details

property	value
status	complete
benchmark	ex_paper1.c.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n025.star.cs.uiowa.edu
space	Flores-Montoya_16

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	37.2411499023 seconds
cpu usage	48.393442917
max memory	6.66640384E8

stage attributes

key	value
output-size	846734
starexec-result	WORST_CASE(Omega(n^2), O(n^3))

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^2), O(n^3)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^3). (0) CpxIntTrs (1) Koat Proof [FINISHED, 5938 ms] (2) BOUNDS(1, n^3) (3) Loat Proof [FINISHED, 2770 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_p1_start(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb0_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_bb0_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_0(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_0(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_1(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_1(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_2(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_2(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_3(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_3(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb1_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v_x > 0 eval_p1_3(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb12_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v_x <= 0 eval_p1_bb1_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1__critedge_in(v_x, v_y, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v_y > 0 eval_p1_bb1_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb11_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v_y <= 0 eval_p1__critedge_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb2_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v__0 > 0 eval_p1__critedge_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb6_in(v__0, v__01, v__1, v__01, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v__0 <= 0 eval_p1_bb2_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb3_in(v__0, v__01, v__01 + 1, v__2, v_10, v__0 - 1, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_bb3_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb4_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v__1 > 0 eval_p1_bb3_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1__critedge_in(v_3, v__1, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v__1 <= 0 eval_p1_bb4_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_7(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_7(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_8(v__0, v__01, v__1, v__2, v_10, v_3, nondef_0, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_8(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb5_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v_6 < 0 eval_p1_8(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb5_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v_6 > 0 eval_p1_8(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1__critedge_in(v_3, v__1, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v_6 >= 0 && v_6 <= 0 eval_p1_bb5_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_10(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v__1 - 1, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_10(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_11(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_11(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb3_in(v__0, v__01, v_8, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_bb6_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb7_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v__2 > 0 eval_p1_bb6_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb10_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v__2 <= 0 eval_p1_bb7_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb8_in(v__0, v__01, v__1, v__2, v__2 - 1, v_3, v_6, v_8, 0, v_x, v_y, v_z)) :|: TRUE eval_p1_bb8_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb9_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v_i_0 < v_z eval_p1_bb8_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb6_in(v__0, v__01, v__1, v_10, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: v_i_0 >= v_z eval_p1_bb9_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_14(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_14(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_15(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_15(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_bb8_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0 + 1, v_x, v_y, v_z)) :|: TRUE eval_p1_bb10_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_stop(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_bb11_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_17(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_17(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_18(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_18(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_stop(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_bb12_in(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_19(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_19(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_20(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE eval_p1_20(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z) -> Com_1(eval_p1_stop(v__0, v__01, v__1, v__2, v_10, v_3, v_6, v_8, v_i_0, v_x, v_y, v_z)) :|: TRUE The start-symbols are:[eval_p1_start_12] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 144*ar_0*ar_11 + 144*ar_1*ar_11 + 112*ar_0^2*ar_11 + 112*ar_0*ar_1*ar_11 + 175*ar_0 + 171*ar_1 + 133*ar_0^2 + 133*ar_0*ar_1 + 24) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalp1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalp1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalp1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalp10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalp10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalp11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalp11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalp12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalp12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalp13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalp13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalp1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_0 >= 1 ] (Comp: ?, Cost: 1) evalp13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalp1bb12in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalp1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalp1critedgein(ar_0, ar_1, ar_0, ar_1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_1 >= 1 ] (Comp: ?, Cost: 1) evalp1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalp1bb11in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_1 ] (Comp: ?, Cost: 1) evalp1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalp1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalp1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalp1bb6in(ar_0, ar_1, ar_2, ar_3, ar_3, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalp1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalp1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_3 + 1, ar_2 - 1, ar_7, ar_8, ar_9, ar_10, ar_11)) popout

output may be truncated. 'popout' for the full output.

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actions

all output return to Compl Integ Trans Syste 26843