details

property	value
status	complete
benchmark	Loopus2011_ex1.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n049.star.cs.uiowa.edu
space	Loopus

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	1.99226 seconds
cpu usage	3.00869
user time	2.75585
system time	0.252842
max virtual memory	1.8455936E7
max residence set size	184324.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^1))

output

2.89/1.96 WORST_CASE(?, O(n^1)) 2.89/1.97 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.89/1.97 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.89/1.97 2.89/1.97 2.89/1.97 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.89/1.97 2.89/1.97 (0) CpxIntTrs 2.89/1.97 (1) Koat Proof [FINISHED, 783 ms] 2.89/1.97 (2) BOUNDS(1, n^1) 2.89/1.97 2.89/1.97 2.89/1.97 ---------------------------------------- 2.89/1.97 2.89/1.97 (0) 2.89/1.97 Obligation: 2.89/1.97 Complexity Int TRS consisting of the following rules: 2.89/1.97 eval_Loopus2011_ex1_start(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_bb0_in(v_3, v_i.0, v_i.1, v_j.0, v_n)) :|: TRUE 2.89/1.97 eval_Loopus2011_ex1_bb0_in(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_bb1_in(v_3, 0, v_i.1, v_j.0, v_n)) :|: TRUE 2.89/1.97 eval_Loopus2011_ex1_bb1_in(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_bb2_in(v_3, v_i.0, v_i.1, v_j.0, v_n)) :|: v_i.0 < v_n 2.89/1.97 eval_Loopus2011_ex1_bb1_in(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_bb6_in(v_3, v_i.0, v_i.1, v_j.0, v_n)) :|: v_i.0 >= v_n 2.89/1.97 eval_Loopus2011_ex1_bb2_in(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_bb3_in(v_3, v_i.0, v_i.0 + 1, 0, v_n)) :|: TRUE 2.89/1.97 eval_Loopus2011_ex1_bb3_in(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_bb4_in(v_3, v_i.0, v_i.1, v_j.0, v_n)) :|: v_i.1 < v_n 2.89/1.97 eval_Loopus2011_ex1_bb3_in(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_.critedge_in(v_3, v_i.0, v_i.1, v_j.0, v_n)) :|: v_i.1 >= v_n 2.89/1.97 eval_Loopus2011_ex1_bb4_in(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_2(v_3, v_i.0, v_i.1, v_j.0, v_n)) :|: TRUE 2.89/1.97 eval_Loopus2011_ex1_2(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_2(eval_nondet_start(v_3, v_i.0, v_i.1, v_j.0, v_n), eval_Loopus2011_ex1_3(nondef.0, v_i.0, v_i.1, v_j.0, v_n)) :|: TRUE 2.89/1.97 eval_Loopus2011_ex1_3(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_bb5_in(v_3, v_i.0, v_i.1, v_j.0, v_n)) :|: v_3 > 0 2.89/1.97 eval_Loopus2011_ex1_3(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_.critedge_in(v_3, v_i.0, v_i.1, v_j.0, v_n)) :|: v_3 <= 0 2.89/1.97 eval_Loopus2011_ex1_bb5_in(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_bb3_in(v_3, v_i.0, v_i.1 + 1, v_j.0 + 1, v_n)) :|: TRUE 2.89/1.97 eval_Loopus2011_ex1_.critedge_in(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_bb1_in(v_3, v_i.1 - 1, v_i.1, v_j.0, v_n)) :|: v_j.0 > 0 2.89/1.97 eval_Loopus2011_ex1_.critedge_in(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_bb1_in(v_3, v_i.1, v_i.1, v_j.0, v_n)) :|: v_j.0 <= 0 2.89/1.97 eval_Loopus2011_ex1_bb6_in(v_3, v_i.0, v_i.1, v_j.0, v_n) -> Com_1(eval_Loopus2011_ex1_stop(v_3, v_i.0, v_i.1, v_j.0, v_n)) :|: TRUE 2.89/1.97 2.89/1.97 The start-symbols are:[eval_Loopus2011_ex1_start_5] 2.89/1.97 2.89/1.97 2.89/1.97 ---------------------------------------- 2.89/1.97 2.89/1.97 (1) Koat Proof (FINISHED) 2.89/1.97 YES(?, 208*ar_1 + 6) 2.89/1.97 2.89/1.97 2.89/1.97 2.89/1.97 Initial complexity problem: 2.89/1.97 2.89/1.97 1: T: 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb1in(0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_0 + 1 ] 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_1 ] 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4, ar_5)) 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_2 + 1 ] 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_1 ] 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex120(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex13(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5)) 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalLoopus2011ex120(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalLoopus2011ex121(ar_0, ar_1, ar_2, ar_3, ar_4, g)) 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 ] 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb3in(ar_0, ar_1, ar_2 + 1, ar_3 + 1, ar_4, ar_5)) 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb1in(ar_2 - 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 1 ] 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb1in(ar_2, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_3 ] 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.89/1.97 2.89/1.97 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.89/1.97 2.89/1.97 start location: koat_start 2.89/1.97 2.89/1.97 leaf cost: 0 2.89/1.97 2.89/1.97 2.89/1.97 2.89/1.97 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.89/1.97 2.89/1.97 2: T: 2.89/1.97 2.89/1.97 (Comp: 1, Cost: 1) evalLoopus2011ex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.89/1.97 2.89/1.97 (Comp: 1, Cost: 1) evalLoopus2011ex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb1in(0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_0 + 1 ] 2.89/1.97 2.89/1.97 (Comp: ?, Cost: 1) evalLoopus2011ex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalLoopus2011ex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_1 ] popout

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all output return to Complexity_C_Integer 2019-03-21 04.38