/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 647 ms]
(2) BOUNDS(INF, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f17(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O) -> Com_1(f17(A, Q, C, 1 + D, P, F, G, H, I, J, K, L, M, N, O)) :|: A >= B + 1 && C >= 0 && D >= 0
f17(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O) -> Com_1(f17(A, Q, C, 1 + D, P, F, G, H, I, J, K, L, M, N, O)) :|: B >= A + 1 && C >= 0 && D >= 0
f18(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O) -> Com_1(f17(A, Q, C, 1, P, F, G, H, I, J, K, L, M, N, O)) :|: F >= 0 && A >= B + 1
f18(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O) -> Com_1(f17(A, Q, C, 1, P, F, G, H, I, J, K, L, M, N, O)) :|: F >= 0 && B >= A + 1
f17(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O) -> Com_1(f20(B, B, C, D, E, F, P, H, I, J, K, L, M, N, O)) :|: C >= 0 && D >= 0 && B >= A && B <= A
f22(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O) -> Com_1(f18(A, H, C, D, E, F, Q, H, 2, P, P, P, P, 3, 0)) :|: A >= H + 1 && F >= 0
f22(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O) -> Com_1(f18(A, H, C, D, E, F, Q, H, 2, P, P, P, P, 3, 0)) :|: H >= A + 1 && F >= 0

The start-symbols are:[f22_15]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f22

      0: f17 -> f17 : B'=free, D'=1+D, E'=free_1, [ A>=1+B && C>=0 && D>=0 ], cost: 1

      1: f17 -> f17 : B'=free_2, D'=1+D, E'=free_3, [ B>=1+A && C>=0 && D>=0 ], cost: 1

      4: f17 -> f20 : A'=B, G'=free_8, [ C>=0 && D>=0 && B==A ], cost: 1

      2: f18 -> f17 : B'=free_4, D'=1, E'=free_5, [ F>=0 && A>=1+B ], cost: 1

      3: f18 -> f17 : B'=free_6, D'=1, E'=free_7, [ F>=0 && B>=1+A ], cost: 1

      5: f22 -> f18 : B'=H, G'=free_9, Q'=2, J'=free_10, K'=free_10, L'=free_10, M'=free_10, N'=3, O'=0, [ A>=1+H && F>=0 ], cost: 1

      6: f22 -> f18 : B'=H, G'=free_11, Q'=2, J'=free_12, K'=free_12, L'=free_12, M'=free_12, N'=3, O'=0, [ H>=1+A && F>=0 ], cost: 1



Checking for constant complexity:

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

      5: f22 -> f18 : B'=H, G'=free_9, Q'=2, J'=free_10, K'=free_10, L'=free_10, M'=free_10, N'=3, O'=0, [ A>=1+H && F>=0 ], cost: 1



Removed unreachable and leaf rules:

   Start location: f22

      0: f17 -> f17 : B'=free, D'=1+D, E'=free_1, [ A>=1+B && C>=0 && D>=0 ], cost: 1

      1: f17 -> f17 : B'=free_2, D'=1+D, E'=free_3, [ B>=1+A && C>=0 && D>=0 ], cost: 1

      2: f18 -> f17 : B'=free_4, D'=1, E'=free_5, [ F>=0 && A>=1+B ], cost: 1

      3: f18 -> f17 : B'=free_6, D'=1, E'=free_7, [ F>=0 && B>=1+A ], cost: 1

      5: f22 -> f18 : B'=H, G'=free_9, Q'=2, J'=free_10, K'=free_10, L'=free_10, M'=free_10, N'=3, O'=0, [ A>=1+H && F>=0 ], cost: 1

      6: f22 -> f18 : B'=H, G'=free_11, Q'=2, J'=free_12, K'=free_12, L'=free_12, M'=free_12, N'=3, O'=0, [ H>=1+A && F>=0 ], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 0.

   Accelerating the following rules:

      0: f17 -> f17 : B'=free, D'=1+D, E'=free_1, [ A>=1+B && C>=0 && D>=0 ], cost: 1

      1: f17 -> f17 : B'=free_2, D'=1+D, E'=free_3, [ B>=1+A && C>=0 && D>=0 ], cost: 1



   Accelerated rule 0 with NONTERM (after strengthening guard), yielding the new rule 7.

   Accelerated rule 1 with NONTERM (after strengthening guard), yielding the new rule 8.

   Removing the simple loops:.



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

   Start location: f22

      0: f17 -> f17 : B'=free, D'=1+D, E'=free_1, [ A>=1+B && C>=0 && D>=0 ], cost: 1

      1: f17 -> f17 : B'=free_2, D'=1+D, E'=free_3, [ B>=1+A && C>=0 && D>=0 ], cost: 1

      7: f17 -> [4] : [ A>=1+B && C>=0 && D>=0 && A>=1+free ], cost: NONTERM

      8: f17 -> [4] : [ B>=1+A && C>=0 && D>=0 && free_2>=1+A ], cost: NONTERM

      2: f18 -> f17 : B'=free_4, D'=1, E'=free_5, [ F>=0 && A>=1+B ], cost: 1

      3: f18 -> f17 : B'=free_6, D'=1, E'=free_7, [ F>=0 && B>=1+A ], cost: 1

      5: f22 -> f18 : B'=H, G'=free_9, Q'=2, J'=free_10, K'=free_10, L'=free_10, M'=free_10, N'=3, O'=0, [ A>=1+H && F>=0 ], cost: 1

      6: f22 -> f18 : B'=H, G'=free_11, Q'=2, J'=free_12, K'=free_12, L'=free_12, M'=free_12, N'=3, O'=0, [ H>=1+A && F>=0 ], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f22

