details

property	value
status	complete
benchmark	ex03.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n042.star.cs.uiowa.edu
space	ABC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	12.0651540756 seconds
cpu usage	16.880414943
max memory	3.26672384E8

stage attributes

key	value
output-size	37809
starexec-result	WORST_CASE(Omega(n^4), O(n^5))

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^4), O(n^5)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^4, 3 + max(1, 1 + 3 * Arg_1 * max(1, -1 + 3 * Arg_1) + min(2 + -6 * Arg_1, -2)) * nat(-1 + Arg_1) * max(3, -1 + 2 * Arg_1) * max(1, -1 + 3 * Arg_1) + nat(-4 * Arg_4) * max(1, -1 + 3 * Arg_1) + max(1, 1 + 3 * Arg_1 * max(1, -1 + 3 * Arg_1) + min(2 + -6 * Arg_1, -2)) + max(1, 1 + 3 * Arg_1 * max(1, -1 + 3 * Arg_1) + min(2 + -6 * Arg_1, -2)) * nat(-1 + Arg_1) + max(1, 1 + 3 * Arg_1 * max(1, -1 + 3 * Arg_1) + min(2 + -6 * Arg_1, -2)) * nat(-1 + Arg_1) * max(3, -1 + 2 * Arg_1) + max(1, 1 + 3 * Arg_1 * max(1, -1 + 3 * Arg_1) + min(2 + -6 * Arg_1, -2)) * max(9, -2 + 11 * Arg_1) + max(1, 1 + 3 * Arg_1 * max(1, -1 + 3 * Arg_1) + min(2 + -6 * Arg_1, -2)) * nat(-2 + 2 * Arg_1) + nat(-4 * Arg_4) + max(4 + 6 * Arg_1 * max(-2 + 6 * Arg_1, 4) + min(8 + -24 * Arg_1, -8), 4) + nat(-2 + 3 * Arg_1) + max(1, 1 + Arg_1)). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 10.4 s] (2) BOUNDS(1, 3 + max(1, 1 + 3 * Arg_1 * max(1, -1 + 3 * Arg_1) + min(2 + -6 * Arg_1, -2)) * nat(-1 + Arg_1) * max(3, -1 + 2 * Arg_1) * max(1, -1 + 3 * Arg_1) + nat(-4 * Arg_4) * max(1, -1 + 3 * Arg_1) + max(1, 1 + 3 * Arg_1 * max(1, -1 + 3 * Arg_1) + min(2 + -6 * Arg_1, -2)) + max(1, 1 + 3 * Arg_1 * max(1, -1 + 3 * Arg_1) + min(2 + -6 * Arg_1, -2)) * nat(-1 + Arg_1) + max(1, 1 + 3 * Arg_1 * max(1, -1 + 3 * Arg_1) + min(2 + -6 * Arg_1, -2)) * nat(-1 + Arg_1) * max(3, -1 + 2 * Arg_1) + max(1, 1 + 3 * Arg_1 * max(1, -1 + 3 * Arg_1) + min(2 + -6 * Arg_1, -2)) * max(9, -2 + 11 * Arg_1) + max(1, 1 + 3 * Arg_1 * max(1, -1 + 3 * Arg_1) + min(2 + -6 * Arg_1, -2)) * nat(-2 + 2 * Arg_1) + nat(-4 * Arg_4) + max(4 + 6 * Arg_1 * max(-2 + 6 * Arg_1, 4) + min(8 + -24 * Arg_1, -8), 4) + nat(-2 + 3 * Arg_1) + max(1, 1 + Arg_1)) (3) Loat Proof [FINISHED, 2115 ms] (4) BOUNDS(n^4, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalfstart(A, B, C, D, E) -> Com_1(evalfentryin(A, B, C, D, E)) :|: TRUE evalfentryin(A, B, C, D, E) -> Com_1(evalfbb10in(1, B, C, D, E)) :|: TRUE evalfbb10in(A, B, C, D, E) -> Com_1(evalfbb8in(A, B, 1, D, E)) :|: B >= A evalfbb10in(A, B, C, D, E) -> Com_1(evalfreturnin(A, B, C, D, E)) :|: A >= B + 1 evalfbb8in(A, B, C, D, E) -> Com_1(evalfbb6in(A, B, C, A + 1, E)) :|: A >= C evalfbb8in(A, B, C, D, E) -> Com_1(evalfbb10in(A + 1, B, C, D, E)) :|: C >= A + 1 evalfbb6in(A, B, C, D, E) -> Com_1(evalfbb4in(A, B, C, D, 1)) :|: B >= D evalfbb6in(A, B, C, D, E) -> Com_1(evalfbb7in(A, B, C, D, E)) :|: D >= B + 1 evalfbb4in(A, B, C, D, E) -> Com_1(evalfbb3in(A, B, C, D, E)) :|: D >= E evalfbb4in(A, B, C, D, E) -> Com_1(evalfbb5in(A, B, C, D, E)) :|: E >= D + 