details

property	value
status	complete
benchmark	nestedLoop.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n154.star.cs.uiowa.edu
space	WTC_V2

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	48.3583 seconds
cpu usage	50.2081
user time	47.9056
system time	2.30254
max virtual memory	1.8786384E7
max residence set size	336936.0

stage attributes

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

output

50.07/48.29 WORST_CASE(?, O(n^3)) 50.07/48.31 proof of /export/starexec/sandbox/output/output_files/bench.koat 50.07/48.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 50.07/48.31 50.07/48.31 50.07/48.31 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3). 50.07/48.31 50.07/48.31 (0) CpxIntTrs 50.07/48.31 (1) Koat Proof [FINISHED, 47.1 s] 50.07/48.31 (2) BOUNDS(1, n^3) 50.07/48.31 50.07/48.31 50.07/48.31 ---------------------------------------- 50.07/48.31 50.07/48.31 (0) 50.07/48.31 Obligation: 50.07/48.31 Complexity Int TRS consisting of the following rules: 50.07/48.31 eval_nestedLoop_start(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb0_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 50.07/48.31 eval_nestedLoop_bb0_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb1_in(v_11, v_12, v_3, v_7, v_N, 0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 <= v_n && 0 <= v_m && 0 <= v_N 50.07/48.31 eval_nestedLoop_bb0_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb7_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 > v_n 50.07/48.31 eval_nestedLoop_bb0_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb7_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 > v_m 50.07/48.31 eval_nestedLoop_bb0_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb7_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 > v_N 50.07/48.31 eval_nestedLoop_bb1_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_0(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 50.07/48.31 eval_nestedLoop_0(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_2(eval_nondet_start(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n), eval_nestedLoop_1(v_11, v_12, nondef.0, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 50.07/48.31 eval_nestedLoop_1(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb2_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.0, 0, v_k.0, v_m, v_n)) :|: v_3 > 0 && v_i.0 < v_n 50.07/48.31 eval_nestedLoop_1(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb7_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_3 <= 0 50.07/48.31 eval_nestedLoop_1(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb7_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_i.0 >= v_n 50.07/48.31 eval_nestedLoop_bb2_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_2(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 50.07/48.31 eval_nestedLoop_2(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_2(eval_nondet_start(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n), eval_nestedLoop_3(v_11, v_12, v_3, nondef.1, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 50.07/48.31 eval_nestedLoop_3(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb3_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_7 > 0 && v_j.0 < v_m 50.07/48.31 eval_nestedLoop_3(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb6_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_7 <= 0 50.07/48.31 eval_nestedLoop_3(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb6_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_j.0 >= v_m 50.07/48.31 eval_nestedLoop_bb3_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb4_in(v_j.0 + 1, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_i.1, v_m, v_n)) :|: TRUE 50.07/48.31 eval_nestedLoop_bb4_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_6(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 50.07/48.31 eval_nestedLoop_6(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_2(eval_nondet_start(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n), eval_nestedLoop_7(v_11, nondef.2, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 50.07/48.31 eval_nestedLoop_7(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb5_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_12 > 0 && v_k.0 < v_N 50.07/48.31 eval_nestedLoop_7(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb2_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_k.0, v_11, v_k.0, v_m, v_n)) :|: v_12 <= 0 50.07/48.31 eval_nestedLoop_7(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb2_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_k.0, v_11, v_k.0, v_m, v_n)) :|: v_k.0 >= v_N 50.07/48.31 eval_nestedLoop_bb5_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb4_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0 + 1, v_m, v_n)) :|: TRUE 50.07/48.31 eval_nestedLoop_bb6_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb1_in(v_11, v_12, v_3, v_7, v_N, v_i.1 + 1, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 50.07/48.31 eval_nestedLoop_bb7_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_stop(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 50.07/48.31 50.07/48.31 The start-symbols are:[eval_nestedLoop_start_11] 50.07/48.31 50.07/48.31 50.07/48.31 ---------------------------------------- 50.07/48.31 50.07/48.31 (1) Koat Proof (FINISHED) 50.07/48.31 YES(?, 21960*ar_0 + 54750*ar_0*ar_1 + 26745*ar_1 + 2880*ar_0*ar_1*ar_2 + 1440*ar_1*ar_2 + 1152*ar_0*ar_2 + 2520*ar_0^2*ar_1 + 1008*ar_0^2 + 576*ar_2 + 10742) 50.07/48.31 50.07/48.31 50.07/48.31 50.07/48.31 Initial complexity problem: 50.07/48.31 50.07/48.31 1: T: 50.07/48.31 50.07/48.31 (Comp: ?, Cost: 1) evalnestedLoopstart(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(evalnestedLoopbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 50.07/48.31 50.07/48.31 (Comp: ?, Cost: 1) evalnestedLoopbb0in(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(evalnestedLoopbb1in(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_0 >= 0 /\ ar_1 >= 0 /\ ar_2 >= 0 ] 50.07/48.31 50.07/48.31 (Comp: ?, Cost: 1) evalnestedLoopbb0in(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(evalnestedLoopbb7in(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 + 1 ] 50.07/48.31 50.07/48.31 (Comp: ?, Cost: 1) evalnestedLoopbb0in(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(evalnestedLoopbb7in(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 + 1 ] 50.07/48.31 50.07/48.31 (Comp: ?, Cost: 1) evalnestedLoopbb0in(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(evalnestedLoopbb7in(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_2 + 1 ] 50.07/48.31 50.07/48.31 (Comp: ?, Cost: 1) evalnestedLoopbb1in(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(evalnestedLoop0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 50.07/48.31 50.07/48.31 (Comp: ?, Cost: 1) evalnestedLoop00(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(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoop01(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(evalnestedLoop1(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoop0(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_2(evalnestedLoop00(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11), evalnestedLoop01(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoop1(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(evalnestedLoopbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_3, 0, ar_8, ar_9, ar_10, ar_11)) [ ar_4 >= 1 /\ ar_0 >= ar_3 + 1 ] 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoop1(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(evalnestedLoopbb7in(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_4 ] 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoop1(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(evalnestedLoopbb7in(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_3 >= ar_0 ] 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoopbb2in(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(evalnestedLoop2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoop20(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(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoop21(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(evalnestedLoop3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_5, ar_9, ar_10, ar_11)) 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoop2(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_2(evalnestedLoop20(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11), evalnestedLoop21(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoop3(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(evalnestedLoopbb3in(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_8 >= 1 /\ ar_1 >= ar_7 + 1 ] 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoop3(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(evalnestedLoopbb6in(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_8 ] 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoop3(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(evalnestedLoopbb6in(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_7 >= ar_1 ] 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoopbb3in(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(evalnestedLoopbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_7 + 1, ar_6, ar_11)) 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoopbb4in(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(evalnestedLoop6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 50.11/48.31 50.11/48.31 (Comp: ?, Cost: 1) evalnestedLoop60(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(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 50.11/48.31 popout

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all output return to Complexity_C_Integer 2019-03-21 04.38