details

property	value
status	complete
benchmark	heapsort.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n114.star.cs.uiowa.edu
space	WTC_V2

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	4.16514110565 seconds
cpu usage	5.64025353
max memory	5.34212608E8

stage attributes

key	value
output-size	127632
starexec-result	WORST_CASE(?, O(n^1))

output

/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 2887 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_heapsort_start(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb0_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: TRUE eval_heapsort_bb0_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb1_in(v_14, v_3, v_5, v_9, 1, v_max.1, v_max.3, v_size)) :|: TRUE eval_heapsort_bb1_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb2_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_size > 0 && v_i.0 >= 1 eval_heapsort_bb1_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb11_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_size <= 0 eval_heapsort_bb1_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb11_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_i.0 < 1 eval_heapsort_bb2_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb3_in(v_14, 2 * v_i.0, 2 * v_i.0 + 1, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: 2 * v_i.0 <= v_size eval_heapsort_bb2_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb5_in(v_14, 2 * v_i.0, 2 * v_i.0 + 1, v_9, v_i.0, v_i.0, v_max.3, v_size)) :|: 2 * v_i.0 > v_size eval_heapsort_bb3_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb11_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_3 < 1 eval_heapsort_bb3_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb11_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_3 > v_size eval_heapsort_bb3_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb4_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_3 >= 1 && v_3 <= v_size eval_heapsort_bb4_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_4(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: TRUE eval_heapsort_4(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_2(eval_nondet_start(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size), eval_heapsort_5(v_14, v_3, v_5, nondef.0, v_i.0, v_max.1, v_max.3, v_size)) :|: TRUE eval_heapsort_5(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb5_in(v_14, v_3, v_5, v_9, v_i.0, v_3, v_max.3, v_size)) :|: v_9 > 0 eval_heapsort_5(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb5_in(v_14, v_3, v_5, v_9, v_i.0, v_i.0, v_max.3, v_size)) :|: v_9 <= 0 eval_heapsort_bb5_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb6_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_5 <= v_size eval_heapsort_bb5_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb8_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.1, v_size)) :|: v_5 > v_size eval_heapsort_bb6_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb11_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_5 < 1 eval_heapsort_bb6_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb11_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_5 > v_size eval_heapsort_bb6_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb7_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_5 >= 1 && v_5 <= v_size eval_heapsort_bb7_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_7(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: TRUE eval_heapsort_7(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_2(eval_nondet_start(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size), eval_heapsort_8(nondef.1, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: TRUE eval_heapsort_8(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb8_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_5, v_size)) :|: v_14 > 0 eval_heapsort_8(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb8_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.1, v_size)) :|: v_14 <= 0 eval_heapsort_bb8_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb9_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_i.0 < v_max.3 eval_heapsort_bb8_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb9_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_i.0 > v_max.3 eval_heapsort_bb8_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb11_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_i.0 >= v_max.3 && v_i.0 <= v_max.3 eval_heapsort_bb9_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb11_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_i.0 < 1 eval_heapsort_bb9_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb11_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_i.0 > v_size eval_heapsort_bb9_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb10_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_i.0 >= 1 && v_i.0 <= v_size eval_heapsort_bb10_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb11_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_max.3 < 1 eval_heapsort_bb10_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb11_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: v_max.3 > v_size eval_heapsort_bb10_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_bb1_in(v_14, v_3, v_5, v_9, v_max.3, v_max.1, v_max.3, v_size)) :|: v_max.3 >= 1 && v_max.3 <= v_size eval_heapsort_bb11_in(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size) -> Com_1(eval_heapsort_stop(v_14, v_3, v_5, v_9, v_i.0, v_max.1, v_max.3, v_size)) :|: TRUE The start-symbols are:[eval_heapsort_start_8] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 448*ar_1 + 15) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalheapsortstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalheapsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) (Comp: ?, Cost: 1) evalheapsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalheapsortbb1in(1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) (Comp: ?, Cost: 1) evalheapsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalheapsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_1 >= 1 /\ ar_0 >= 1 ] (Comp: ?, Cost: 1) evalheapsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalheapsortbb11in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 >= ar_1 ] (Comp: ?, Cost: 1) evalheapsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalheapsortbb11in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalheapsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalheapsortbb3in(ar_0, ar_1, 2*ar_0, 2*ar_0 + 1, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_1 >= 2*ar_0 ] (Comp: ?, Cost: 1) evalheapsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalheapsortbb5in(ar_0, ar_1, 2*ar_0, 2*ar_0 + 1, ar_0, ar_5, ar_6, ar_7, ar_8)) [ 2*ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalheapsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalheapsortbb11in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalheapsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalheapsortbb11in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_2 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalheapsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalheapsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_2 >= 1 /\ ar_1 >= ar_2 ] (Comp: ?, Cost: 1) evalheapsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalheapsort4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) (Comp: ?, Cost: 1) evalheapsort40(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)) (Comp: ?, Cost: 1) evalheapsort41(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalheapsort5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6, ar_7, ar_8)) (Comp: ?, Cost: 1) evalheapsort4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_2(evalheapsort40(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, j, ar_7, ar_8), evalheapsort41(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, j, ar_7, ar_8)) (Comp: ?, Cost: 1) evalheapsort5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalheapsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5, ar_6, ar_7, ar_8)) [ ar_5 >= 1 ] popout

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all output return to Compl C Integ Progr 85445