details

property	value
status	complete
benchmark	speed_pldi10_ex1.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n046.star.cs.uiowa.edu
space	C4B_examples

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	2.96921 seconds
cpu usage	3.83951
user time	3.55625
system time	0.283263
max virtual memory	1.8597884E7
max residence set size	185004.0

stage attributes

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

output

3.69/2.93 WORST_CASE(?, O(n^2)) 3.69/2.94 proof of /export/starexec/sandbox2/output/output_files/bench.koat 3.69/2.94 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.69/2.94 3.69/2.94 3.69/2.94 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 3.69/2.94 3.69/2.94 (0) CpxIntTrs 3.69/2.94 (1) Koat Proof [FINISHED, 1590 ms] 3.69/2.94 (2) BOUNDS(1, n^2) 3.69/2.94 3.69/2.94 3.69/2.94 ---------------------------------------- 3.69/2.94 3.69/2.94 (0) 3.69/2.94 Obligation: 3.69/2.94 Complexity Int TRS consisting of the following rules: 3.69/2.94 eval_speed_pldi10_ex1_start(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_bb0_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n)) :|: TRUE 3.69/2.94 eval_speed_pldi10_ex1_bb0_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_bb1_in(v_n, v_.1, v_.2, v_3, 0, v_j.0, v_j.1, v_n)) :|: TRUE 3.69/2.94 eval_speed_pldi10_ex1_bb1_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_bb2_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n)) :|: v_i.0 < v_.0 3.69/2.94 eval_speed_pldi10_ex1_bb1_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_bb8_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n)) :|: v_i.0 >= v_.0 3.69/2.94 eval_speed_pldi10_ex1_bb2_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_bb3_in(v_.0, v_.0, v_.2, v_3, v_i.0, v_i.0 + 1, v_j.1, v_n)) :|: TRUE 3.69/2.94 eval_speed_pldi10_ex1_bb3_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_bb4_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n)) :|: v_j.0 < v_.1 3.69/2.94 eval_speed_pldi10_ex1_bb3_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_bb7_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n)) :|: v_j.0 >= v_.1 3.69/2.94 eval_speed_pldi10_ex1_bb4_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_2(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n)) :|: TRUE 3.69/2.94 eval_speed_pldi10_ex1_2(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_2(eval_nondet_start(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n), eval_speed_pldi10_ex1_3(v_.0, v_.1, v_.2, nondef.0, v_i.0, v_j.0, v_j.1, v_n)) :|: TRUE 3.69/2.94 eval_speed_pldi10_ex1_3(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_bb5_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n)) :|: v_3 > 0 3.69/2.94 eval_speed_pldi10_ex1_3(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_bb6_in(v_.0, v_.1, v_.1, v_3, v_i.0, v_j.0, v_j.0, v_n)) :|: v_3 <= 0 3.69/2.94 eval_speed_pldi10_ex1_bb5_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_bb6_in(v_.0, v_.1, v_.1 - 1, v_3, v_i.0, v_j.0, v_j.0 - 1, v_n)) :|: TRUE 3.69/2.94 eval_speed_pldi10_ex1_bb6_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_bb3_in(v_.0, v_.2, v_.2, v_3, v_i.0, v_j.1 + 1, v_j.1, v_n)) :|: TRUE 3.69/2.94 eval_speed_pldi10_ex1_bb7_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_bb1_in(v_.1, v_.1, v_.2, v_3, v_i.0 + 1, v_j.0, v_j.1, v_n)) :|: TRUE 3.69/2.94 eval_speed_pldi10_ex1_bb8_in(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n) -> Com_1(eval_speed_pldi10_ex1_stop(v_.0, v_.1, v_.2, v_3, v_i.0, v_j.0, v_j.1, v_n)) :|: TRUE 3.69/2.94 3.69/2.94 The start-symbols are:[eval_speed_pldi10_ex1_start_8] 3.69/2.94 3.69/2.94 3.69/2.94 ---------------------------------------- 3.69/2.94 3.69/2.94 (1) Koat Proof (FINISHED) 3.69/2.94 YES(?, 248*ar_1 + 784*ar_1^2 + 6) 3.69/2.94 3.69/2.94 3.69/2.94 3.69/2.94 Initial complexity problem: 3.69/2.94 3.69/2.94 1: T: 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb1in(ar_1, ar_1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= ar_2 + 1 ] 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_2 >= ar_0 ] 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb3in(ar_0, ar_1, ar_2, ar_0, ar_2 + 1, ar_5, ar_6, ar_7, ar_8)) 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_3 >= ar_4 + 1 ] 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_4 >= ar_3 ] 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex120(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6, ar_7, ar_8)) 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_2(evalspeedpldi10ex120(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, j, ar_7, ar_8), evalspeedpldi10ex121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, j, ar_7, ar_8)) 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_5 >= 1 ] 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_3, ar_4)) [ 0 >= ar_5 ] 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_3 - 1, ar_4 - 1)) 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb3in(ar_0, ar_1, ar_2, ar_7, ar_8 + 1, ar_5, ar_6, ar_7, ar_8)) 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb1in(ar_3, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1bb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.69/2.94 3.69/2.94 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 <= 0 ] 3.69/2.94 3.69/2.94 start location: koat_start 3.69/2.94 3.69/2.94 leaf cost: 0 3.69/2.94 3.69/2.94 3.69/2.94 3.69/2.94 Repeatedly propagating knowledge in problem 1 produces the following problem: 3.69/2.94 3.69/2.94 2: T: 3.69/2.94 3.69/2.94 (Comp: 1, Cost: 1) evalspeedpldi10ex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.69/2.94 3.69/2.94 (Comp: 1, Cost: 1) evalspeedpldi10ex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb1in(ar_1, ar_1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= ar_2 + 1 ] 3.69/2.94 3.69/2.94 (Comp: ?, Cost: 1) evalspeedpldi10ex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpldi10ex1bb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_2 >= ar_0 ] popout

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all output return to Complexity_C_Integer 2019-03-21 04.38