details

property	value
status	complete
benchmark	perfectg.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n101.star.cs.uiowa.edu
space	WTC_V2

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	2.04725 seconds
cpu usage	3.22299
user time	2.94221
system time	0.280786
max virtual memory	1.8503184E7
max residence set size	184364.0

stage attributes

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

output

3.11/2.01 WORST_CASE(?, O(n^2)) 3.11/2.02 proof of /export/starexec/sandbox2/output/output_files/bench.koat 3.11/2.02 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.11/2.02 3.11/2.02 3.11/2.02 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 3.11/2.02 3.11/2.02 (0) CpxIntTrs 3.11/2.02 (1) Koat Proof [FINISHED, 785 ms] 3.11/2.02 (2) BOUNDS(1, n^2) 3.11/2.02 3.11/2.02 3.11/2.02 ---------------------------------------- 3.11/2.02 3.11/2.02 (0) 3.11/2.02 Obligation: 3.11/2.02 Complexity Int TRS consisting of the following rules: 3.11/2.02 eval_perfectg_start(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_bb0_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2)) :|: TRUE 3.11/2.02 eval_perfectg_bb0_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_bb2_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, nondef.0)) :|: v_x <= 1 3.11/2.02 eval_perfectg_bb0_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_bb1_in(v_2, v_x, v_x, v_y2.1, v_x, v_y3.2)) :|: v_x > 1 3.11/2.02 eval_perfectg_bb1_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_bb2_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.0)) :|: v_y1.0 - 1 >= 0 && v_y1.0 - 1 <= 0 3.11/2.02 eval_perfectg_bb1_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_bb3_in(v_y1.0 - 1, v_x, v_y1.0, v_x, v_y3.0, v_y3.2)) :|: v_y1.0 - 1 < 0 3.11/2.02 eval_perfectg_bb1_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_bb3_in(v_y1.0 - 1, v_x, v_y1.0, v_x, v_y3.0, v_y3.2)) :|: v_y1.0 - 1 > 0 3.11/2.02 eval_perfectg_bb2_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_stop(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2)) :|: v_y3.2 < 0 3.11/2.02 eval_perfectg_bb2_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_stop(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2)) :|: v_y3.2 > 0 3.11/2.02 eval_perfectg_bb2_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_stop(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2)) :|: v_y3.2 >= 0 && v_y3.2 <= 0 3.11/2.02 eval_perfectg_bb3_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_bb4_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2)) :|: v_y2.1 < v_2 3.11/2.02 eval_perfectg_bb3_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_bb5_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2)) :|: v_y2.1 >= v_2 3.11/2.02 eval_perfectg_bb4_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_bb1_in(v_2, v_x, v_2, v_y2.1, v_y3.0, v_y3.2)) :|: v_y2.1 < 0 3.11/2.02 eval_perfectg_bb4_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_bb1_in(v_2, v_x, v_2, v_y2.1, v_y3.0, v_y3.2)) :|: v_y2.1 > 0 3.11/2.02 eval_perfectg_bb4_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_bb1_in(v_2, v_x, v_2, v_y2.1, v_y3.0 - v_2, v_y3.2)) :|: v_y2.1 >= 0 && v_y2.1 <= 0 3.11/2.02 eval_perfectg_bb5_in(v_2, v_x, v_y1.0, v_y2.1, v_y3.0, v_y3.2) -> Com_1(eval_perfectg_bb3_in(v_2, v_x, v_y1.0, v_y2.1 - v_2, v_y3.0, v_y3.2)) :|: TRUE 3.11/2.02 3.11/2.02 The start-symbols are:[eval_perfectg_start_6] 3.11/2.02 3.11/2.02 3.11/2.02 ---------------------------------------- 3.11/2.02 3.11/2.02 (1) Koat Proof (FINISHED) 3.11/2.02 YES(?, 4*ar_0^2 + 9*ar_0 + 11) 3.11/2.02 3.11/2.02 3.11/2.02 3.11/2.02 Initial complexity problem: 3.11/2.02 3.11/2.02 1: T: 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb2in(ar_0, g, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_0 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb1in(ar_0, ar_1, ar_0, ar_0, ar_4, ar_5)) [ ar_0 >= 2 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb2in(ar_0, ar_3, ar_2, ar_3, ar_4, ar_5)) [ ar_2 = 1 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb3in(ar_0, ar_1, ar_2, ar_3, ar_2 - 1, ar_0)) [ 0 >= ar_2 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb3in(ar_0, ar_1, ar_2, ar_3, ar_2 - 1, ar_0)) [ ar_2 >= 2 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_1 + 1 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 = 0 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_5 + 1 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= ar_4 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb1in(ar_0, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb1in(ar_0, ar_1, ar_4, ar_3, ar_4, ar_5)) [ ar_5 >= 1 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb1in(ar_0, ar_1, ar_4, ar_3 - ar_4, ar_4, ar_5)) [ ar_5 = 0 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - ar_4)) 3.11/2.02 3.11/2.02 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 3.11/2.02 3.11/2.02 start location: koat_start 3.11/2.02 3.11/2.02 leaf cost: 0 3.11/2.02 3.11/2.02 3.11/2.02 3.11/2.02 Repeatedly propagating knowledge in problem 1 produces the following problem: 3.11/2.02 3.11/2.02 2: T: 3.11/2.02 3.11/2.02 (Comp: 1, Cost: 1) evalperfectgstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.11/2.02 3.11/2.02 (Comp: 1, Cost: 1) evalperfectgbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb2in(ar_0, g, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_0 ] 3.11/2.02 3.11/2.02 (Comp: 1, Cost: 1) evalperfectgbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb1in(ar_0, ar_1, ar_0, ar_0, ar_4, ar_5)) [ ar_0 >= 2 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb2in(ar_0, ar_3, ar_2, ar_3, ar_4, ar_5)) [ ar_2 = 1 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb3in(ar_0, ar_1, ar_2, ar_3, ar_2 - 1, ar_0)) [ 0 >= ar_2 ] 3.11/2.02 3.11/2.02 (Comp: ?, Cost: 1) evalperfectgbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalperfectgbb3in(ar_0, ar_1, ar_2, ar_3, ar_2 - 1, ar_0)) [ ar_2 >= 2 ] popout

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all output return to Complexity_C_Integer 2019-03-21 04.38