cost: 3



Chained accelerated rules (with incoming rules):

   Start location: evalgcdstart

     12: evalgcdstart -> evalgcdbb7in : A'=B, B'=A, [ A>=1 && B>=1 ], cost: 2

     17: evalgcdstart -> evalgcdbb7in : A'=-A+B, B'=A, [ A>=1 && B>=1 && B>=1+A ], cost: 5

     18: evalgcdstart -> evalgcdbb7in : A'=B, B'=A-B, [ A>=1 && B>=1 && A>=1+B ], cost: 5



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

   Start location: evalgcdstart

     <empty>



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: evalgcdstart

     <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:  []



WORST_CASE(Omega(1),?)


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(2)
BOUNDS(1, INF)