details

property	value
status	complete
benchmark	sipma91.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n023.star.cs.uiowa.edu
space	WTC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.654266119 seconds
cpu usage	8.057594452
max memory	4.39873536E8

stage attributes

key	value
output-size	28745
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(6, 24354 + -221 * Arg_0) + nat(101 + -1 * Arg_0) + nat(111 + -1 * Arg_0) + nat(60702 + -551 * Arg_0) + max(2, 113 + -1 * Arg_0) + nat(max(2, 113 + -1 * Arg_0) * max(24348 + -221 * Arg_0, -183) + nat(24348 + -221 * Arg_0) * max(24348 + -221 * Arg_0, -183)) + max(4, 448 + -4 * Arg_0) + nat(max(1, 112 + -1 * Arg_0) * max(24348 + -221 * Arg_0, -183) + nat(24348 + -221 * Arg_0) * max(24348 + -221 * Arg_0, -183))). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 2969 ms] (2) BOUNDS(1, max(6, 24354 + -221 * Arg_0) + nat(101 + -1 * Arg_0) + nat(111 + -1 * Arg_0) + nat(60702 + -551 * Arg_0) + max(2, 113 + -1 * Arg_0) + nat(max(2, 113 + -1 * Arg_0) * max(24348 + -221 * Arg_0, -183) + nat(24348 + -221 * Arg_0) * max(24348 + -221 * Arg_0, -183)) + max(4, 448 + -4 * Arg_0) + nat(max(1, 112 + -1 * Arg_0) * max(24348 + -221 * Arg_0, -183) + nat(24348 + -221 * Arg_0) * max(24348 + -221 * Arg_0, -183))) (3) Loat Proof [FINISHED, 522 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalsipma91start(A, B, C, D) -> Com_1(evalsipma91entryin(A, B, C, D)) :|: TRUE evalsipma91entryin(A, B, C, D) -> Com_1(evalsipma91returnin(A, B, C, D)) :|: A >= 101 evalsipma91entryin(A, B, C, D) -> Com_1(evalsipma91bb3in(1, A, C, D)) :|: 100 >= A evalsipma91bb3in(A, B, C, D) -> Com_1(evalsipma91bb2in(A, B, C, D)) :|: 100 >= B evalsipma91bb3in(A, B, C, D) -> Com_1(evalsipma91bb11in(A, B, C, D)) :|: B >= 101 evalsipma91bb2in(A, B, C, D) -> Com_1(evalsipma91bb3in(A + 1, B + 11, C, D)) :|: TRUE evalsipma91bb11in(A, B, C, D) -> Com_1(evalsipma91bb5in(A, B, C, D)) :|: A >= 2 evalsipma91bb11in(A, B, C, D) -> Com_1(evalsipma91returnin(A, B, C, D)) :|: 1 >= A evalsipma91bb5in(A, B, C, D) -> Com_1(evalsipma91bb8in(A, B, B - 10, A - 1)) :|: 110 >= B evalsipma91bb5in(A, B, C, D) -> Com_1(evalsipma91bb8in(A, B, B - 10, A - 1)) :|: 1 >= A evalsipma91bb5in(A, B, C, D) -> Com_1(evalsipma91bb8in(A, B, B - 10, A - 1)) :|: A >= 3 evalsipma91bb5in(A, B, C, D) -> Com_1(evalsipma91bb11in(A - 1, B - 10, C, D)) :|: B >= 111 && A >= 2 && A <= 2 evalsipma91bb8in(A, B, C, D) -> Com_1(evalsipma91bb11in(D, C + 1, C, D)) :|: C >= 101 evalsipma91bb8in(A, B, C, D) -> Com_1(evalsipma91bb11in(D, C + 11, C, D)) :|: C >= 101 && 100 >= C evalsipma91bb8in(A, B, C, D) -> Com_1(evalsipma91bb11in(D + 1, C + 1, C, D)) :|: 100 >= C && C >= 101 evalsipma91bb8in(A, B, C, D) -> Com_1(evalsipma91bb11in(D + 1, C + 11, C, D)) :|: 100 >= C evalsipma91returnin(A, B, C, D) -> Com_1(evalsipma91stop(A, B, C, D)) :|: TRUE The start-symbols are:[evalsipma91start_4] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, 6+max([0, max([-183, -404+221*max([1, 112-Arg_0])])])+max([0, 101-Arg_0])+max([2, 2*max([1, 112-Arg_0])])+max([1, 112-Arg_0])+max([0, (max([1, 112-Arg_0])+max([0, max([-183, -404+221*max([1, 112-Arg_0])])]))*max([-183, -404+221*max([1, 112-Arg_0])])])+max([0, 111-Arg_0])+max([0, max([-459, -1010+551*max([1, 112-Arg_0])])])+max([0, (1+max([1, 112-Arg_0])+max([0, max([-183, -404+221*max([1, 112-Arg_0])])]))*max([-183, -404+221*max([1, 112-Arg_0])])])+max([1, 112-Arg_0])+max([2, 113-Arg_0]) {O(n^2)}) Initial Complexity Problem: Start: evalsipma91start Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3 