details

property	value
status	complete
benchmark	heapsort.c.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n122.star.cs.uiowa.edu
space	Flores-Montoya_16

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	21.3562 seconds
cpu usage	40.1751
user time	39.0638
system time	1.11134
max virtual memory	1.9006068E7
max residence set size	369636.0

stage attributes

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

output

40.07/21.33 WORST_CASE(?, O(n^1)) 40.07/21.34 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 40.07/21.34 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 40.07/21.34 40.07/21.34 40.07/21.34 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 40.07/21.34 40.07/21.34 (0) CpxIntTrs 40.07/21.34 (1) Koat Proof [FINISHED, 2630 ms] 40.07/21.34 (2) BOUNDS(1, n^1) 40.07/21.34 40.07/21.34 40.07/21.34 ---------------------------------------- 40.07/21.34 40.07/21.34 (0) 40.07/21.34 Obligation: 40.07/21.34 Complexity Int TRS consisting of the following rules: 40.07/21.34 eval_heapsort_start(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb0_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_bb0_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_0(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_0(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_1(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_1(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_2(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_2(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_3(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_3(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_4(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_4(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_5(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_5(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_6(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_6(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_7(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_7(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_8(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_8(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_9(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_9(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb1_in(v_13, v_2, v_4, v_8, 1, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_bb1_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb2_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_size > 0 && v_i_0 >= 1 40.07/21.34 eval_heapsort_bb1_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb11_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_size <= 0 40.07/21.34 eval_heapsort_bb1_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb11_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_i_0 < 1 40.07/21.34 eval_heapsort_bb2_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb3_in(v_13, 2 * v_i_0, 2 * v_i_0 + 1, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: 2 * v_i_0 <= v_size 40.07/21.34 eval_heapsort_bb2_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb5_in(v_13, 2 * v_i_0, 2 * v_i_0 + 1, v_8, v_i_0, v_i_0, v_max_3, v_size)) :|: 2 * v_i_0 > v_size 40.07/21.34 eval_heapsort_bb3_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb11_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_2 < 1 40.07/21.34 eval_heapsort_bb3_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb11_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_2 > v_size 40.07/21.34 eval_heapsort_bb3_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb4_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_2 >= 1 && v_2 <= v_size 40.07/21.34 eval_heapsort_bb4_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_14(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_14(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_15(v_13, v_2, v_4, nondef_0, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_15(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb5_in(v_13, v_2, v_4, v_8, v_i_0, v_2, v_max_3, v_size)) :|: v_8 > 0 40.07/21.34 eval_heapsort_15(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb5_in(v_13, v_2, v_4, v_8, v_i_0, v_i_0, v_max_3, v_size)) :|: v_8 <= 0 40.07/21.34 eval_heapsort_bb5_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb6_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_4 <= v_size 40.07/21.34 eval_heapsort_bb5_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb8_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_1, v_size)) :|: v_4 > v_size 40.07/21.34 eval_heapsort_bb6_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb11_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_4 < 1 40.07/21.34 eval_heapsort_bb6_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb11_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_4 > v_size 40.07/21.34 eval_heapsort_bb6_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb7_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_4 >= 1 && v_4 <= v_size 40.07/21.34 eval_heapsort_bb7_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_17(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_17(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_18(nondef_1, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 eval_heapsort_18(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb8_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_4, v_size)) :|: v_13 > 0 40.07/21.34 eval_heapsort_18(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb8_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_1, v_size)) :|: v_13 <= 0 40.07/21.34 eval_heapsort_bb8_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb9_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_i_0 < v_max_3 40.07/21.34 eval_heapsort_bb8_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb9_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_i_0 > v_max_3 40.07/21.34 eval_heapsort_bb8_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb11_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_i_0 >= v_max_3 && v_i_0 <= v_max_3 40.07/21.34 eval_heapsort_bb9_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb11_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_i_0 < 1 40.07/21.34 eval_heapsort_bb9_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb11_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_i_0 > v_size 40.07/21.34 eval_heapsort_bb9_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb10_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_i_0 >= 1 && v_i_0 <= v_size 40.07/21.34 eval_heapsort_bb10_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb11_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_max_3 < 1 40.07/21.34 eval_heapsort_bb10_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb11_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: v_max_3 > v_size 40.07/21.34 eval_heapsort_bb10_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_bb1_in(v_13, v_2, v_4, v_8, v_max_3, v_max_1, v_max_3, v_size)) :|: v_max_3 >= 1 && v_max_3 <= v_size 40.07/21.34 eval_heapsort_bb11_in(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size) -> Com_1(eval_heapsort_stop(v_13, v_2, v_4, v_8, v_i_0, v_max_1, v_max_3, v_size)) :|: TRUE 40.07/21.34 40.07/21.34 The start-symbols are:[eval_heapsort_start_8] 40.07/21.34 40.07/21.34 40.07/21.34 ---------------------------------------- 40.07/21.34 40.07/21.34 (1) Koat Proof (FINISHED) 40.07/21.34 YES(?, 288*ar_1 + 25) 40.07/21.34 40.07/21.34 40.07/21.34 40.07/21.34 Initial complexity problem: 40.07/21.34 40.07/21.34 1: T: 40.07/21.34 40.07/21.34 (Comp: ?, Cost: 1) evalheapsortstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalheapsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 40.07/21.34 40.07/21.34 (Comp: ?, Cost: 1) evalheapsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalheapsort0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 40.07/21.34 40.07/21.34 (Comp: ?, Cost: 1) evalheapsort0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalheapsort1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 40.07/21.34 40.07/21.34 (Comp: ?, Cost: 1) evalheapsort1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalheapsort2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 40.07/21.34 40.07/21.34 (Comp: ?, Cost: 1) evalheapsort2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalheapsort3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 40.07/21.34 40.07/21.34 (Comp: ?, Cost: 1) evalheapsort3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalheapsort4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 40.07/21.34 40.07/21.34 (Comp: ?, Cost: 1) evalheapsort4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalheapsort5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 40.07/21.34 40.07/21.34 (Comp: ?, Cost: 1) evalheapsort5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalheapsort6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 40.07/21.34 40.07/21.34 (Comp: ?, Cost: 1) evalheapsort6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalheapsort7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 40.07/21.34 40.07/21.34 (Comp: ?, Cost: 1) evalheapsort7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalheapsort8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 40.07/21.34 40.07/21.34 (Comp: ?, Cost: 1) evalheapsort8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalheapsort9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 40.07/21.34 40.07/21.34 (Comp: ?, Cost: 1) evalheapsort9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalheapsortbb1in(1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 40.07/21.34 40.07/21.34 (Comp: ?, Cost: 1) evalheapsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalheapsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 >= 1 /\ ar_0 >= 1 ] popout

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all output return to Complexity_ITS 2019-03-21 04.46