details

property	value
status	complete
benchmark	perfect.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n066.star.cs.uiowa.edu
space	WTC_V2

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	2.43962 seconds
cpu usage	2.94634
user time	2.64787
system time	0.298472
max virtual memory	1.8539808E7
max residence set size	206032.0

stage attributes

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

output

2.80/1.95 WORST_CASE(?, O(n^2)) 2.80/1.96 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.80/1.96 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.80/1.96 2.80/1.96 2.80/1.96 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.80/1.96 2.80/1.96 (0) CpxIntTrs 2.80/1.96 (1) Koat Proof [FINISHED, 672 ms] 2.80/1.96 (2) BOUNDS(1, n^2) 2.80/1.96 2.80/1.96 2.80/1.96 ---------------------------------------- 2.80/1.96 2.80/1.96 (0) 2.80/1.96 Obligation: 2.80/1.96 Complexity Int TRS consisting of the following rules: 2.80/1.96 eval_perfect_start(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb0_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: TRUE 2.80/1.96 eval_perfect_bb0_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_x <= 1 2.80/1.96 eval_perfect_bb0_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb1_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_x > 1 2.80/1.96 eval_perfect_bb1_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb2_in(v_x, v_x - 1, v_y2.1, v_x)) :|: TRUE 2.80/1.96 eval_perfect_bb2_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb3_in(v_x, v_y1.0, v_x, v_y3.0)) :|: v_y1.0 > 0 2.80/1.96 eval_perfect_bb2_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb6_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y1.0 <= 0 2.90/2.37 eval_perfect_bb3_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb4_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y2.1 >= v_y1.0 2.90/2.37 eval_perfect_bb3_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb5_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y2.1 < v_y1.0 2.90/2.37 eval_perfect_bb4_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb3_in(v_x, v_y1.0, v_y2.1 - v_y1.0, v_y3.0)) :|: TRUE 2.90/2.37 eval_perfect_bb5_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb2_in(v_x, v_y1.0 - 1, v_y2.1, v_y3.0 - v_y1.0)) :|: v_y2.1 >= 0 && v_y2.1 <= 0 2.90/2.37 eval_perfect_bb5_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb2_in(v_x, v_y1.0 - 1, v_y2.1, v_y3.0)) :|: v_y2.1 < 0 2.90/2.37 eval_perfect_bb5_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb2_in(v_x, v_y1.0 - 1, v_y2.1, v_y3.0)) :|: v_y2.1 > 0 2.90/2.37 eval_perfect_bb6_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y3.0 < 0 2.90/2.37 eval_perfect_bb6_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y3.0 > 0 2.90/2.37 eval_perfect_bb6_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y3.0 >= 0 && v_y3.0 <= 0 2.90/2.37 eval_perfect_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_stop(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: TRUE 2.90/2.37 2.90/2.37 The start-symbols are:[eval_perfect_start_4] 2.90/2.37 2.90/2.37 2.90/2.37 ---------------------------------------- 2.90/2.37 2.90/2.37 (1) Koat Proof (FINISHED) 2.90/2.37 YES(?, 13*ar_0 + 4*ar_0^2 + 28) 2.90/2.37 2.90/2.37 2.90/2.37 2.90/2.37 Initial complexity problem: 2.90/2.37 2.90/2.37 1: T: 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb0in(ar_0, ar_1, ar_2, ar_3)) 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb7in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_0 ] 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ] 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb2in(ar_0, ar_0 - 1, ar_0, ar_3)) 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb3in(ar_0, ar_1, ar_2, ar_0)) [ ar_1 >= 1 ] 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 ] 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 ] 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 + 1 ] 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb3in(ar_0, ar_1, ar_2, ar_3 - ar_1)) 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb2in(ar_0, ar_1 - 1, ar_2 - ar_1, ar_3)) [ ar_3 = 0 ] 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb2in(ar_0, ar_1 - 1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ] 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb2in(ar_0, ar_1 - 1, ar_2, ar_3)) [ ar_3 >= 1 ] 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb7in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ] 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb7in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ] 2.90/2.37 2.90/2.37 (Comp: ?, Cost: 1) evalperfectbb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectstop(ar_0, ar_1, ar_2, ar_3)) 2.90/2.37 2.90/2.37 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.90/2.37 2.90/2.37 start location: koat_start 2.90/2.37 2.90/2.37 leaf cost: 0 2.90/2.37 2.90/2.37 2.90/2.37 2.90/2.37 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.90/2.37 2.90/2.37 2: T: 2.90/2.37 2.90/2.37 (Comp: 1, Cost: 1) evalperfectstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb0in(ar_0, ar_1, ar_2, ar_3)) 2.90/2.37 2.90/2.37 (Comp: 1, Cost: 1) evalperfectbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb7in(ar_0, ar_1, ar_2, ar_3)) [ 1 >= ar_0 ] 2.90/2.37 2.90/2.37 (Comp: 1, Cost: 1) evalperfectbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ] 2.90/2.37 2.90/2.37 (Comp: 1, Cost: 1) evalperfectbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalperfectbb2in(ar_0, ar_0 - 1, ar_0, ar_3)) 2.90/2.37 popout

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all output return to Complexity_C_Integer 2019-03-21 04.38