/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(NON_POLY, ?)
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 127 ms]
(2) BOUNDS(INF, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f300(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f1(S, T, U, V, W, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: TRUE
f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f1(A, B, C, D, E, F, G, 256, S, T, U, V, W, Y, O, P, Q, R)) :|: G >= 1 + F && X >= 1 && H >= 256 && H <= 256
f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f1(A, B, C, D, E, F, G, H, S, T, U, V, W, N, O, P, Q, R)) :|: G >= 1 + F && 0 >= H
f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f3(A, B, C, D, E, F, G, H, S, T, K, L, M, N, 0, 0, 0, R)) :|: F >= G
f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f2(A, B, C, D, E, F, G, H, S, T, U, V, W, Y, H, H, H, X)) :|: H >= 1 && G >= 1 + F && H >= 257
f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f2(A, B, C, D, E, F, G, H, S, T, U, V, W, Y, H, H, H, X)) :|: H >= 1 && G >= 1 + F && 255 >= H

The start-symbols are:[f300_18]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f300

      0: f300 -> f1 : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [], cost: 1

      1: f1 -> f1 : H'=256, Q'=free_7, J'=free_9, K'=free_11, L'=free_6, M'=free_8, N'=free_5, [ F>=1+G && free_10>=1 && H==256 ], cost: 1

      2: f1 -> f1 : Q'=free_13, J'=free_15, K'=free_16, L'=free_12, M'=free_14, [ F>=1+G && 0>=H ], cost: 1

      3: f1 -> f3 : Q'=free_17, J'=free_18, O'=0, P'=0, Q_1'=0, [ G>=F ], cost: 1

      4: f1 -> f2 : Q'=free_21, J'=free_23, K'=free_25, L'=free_20, M'=free_22, N'=free_19, O'=H, P'=H, Q_1'=H, R'=free_24, [ H>=1 && F>=1+G && H>=257 ], cost: 1

      5: f1 -> f2 : Q'=free_28, J'=free_30, K'=free_32, L'=free_27, M'=free_29, N'=free_26, O'=H, P'=H, Q_1'=H, R'=free_31, [ H>=1 && F>=1+G && 255>=H ], cost: 1



Removed unreachable and leaf rules:

   Start location: f300

      0: f300 -> f1 : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [], cost: 1

      1: f1 -> f1 : H'=256, Q'=free_7, J'=free_9, K'=free_11, L'=free_6, M'=free_8, N'=free_5, [ F>=1+G && free_10>=1 && H==256 ], cost: 1

      2: f1 -> f1 : Q'=free_13, J'=free_15, K'=free_16, L'=free_12, M'=free_14, [ F>=1+G && 0>=H ], cost: 1



Simplified all rules, resulting in:

   Start location: f300

      0: f300 -> f1 : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [], cost: 1

      1: f1 -> f1 : H'=256, Q'=free_7, J'=free_9, K'=free_11, L'=free_6, M'=free_8, N'=free_5, [ F>=1+G && H==256 ], cost: 1

      2: f1 -> f1 : Q'=free_13, J'=free_15, K'=free_16, L'=free_12, M'=free_14, [ F>=1+G && 0>=H ], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 1.

   Accelerating the following rules:

      1: f1 -> f1 : H'=256, Q'=free_7, J'=free_9, K'=free_11, L'=free_6, M'=free_8, N'=free_5, [ F>=1+G && H==256 ], cost: 1

      2: f1 -> f1 : Q'=free_13, J'=free_15, K'=free_16, L'=free_12, M'=free_14, [ F>=1+G && 0>=H ], cost: 1



   Accelerated rule 1 with NONTERM, yielding the new rule 6.

   Accelerated rule 2 with NONTERM, yielding the new rule 7.

   Removing the simple loops: 1 2.



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

   Start location: f300

      0: f300 -> f1 : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [], cost: 1

      6: f1 -> [4] : [ F>=1+G && H==256 ], cost: INF

      7: f1 -> [4] : [ F>=1+G && 0>=H ], cost: INF



Chained accelerated rules (with incoming rules):

   Start location: f300

      0: f300 -> f1 : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [], cost: 1

      8: f300 -> [4] : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [ F>=1+G && H==256 ], cost: INF

      9: f300 -> [4] : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [ F>=1+G && 0>=H ], cost: INF



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

   Start location: f300

      8: f300 -> [4] : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [ F>=1+G && H==256 ], cost: INF

      9: f300 -> [4] : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [ F>=1+G && 0>=H ], cost: INF



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f300

      8: f300 -> [4] : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [ F>=1+G && H==256 ], cost: INF

      9: f300 -> [4] : A'=free_1, B'=free_3, C'=free_4, D'=free, E'=free_2, [ F>=1+G && 0>=H ], cost: INF



Computing asymptotic complexity for rule 8

   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:  [ F>=1+G && H==256 ]



NO


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(2)
BOUNDS(INF, INF)