Temp_Vars: Locations: evalsipma91bb11in, evalsipma91bb2in, evalsipma91bb3in, evalsipma91bb5in, evalsipma91bb8in, evalsipma91entryin, evalsipma91returnin, evalsipma91start, evalsipma91stop Transitions: evalsipma91bb11in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb5in(Arg_0,Arg_1,Arg_2,Arg_3):|:101 <= Arg_1 && 102 <= Arg_0+Arg_1 && 1 <= Arg_0 && 2 <= Arg_0 evalsipma91bb11in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:101 <= Arg_1 && 102 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_0 <= 1 evalsipma91bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb3in(Arg_0+1,Arg_1+11,Arg_2,Arg_3):|:Arg_1 <= 100 && Arg_1 <= 99+Arg_0 && 1 <= Arg_0 evalsipma91bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb11in(Arg_0,Arg_1,Arg_2,Arg_3):|:1 <= Arg_0 && 101 <= Arg_1 evalsipma91bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb2in(Arg_0,Arg_1,Arg_2,Arg_3):|:1 <= Arg_0 && Arg_1 <= 100 evalsipma91bb5in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb11in(Arg_0-1,Arg_1-10,Arg_2,Arg_3):|:101 <= Arg_1 && 103 <= Arg_0+Arg_1 && 2 <= Arg_0 && 111 <= Arg_1 && Arg_0 <= 2 && 2 <= Arg_0 evalsipma91bb5in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb8in(Arg_0,Arg_1,Arg_1-10,Arg_0-1):|:101 <= Arg_1 && 103 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_1 <= 110 evalsipma91bb5in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb8in(Arg_0,Arg_1,Arg_1-10,Arg_0-1):|:101 <= Arg_1 && 103 <= Arg_0+Arg_1 && 2 <= Arg_0 && 3 <= Arg_0 evalsipma91bb8in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb11in(Arg_3,Arg_2+1,Arg_2,Arg_3):|:1+Arg_3 <= Arg_0 && 1 <= Arg_3 && 92 <= Arg_2+Arg_3 && 102 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && Arg_0 <= 1+Arg_3 && 10+Arg_2 <= Arg_1 && 91 <= Arg_2 && 192 <= Arg_1+Arg_2 && Arg_1 <= 10+Arg_2 && 93 <= Arg_0+Arg_2 && 101 <= Arg_1 && 103 <= Arg_0+Arg_1 && 2 <= Arg_0 && 101 <= Arg_2 evalsipma91bb8in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb11in(Arg_3+1,Arg_2+11,Arg_2,Arg_3):|:1+Arg_3 <= Arg_0 && 1 <= Arg_3 && 92 <= Arg_2+Arg_3 && 102 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && Arg_0 <= 1+Arg_3 && 10+Arg_2 <= Arg_1 && 91 <= Arg_2 && 192 <= Arg_1+Arg_2 && Arg_1 <= 10+Arg_2 && 93 <= Arg_0+Arg_2 && 101 <= Arg_1 && 103 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_2 <= 100 evalsipma91entryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb3in(1,Arg_0,Arg_2,Arg_3):|:Arg_0 <= 100 evalsipma91entryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:101 <= Arg_0 evalsipma91returnin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91stop(Arg_0,Arg_1,Arg_2,Arg_3):|: evalsipma91start(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91entryin(Arg_0,Arg_1,Arg_2,Arg_3):|: Timebounds: Overall timebound: 6+max([0, max([-183, -404+221*max([1, 112-Arg_0])])])+max([0, 101-Arg_0])+max([2, 2*max([1, 112-Arg_0])])+max([1, 112-Arg_0])+max([0, (max([1, 112-Arg_0])+max([0, max([-183, -404+221*max([1, 112-Arg_0])])]))*max([-183, -404+221*max([1, 112-Arg_0])])])+max([0, 111-Arg_0])+max([0, max([-459, -1010+551*max([1, 112-Arg_0])])])+max([0, (1+max([1, 112-Arg_0])+max([0, max([-183, -404+221*max([1, 112-Arg_0])])]))*max([-183, -404+221*max([1, 112-Arg_0])])])+max([1, 112-Arg_0])+max([2, 113-Arg_0]) {O(n^2)} 6: evalsipma91bb11in->evalsipma91bb5in: max([0, (1+max([1, 112-Arg_0])+max([0, max([-183, -404+221*max([1, 112-Arg_0])])]))*max([-183, -404+221*max([1, 112-Arg_0])])])+max([2, 113-Arg_0]) {O(n^2)} popout

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all output return to Compl Integ Trans Syste 26843