      2: f18 -> f17 : B'=free_4, D'=1, E'=free_5, [ F>=0 && A>=1+B ], cost: 1

      3: f18 -> f17 : B'=free_6, D'=1, E'=free_7, [ F>=0 && B>=1+A ], cost: 1

      9: f18 -> f17 : B'=free, D'=2, E'=free_1, [ F>=0 && A>=1+B && C>=0 ], cost: 2

     10: f18 -> f17 : B'=free, D'=2, E'=free_1, [ F>=0 && B>=1+A && C>=0 ], cost: 2

     11: f18 -> f17 : B'=free_2, D'=2, E'=free_3, [ F>=0 && A>=1+B && C>=0 ], cost: 2

     12: f18 -> f17 : B'=free_2, D'=2, E'=free_3, [ F>=0 && B>=1+A && C>=0 ], cost: 2

     13: f18 -> [4] : B'=free_4, D'=1, E'=free_5, [ F>=0 && A>=1+B && A>=1+free_4 && C>=0 ], cost: NONTERM

     14: f18 -> [4] : B'=free_6, D'=1, E'=free_7, [ F>=0 && B>=1+A && A>=1+free_6 && C>=0 ], cost: NONTERM

     15: f18 -> [4] : B'=free_4, D'=1, E'=free_5, [ F>=0 && A>=1+B && free_4>=1+A && C>=0 ], cost: NONTERM

     16: f18 -> [4] : B'=free_6, D'=1, E'=free_7, [ F>=0 && B>=1+A && free_6>=1+A && C>=0 ], cost: NONTERM

      5: f22 -> f18 : B'=H, G'=free_9, Q'=2, J'=free_10, K'=free_10, L'=free_10, M'=free_10, N'=3, O'=0, [ A>=1+H && F>=0 ], cost: 1

      6: f22 -> f18 : B'=H, G'=free_11, Q'=2, J'=free_12, K'=free_12, L'=free_12, M'=free_12, N'=3, O'=0, [ H>=1+A && F>=0 ], cost: 1



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

   Start location: f22

     13: f18 -> [4] : B'=free_4, D'=1, E'=free_5, [ F>=0 && A>=1+B && A>=1+free_4 && C>=0 ], cost: NONTERM

     14: f18 -> [4] : B'=free_6, D'=1, E'=free_7, [ F>=0 && B>=1+A && A>=1+free_6 && C>=0 ], cost: NONTERM

     15: f18 -> [4] : B'=free_4, D'=1, E'=free_5, [ F>=0 && A>=1+B && free_4>=1+A && C>=0 ], cost: NONTERM

     16: f18 -> [4] : B'=free_6, D'=1, E'=free_7, [ F>=0 && B>=1+A && free_6>=1+A && C>=0 ], cost: NONTERM

      5: f22 -> f18 : B'=H, G'=free_9, Q'=2, J'=free_10, K'=free_10, L'=free_10, M'=free_10, N'=3, O'=0, [ A>=1+H && F>=0 ], cost: 1

      6: f22 -> f18 : B'=H, G'=free_11, Q'=2, J'=free_12, K'=free_12, L'=free_12, M'=free_12, N'=3, O'=0, [ H>=1+A && F>=0 ], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: f22

     17: f22 -> [4] : B'=free_4, D'=1, E'=free_5, G'=free_9, Q'=2, J'=free_10, K'=free_10, L'=free_10, M'=free_10, N'=3, O'=0, [ A>=1+H && F>=0 && A>=1+free_4 && C>=0 ], cost: NONTERM

     18: f22 -> [4] : B'=free_4, D'=1, E'=free_5, G'=free_9, Q'=2, J'=free_10, K'=free_10, L'=free_10, M'=free_10, N'=3, O'=0, [ A>=1+H && F>=0 && free_4>=1+A && C>=0 ], cost: NONTERM

     19: f22 -> [4] : B'=free_6, D'=1, E'=free_7, G'=free_11, Q'=2, J'=free_12, K'=free_12, L'=free_12, M'=free_12, N'=3, O'=0, [ H>=1+A && F>=0 && A>=1+free_6 && C>=0 ], cost: NONTERM

     20: f22 -> [4] : B'=free_6, D'=1, E'=free_7, G'=free_11, Q'=2, J'=free_12, K'=free_12, L'=free_12, M'=free_12, N'=3, O'=0, [ H>=1+A && F>=0 && free_6>=1+A && C>=0 ], cost: NONTERM



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f22

     17: f22 -> [4] : B'=free_4, D'=1, E'=free_5, G'=free_9, Q'=2, J'=free_10, K'=free_10, L'=free_10, M'=free_10, N'=3, O'=0, [ A>=1+H && F>=0 && A>=1+free_4 && C>=0 ], cost: NONTERM

     18: f22 -> [4] : B'=free_4, D'=1, E'=free_5, G'=free_9, Q'=2, J'=free_10, K'=free_10, L'=free_10, M'=free_10, N'=3, O'=0, [ A>=1+H && F>=0 && free_4>=1+A && C>=0 ], cost: NONTERM

     19: f22 -> [4] : B'=free_6, D'=1, E'=free_7, G'=free_11, Q'=2, J'=free_12, K'=free_12, L'=free_12, M'=free_12, N'=3, O'=0, [ H>=1+A && F>=0 && A>=1+free_6 && C>=0 ], cost: NONTERM

     20: f22 -> [4] : B'=free_6, D'=1, E'=free_7, G'=free_11, Q'=2, J'=free_12, K'=free_12, L'=free_12, M'=free_12, N'=3, O'=0, [ H>=1+A && F>=0 && free_6>=1+A && C>=0 ], cost: NONTERM



Computing asymptotic complexity for rule 17

   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>=1+H && F>=0 && A>=1+free_4 && C>=0 ]



NO


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(2)
BOUNDS(INF, INF)