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Compl Integ Trans Syste 26843 pair #381744725
details
property
value
status
complete
benchmark
perfect2.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n046.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
12.860172987 seconds
cpu usage
16.06037609
max memory
4.6854144E8
stage attributes
key
value
output-size
17881
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(7 + Arg_0 * max(18, 9 * Arg_0), 7) + nat(Arg_0 * max(18, 9 * Arg_0)) * nat(Arg_0) + max(3, 3 * Arg_0) * nat(Arg_0) + max(6 * Arg_0, 6) + nat(7 * Arg_0) + max(3, 3 + Arg_0)). (0) CpxIntTrs (1) Loat Proof [FINISHED, 1812 ms] (2) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_perfect2_start(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb0_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE eval_perfect2_bb0_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_0(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE eval_perfect2_0(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_1(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE eval_perfect2_1(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_x <= 0 eval_perfect2_1(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb1_in(v__y3_0, v_1, v_8, v_x, v_x, v_y2_1, v_x)) :|: v_x > 0 eval_perfect2_bb1_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb2_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y1_0 - 1 >= 0 && v_y1_0 - 1 <= 0 eval_perfect2_bb1_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb4_in(v__y3_0, v_y1_0 - 1, v_8, v_x, v_y1_0, v_x, v_y3_0)) :|: v_y1_0 - 1 < 0 eval_perfect2_bb1_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb4_in(v__y3_0, v_y1_0 - 1, v_8, v_x, v_y1_0, v_x, v_y3_0)) :|: v_y1_0 - 1 > 0 eval_perfect2_bb2_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y3_0 < 0 eval_perfect2_bb2_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y3_0 > 0 eval_perfect2_bb2_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y3_0 >= 0 && v_y3_0 <= 0 eval_perfect2_bb3_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_stop(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE eval_perfect2_bb4_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb5_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 >= v_1 eval_perfect2_bb4_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb6_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 < v_1 eval_perfect2_bb5_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb4_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1 - v_1, v_y3_0)) :|: TRUE eval_perfect2_bb6_in(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_9(v__y3_0, v_1, v_y3_0 - v_1, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE eval_perfect2_9(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_10(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE eval_perfect2_10(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_11(v_8, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 >= 0 && v_y2_1 <= 0 eval_perfect2_10(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_11(v_y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 < 0 eval_perfect2_10(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_11(v_y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 > 0 eval_perfect2_11(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_12(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE eval_perfect2_12(v__y3_0, v_1, v_8, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect2_bb1_in(v__y3_0, v_1, v_8, v_x, v_1, v_y2_1, v__y3_0)) :|: TRUE The start-symbols are:[eval_perfect2_start_7] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalperfect2start 0: evalperfect2start -> evalperfect2bb0in : [], cost: 1 1: evalperfect2bb0in -> evalperfect20 : [], cost: 1 2: evalperfect20 -> evalperfect21 : [], cost: 1 3: evalperfect21 -> evalperfect2bb3in : [ 0>=A ], cost: 1 4: evalperfect21 -> evalperfect2bb1in : B'=A, C'=A, [ A>=1 ], cost: 1 5: evalperfect2bb1in -> evalperfect2bb2in : [ B==1 ], cost: 1 6: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=A, [ 0>=B ], cost: 1 7: evalperfect2bb1in -> evalperfect2bb4in : D'=-1+B, E'=A, [ B>=2 ], cost: 1 8: evalperfect2bb2in -> evalperfect2bb3in : [ 0>=1+C ], cost: 1 9: evalperfect2bb2in -> evalperfect2bb3in : [ C>=1 ], cost: 1 10: evalperfect2bb2in -> evalperfect2bb3in : [ C==0 ], cost: 1 11: evalperfect2bb3in -> evalperfect2stop : [], cost: 1 12: evalperfect2bb4in -> evalperfect2bb5in : [ E>=D ], cost: 1 13: evalperfect2bb4in -> evalperfect2bb6in : [ D>=1+E ], cost: 1 14: evalperfect2bb5in -> evalperfect2bb4in : E'=-D+E, [], cost: 1 15: evalperfect2bb6in -> evalperfect29 : F'=C-D, [], cost: 1 16: evalperfect29 -> evalperfect210 : [], cost: 1 17: evalperfect210 -> evalperfect211 : G'=F, [ E==0 ], cost: 1 18: evalperfect210 -> evalperfect211 : G'=C, [ 0>=1+E ], cost: 1
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