details

property	value
status	complete
benchmark	realheapsort_step2.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n057.star.cs.uiowa.edu
space	WTC_V2

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	9.63798 seconds
cpu usage	7.78238
user time	7.09889
system time	0.683495
max virtual memory	1.8824764E7
max residence set size	383012.0

stage attributes

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

output

7.66/6.37 WORST_CASE(?, O(n^2)) 7.66/6.39 proof of /export/starexec/sandbox/output/output_files/bench.koat 7.66/6.39 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.66/6.39 7.66/6.39 7.66/6.39 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 7.66/6.39 7.66/6.39 (0) CpxIntTrs 7.66/6.39 (1) Koat Proof [FINISHED, 5002 ms] 7.66/6.39 (2) BOUNDS(1, n^2) 7.66/6.39 7.66/6.39 7.66/6.39 ---------------------------------------- 7.66/6.39 7.66/6.39 (0) 7.66/6.39 Obligation: 7.66/6.39 Complexity Int TRS consisting of the following rules: 7.66/6.39 eval_realheapsort_step2_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb0_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_bb0_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb1_in(v_14, v_15, v_21, v_22, v_N, v_j.0, 0, v_m.0)) :|: v_N > 2 7.66/6.39 eval_realheapsort_step2_bb0_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb11_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: v_N <= 2 7.66/6.39 eval_realheapsort_step2_bb1_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb2_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: v_k.0 <= v_N - 2 7.66/6.39 eval_realheapsort_step2_bb1_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb11_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: v_k.0 > v_N - 2 7.66/6.39 eval_realheapsort_step2_bb2_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_2(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_2(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_2(eval_nondet_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0), eval_realheapsort_step2_3(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_3(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb3_in(v_14, v_15, v_21, v_22, v_N, 0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_bb3_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb4_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: 2 * v_j.0 + 1 <= v_N - v_k.0 - 2 7.66/6.39 eval_realheapsort_step2_bb3_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb10_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: 2 * v_j.0 + 1 > v_N - v_k.0 - 2 7.66/6.39 eval_realheapsort_step2_bb4_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb6_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: 2 * v_j.0 + 1 >= v_N - v_k.0 - 2 && 2 * v_j.0 + 1 <= v_N - v_k.0 - 2 7.66/6.39 eval_realheapsort_step2_bb4_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb5_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: 2 * v_j.0 + 1 < v_N - v_k.0 - 2 7.66/6.39 eval_realheapsort_step2_bb4_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb5_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: 2 * v_j.0 + 1 > v_N - v_k.0 - 2 7.66/6.39 eval_realheapsort_step2_bb5_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_14(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_14(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_2(eval_nondet_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0), eval_realheapsort_step2_15(nondef.1, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_15(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_2(eval_nondet_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0), eval_realheapsort_step2_16(v_14, nondef.2, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_16(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb6_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: v_14 < v_15 7.66/6.39 eval_realheapsort_step2_16(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb7_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: v_14 >= v_15 7.66/6.39 eval_realheapsort_step2_bb6_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb8_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, 2 * v_j.0 + 1)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_bb7_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb8_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, 2 * v_j.0 + 2)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_bb8_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_23(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_23(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_2(eval_nondet_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0), eval_realheapsort_step2_24(v_14, v_15, nondef.3, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_24(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_2(eval_nondet_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0), eval_realheapsort_step2_25(v_14, v_15, v_21, nondef.4, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_25(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb9_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: v_21 > v_22 7.66/6.39 eval_realheapsort_step2_25(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb3_in(v_14, v_15, v_21, v_22, v_N, v_N, v_k.0, v_m.0)) :|: v_21 <= v_22 7.66/6.39 eval_realheapsort_step2_bb9_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_26(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_26(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_2(eval_nondet_start(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0), eval_realheapsort_step2_27(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_27(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb3_in(v_14, v_15, v_21, v_22, v_N, v_m.0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_bb10_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_bb1_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0 + 1, v_m.0)) :|: TRUE 7.66/6.39 eval_realheapsort_step2_bb11_in(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0) -> Com_1(eval_realheapsort_step2_stop(v_14, v_15, v_21, v_22, v_N, v_j.0, v_k.0, v_m.0)) :|: TRUE 7.66/6.39 7.66/6.39 The start-symbols are:[eval_realheapsort_step2_start_8] 7.66/6.39 7.66/6.39 7.66/6.39 ---------------------------------------- 7.66/6.39 7.66/6.39 (1) Koat Proof (FINISHED) 7.66/6.39 YES(?, 7520*ar_0 + 2496*ar_0^2 + 5031) 7.66/6.39 7.66/6.39 7.66/6.39 7.66/6.39 Initial complexity problem: 7.66/6.39 7.66/6.39 1: T: 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb1in(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= 3 ] 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb11in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 2 >= ar_0 ] 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= ar_1 + 2 ] 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb11in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_1 + 1 >= ar_0 ] 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_2(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8), evalrealheapsortstep23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb3in(ar_0, ar_1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= ar_1 + 2*ar_2 + 3 ] 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb10in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 2*ar_2 + ar_1 + 2 >= ar_0 ] 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 = 2*ar_2 + ar_1 + 3 ] 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= ar_1 + 2*ar_2 + 4 ] 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 2*ar_2 + ar_1 + 2 >= ar_0 ] 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep214(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2140(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)) 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2141(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep215(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5, ar_6, ar_7, ar_8)) 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep214(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_2(evalrealheapsortstep2140(ar_0, ar_1, ar_2, ar_3, j, ar_5, ar_6, ar_7, ar_8), evalrealheapsortstep2141(ar_0, ar_1, ar_2, ar_3, j, ar_5, ar_6, ar_7, ar_8)) 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2150(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)) 7.66/6.39 7.66/6.39 (Comp: ?, Cost: 1) evalrealheapsortstep2151(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrealheapsortstep216(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_6, ar_7, ar_8)) 7.66/6.39 popout

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all output return to Complexity_C_Integer 2019-03-21 04.38