details

property	value
status	complete
benchmark	realheapsort_step2.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n102.star.cs.uiowa.edu
space	WTC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	30.6179537773 seconds
cpu usage	36.280368311
max memory	3.80063744E8

stage attributes

key	value
output-size	116234
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 629 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 2758 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalrealheapsortstep2start(A, B, C, D) -> Com_1(evalrealheapsortstep2entryin(A, B, C, D)) :|: TRUE evalrealheapsortstep2entryin(A, B, C, D) -> Com_1(evalrealheapsortstep2bbin(A, B, C, D)) :|: A >= 3 evalrealheapsortstep2entryin(A, B, C, D) -> Com_1(evalrealheapsortstep2returnin(A, B, C, D)) :|: 2 >= A evalrealheapsortstep2bbin(A, B, C, D) -> Com_1(evalrealheapsortstep2bb11in(A, 0, C, D)) :|: TRUE evalrealheapsortstep2bb11in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb1in(A, B, C, D)) :|: A >= 2 + B evalrealheapsortstep2bb11in(A, B, C, D) -> Com_1(evalrealheapsortstep2returnin(A, B, C, D)) :|: B + 1 >= A evalrealheapsortstep2bb1in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb9in(A, B, 0, D)) :|: TRUE evalrealheapsortstep2bb9in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb2in(A, B, C, D)) :|: A >= B + 3 + 2 * C evalrealheapsortstep2bb9in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb10in(A, B, C, D)) :|: 2 * C + 2 + B >= A evalrealheapsortstep2bb2in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb4in(A, B, C, D)) :|: A >= 2 * C + 3 + B && A <= 2 * C + 3 + B evalrealheapsortstep2bb2in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb3in(A, B, C, D)) :|: A >= B + 4 + 2 * C evalrealheapsortstep2bb2in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb3in(A, B, C, D)) :|: 2 * C + 2 + B >= A evalrealheapsortstep2bb3in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb4in(A, B, C, D)) :|: TRUE evalrealheapsortstep2bb3in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb5in(A, B, C, D)) :|: TRUE evalrealheapsortstep2bb4in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb6in(A, B, C, 2 * C + 1)) :|: TRUE evalrealheapsortstep2bb5in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb6in(A, B, C, 2 * C + 2)) :|: TRUE evalrealheapsortstep2bb6in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb7in(A, B, C, D)) :|: TRUE evalrealheapsortstep2bb6in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb9in(A, B, A, D)) :|: TRUE evalrealheapsortstep2bb7in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb9in(A, B, D, D)) :|: TRUE evalrealheapsortstep2bb10in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb11in(A, B + 1, C, D)) :|: TRUE evalrealheapsortstep2returnin(A, B, C, D) -> Com_1(evalrealheapsortstep2stop(A, B, C, D)) :|: TRUE The start-symbols are:[evalrealheapsortstep2start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 86*ar_0 + 60*ar_0^2 + 34) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealheapsortstep2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2entryin(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2returnin(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb11in(ar_0, 0, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 2 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb9in(ar_0, ar_1, 0, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 2*ar_2 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb10in(ar_0, ar_1, ar_2, ar_3)) [ 2*ar_2 + ar_1 + 2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = 2*ar_2 + ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 2*ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb3in(ar_0, ar_1, ar_2, ar_3)) [ 2*ar_2 + ar_1 + 2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb5in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb6in(ar_0, ar_1, ar_2, 2*ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb6in(ar_0, ar_1, ar_2, 2*ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb7in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb9in(ar_0, ar_1, ar_0, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb9in(ar_0, ar_1, ar_3, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb11in(ar_0, ar_1 + 1, ar_2, ar_3)) popout

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job log

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actions

all output return to Compl Integ Trans Syste 26843