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	n059.star.cs.uiowa.edu
space	Flores-Montoya_16

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	39.2024 seconds
cpu usage	50.9494
user time	47.9847
system time	2.96471
max virtual memory	1.9021948E7
max residence set size	377976.0

stage attributes

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

output

50.80/39.13 WORST_CASE(Omega(n^2), O(n^3)) 50.80/39.15 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 50.80/39.15 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 50.80/39.15 50.80/39.15 50.80/39.15 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^3). 50.80/39.15 50.80/39.15 (0) CpxIntTrs 50.80/39.15 (1) Koat Proof [FINISHED, 6116 ms] 50.80/39.15 (2) BOUNDS(1, n^3) 50.80/39.15 (3) Loat Proof [FINISHED, 2820 ms] 50.80/39.15 (4) BOUNDS(n^2, INF) 50.80/39.15 50.80/39.15 50.80/39.15 ---------------------------------------- 50.80/39.15 50.80/39.15 (0) 50.80/39.15 Obligation: 50.80/39.15 Complexity Int TRS consisting of the following rules: 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 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 50.80/39.15 50.80/39.15 The start-symbols are:[eval_p1_start_12] 50.80/39.15 50.80/39.15 50.80/39.15 ---------------------------------------- 50.80/39.15 50.80/39.15 (1) Koat Proof (FINISHED) 50.80/39.15 YES(?, 144*ar_0*ar_11 + 144*ar_1*ar_11 + 112*ar_0^2*ar_11 + 112*ar_0*ar_1*ar_11 + 96*ar_11 + 175*ar_0 + 171*ar_1 + 133*ar_0^2 + 133*ar_0*ar_1 + 138) 50.80/39.15 50.80/39.15 50.80/39.15 50.80/39.15 Initial complexity problem: 50.80/39.15 50.80/39.15 1: T: 50.80/39.15 50.80/39.15 (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)) 50.80/39.15 50.80/39.15 (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)) 50.80/39.15 50.80/39.15 (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)) 50.80/39.15 50.80/39.15 (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)) 50.80/39.15 50.80/39.15 (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)) 50.80/39.15 50.80/39.15 (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 ] 50.80/39.15 50.80/39.15 (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 ] 50.80/39.15 50.80/39.15 (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 ] 50.80/39.15 50.80/39.15 (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 ] 50.80/39.15 50.80/39.15 (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 ] 50.80/39.15 50.80/39.15 (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 ] 50.80/39.15 50.80/39.15 (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)) 50.80/39.15 50.80/39.15 (Comp: ?, Cost: 1) evalp1bb3in(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(evalp1bb4in(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_5 >= 1 ] 50.80/39.15 50.80/39.15 (Comp: ?, Cost: 1) evalp1bb3in(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_6, ar_5, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_5 ] 50.80/39.15 50.80/39.15 (Comp: ?, Cost: 1) evalp1bb4in(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(evalp17(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 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all output return to Complexity_ITS 2019-03-21 04.46