1 evalfbb3in(A, B, C, D, E) -> Com_1(evalfbb4in(A, B, C, D, E + 1)) :|: TRUE evalfbb5in(A, B, C, D, E) -> Com_1(evalfbb6in(A, B, C, D + 1, E)) :|: TRUE evalfbb7in(A, B, C, D, E) -> Com_1(evalfbb8in(A, B, C + 1, D, E)) :|: TRUE evalfreturnin(A, B, C, D, E) -> Com_1(evalfstop(A, B, C, D, E)) :|: TRUE The start-symbols are:[evalfstart_5] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, 3+max([1, 1+(-2+3*Arg_1)*max([1, -1+3*Arg_1])])*max([0, -1+Arg_1])+max([1, 1+(-2+3*Arg_1)*max([1, -1+3*Arg_1])])*max([9, -2+11*Arg_1])+max([1, 1+(-2+3*Arg_1)*max([1, -1+3*Arg_1])])*max([0, -2+2*Arg_1])+(max([1, 1+(-2+3*Arg_1)*max([1, -1+3*Arg_1])])*max([0, -1+Arg_1])*max([3, -1+2*Arg_1])+max([0, -4*Arg_4]))*max([1, -1+3*Arg_1])+max([1, 1+(-2+3*Arg_1)*max([1, -1+3*Arg_1])])*max([0, -1+Arg_1])*max([3, -1+2*Arg_1])+max([1, 1+(-2+3*Arg_1)*max([1, -1+3*Arg_1])])+max([2, 2+(-2+3*Arg_1)*max([4, 2*max([1, -1+3*Arg_1])])])+max([0, -2+3*Arg_1])+max([1, 1+Arg_1])+max([2, 2+(-2+3*Arg_1)*max([4, 2*max([1, -1+3*Arg_1])])])+max([0, -4*Arg_4]) {O(n^5)}) Initial Complexity Problem: Start: evalfstart Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4 Temp_Vars: Locations: evalfbb10in, evalfbb3in, evalfbb4in, evalfbb5in, evalfbb6in, evalfbb7in, evalfbb8in, evalfentryin, evalfreturnin, evalfstart, evalfstop Transitions: evalfbb10in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb8in(Arg_0,Arg_1,1,Arg_3,Arg_4):|:1 <= Arg_0 && Arg_0 <= Arg_1 evalfbb10in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1 <= Arg_0 && Arg_1+1 <= Arg_0 evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1):|:1 <= Arg_4 && 3 <= Arg_3+Arg_4 && 2 <= Arg_2+Arg_4 && 3 <= Arg_1+Arg_4 && 2 <= Arg_0+Arg_4 && Arg_3 <= Arg_1 && 2 <= Arg_3 && 3 <= Arg_2+Arg_3 && 1+Arg_2 <= Arg_3 && 4 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && 1+Arg_0 <= Arg_3 && 1+Arg_2 <= Arg_1 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 3 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 2 <= Arg_1 && 3 <= Arg_0+Arg_1 && 1+Arg_0 <= Arg_1 && 1 <= Arg_0 evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1 <= Arg_4 && 3 <= Arg_3+Arg_4 && 2 <= Arg_2+Arg_4 && 3 <= Arg_1+Arg_4 && 2 <= Arg_0+Arg_4 && Arg_3 <= Arg_1 && 2 <= Arg_3 && 3 <= Arg_2+Arg_3 && 1+Arg_2 <= Arg_3 && 4 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && 1+Arg_0 <= Arg_3 && 1+Arg_2 <= Arg_1 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 3 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 2 <= Arg_1 && 3 <= Arg_0+Arg_1 && 1+Arg_0 <= Arg_1 && 1 <= Arg_0 && Arg_4 <= Arg_3 evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1 <= Arg_4 && 3 <= Arg_3+Arg_4 && 2 <= Arg_2+Arg_4 && 3 <= Arg_1+Arg_4 && 2 <= Arg_0+Arg_4 && Arg_3 <= Arg_1 && 2 <= Arg_3 && 3 <= Arg_2+Arg_3 && 1+Arg_2 <= Arg_3 && 4 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && 1+Arg_0 <= Arg_3 && 1+Arg_2 <= Arg_1 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 3 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 2 <= Arg_1 && 3 <= Arg_0+Arg_1 && 1+Arg_0 <= Arg_1 && 1 <= Arg_0 && Arg_3+1 <= Arg_4 evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4):|:3 <= Arg_4 && 5 <= Arg_3+Arg_4 && 1+Arg_3 <= Arg_4 && 4 <= Arg_2+Arg_4 && 2+Arg_2 <= Arg_4 && 5 <= Arg_1+Arg_4 && 4 <= Arg_0+Arg_4 && 2+Arg_0 <= Arg_4 && Arg_3 <= Arg_1 && 2 <= Arg_3 && 3 <= Arg_2+Arg_3 && 1+Arg_2 <= Arg_3 && 4 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && 1+Arg_0 <= Arg_3 && 1+Arg_2 <= Arg_1 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 3 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 2 <= Arg_1 && 3 <= Arg_0+Arg_1 && 1+Arg_0 <= Arg_1 && 1 <= Arg_0 evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,1):|:Arg_3 <= 1+Arg_1 && 2 <= Arg_3 && 3 <= Arg_2+Arg_3 && 1+Arg_2 <= Arg_3 && 3 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && 1+Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 1 <= Arg_0 && Arg_3 <= Arg_1 evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_3 <= 1+Arg_1 && 2 <= Arg_3 && 3 <= Arg_2+Arg_3 && 1+Arg_2 <= Arg_3 && 3 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && 1+Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 1 <= Arg_0 && Arg_1+1 <= Arg_3 evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb8in(Arg_0,Arg_1,Arg_2+1,Arg_3,Arg_4):|:Arg_3 <= 1+Arg_1 && 2 <= Arg_3 && 3 <= Arg_2+Arg_3 && 1+Arg_2 <= Arg_3 && 3 <= Arg_1+Arg_3 && 1+Arg_1 <= Arg_3 && 3 <= Arg_0+Arg_3 && 1+Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_2 <= Arg_0 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 1 <= Arg_0 evalfbb8in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb10in(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_4):|:1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 1 <= Arg_0 && Arg_0+1 <= Arg_2 evalfbb8in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_0+1,Arg_4):|:1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 1 <= Arg_0 && Arg_2 <= Arg_0 evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb10in(1,Arg_1,Arg_2,Arg_3,Arg_4):|: evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfstop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:1+Arg_1 <= Arg_0 && 1 <= Arg_0 evalfstart(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|: Timebounds: Overall timebound: 3+max([1, 1+(-2+3*Arg_1)*max([1, -1+3*Arg_1])])*max([0, -1+Arg_1])+max([1, 1+(-2+3*Arg_1)*max([1, -1+3*Arg_1])])*max([9, -2+11*Arg_1])+max([1, 1+(-2+3*Arg_1)*max([1, -1+3*Arg_1])])*max([0, -2+2*Arg_1])+(max([1, 1+(-2+3*Arg_1)*max([1, -1+3*Arg_1])])*max([0, -1+Arg_1])*max([3, -1+2*Arg_1])+max([0, -4*Arg_4]))*max([1, -1+3*Arg_1])+max([1, 1+(-2+3*Arg_1)*max([1, -1+3*Arg_1])])*max([0, -1+Arg_1])*max([3, -1+2*Arg_1])+max([1, 1+(-2+3*Arg_1)*max([1, -1+3*Arg_1])])+max([2, 2+(-2+3*Arg_1)*max([4, 2*max([1, -1+3*Arg_1])])])+max([0, -2+3*Arg_1])+max([1, 1+Arg_1])+max([2, 2+(-2+3*Arg_1)*max([4, 2*max([1, -1+3*Arg_1])])])+max([0, -4*Arg_4]) {O(n^5)} 2: evalfbb10in->evalfbb8in: max([0, Arg_1]) {O(n)} 3: evalfbb10in->evalfreturnin: 1 {O(1)} popout

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all output return to Compl Integ Trans Syste 26843