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Compl Integ Trans Syste 26843 pair #381744641
details
property
value
status
complete
benchmark
perfect.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n089.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
12.0742781162 seconds
cpu usage
17.260907274
max memory
4.57719808E8
stage attributes
key
value
output-size
16530
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(7 + 3 * Arg_0, 13) + max(6, 3 * Arg_0) * nat(Arg_0) + nat(Arg_0 * max(6, 3 * Arg_0)) * nat(Arg_0) + nat(Arg_0 * max(6, 3 * Arg_0)) + nat(8 * Arg_0) + max(3, 3 + Arg_0) + max(8, 4 * Arg_0)). (0) CpxIntTrs (1) Loat Proof [FINISHED, 1882 ms] (2) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_perfect_start(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb0_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE eval_perfect_bb0_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_0(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE eval_perfect_0(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_1(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE eval_perfect_1(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb6_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_x <= 1 eval_perfect_1(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb1_in(v__y3_0, v_1, v_6, v_x, v_x, v_y2_1, v_x)) :|: v_x > 1 eval_perfect_bb1_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb2_in(v__y3_0, v_y1_0_sink - 1, v_6, v_x, v_y1_0_sink, v_x, v_y3_0)) :|: v_y1_0_sink - 1 > 0 eval_perfect_bb1_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb5_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y1_0_sink - 1 <= 0 eval_perfect_bb2_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb3_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y2_1 >= v_1 eval_perfect_bb2_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb4_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y2_1 < v_1 eval_perfect_bb3_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb2_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1 - v_1, v_y3_0)) :|: TRUE eval_perfect_bb4_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_7(v__y3_0, v_1, v_y3_0 - v_1, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE eval_perfect_7(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_8(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE eval_perfect_8(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_9(v_6, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y2_1 >= 0 && v_y2_1 <= 0 eval_perfect_8(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_9(v_y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y2_1 < 0 eval_perfect_8(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_9(v_y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y2_1 > 0 eval_perfect_9(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_10(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE eval_perfect_10(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_11(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE eval_perfect_11(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb1_in(v__y3_0, v_1, v_6, v_x, v_1, v_y2_1, v__y3_0)) :|: TRUE eval_perfect_bb5_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb6_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y3_0 < 0 eval_perfect_bb5_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb6_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y3_0 > 0 eval_perfect_bb5_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_bb6_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: v_y3_0 >= 0 && v_y3_0 <= 0 eval_perfect_bb6_in(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0) -> Com_1(eval_perfect_stop(v__y3_0, v_1, v_6, v_x, v_y1_0_sink, v_y2_1, v_y3_0)) :|: TRUE The start-symbols are:[eval_perfect_start_7] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalperfectstart 0: evalperfectstart -> evalperfectbb0in : [], cost: 1 1: evalperfectbb0in -> evalperfect0 : [], cost: 1 2: evalperfect0 -> evalperfect1 : [], cost: 1 3: evalperfect1 -> evalperfectbb6in : [ 1>=A ], cost: 1 4: evalperfect1 -> evalperfectbb1in : B'=A, C'=A, [ A>=2 ], cost: 1 5: evalperfectbb1in -> evalperfectbb2in : D'=-1+B, E'=A, [ B>=2 ], cost: 1 6: evalperfectbb1in -> evalperfectbb5in : [ 1>=B ], cost: 1 7: evalperfectbb2in -> evalperfectbb3in : [ E>=D ], cost: 1 8: evalperfectbb2in -> evalperfectbb4in : [ D>=1+E ], cost: 1 9: evalperfectbb3in -> evalperfectbb2in : E'=-D+E, [], cost: 1 10: evalperfectbb4in -> evalperfect7 : F'=C-D, [], cost: 1 11: evalperfect7 -> evalperfect8 : [], cost: 1 12: evalperfect8 -> evalperfect9 : G'=F, [ E==0 ], cost: 1 13: evalperfect8 -> evalperfect9 : G'=C, [ 0>=1+E ], cost: 1 14: evalperfect8 -> evalperfect9 : G'=C, [ E>=1 ], cost: 1 15: evalperfect9 -> evalperfect10 : [], cost: 1 16: evalperfect10 -> evalperfect11 : [], cost: 1 17: evalperfect11 -> evalperfectbb1in : B'=D, C'=G, [], cost: 1 18: evalperfectbb5in -> evalperfectbb6in : [ 0>=1+C ], cost: 1
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