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	n086.star.cs.uiowa.edu
space	ABC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	12.3931 seconds
cpu usage	17.0094
user time	16.5304
system time	0.479076
max virtual memory	1.853256E7
max residence set size	231576.0

stage attributes

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

output

16.90/12.35 WORST_CASE(Omega(n^4), O(n^5)) 16.90/12.36 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 16.90/12.36 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 16.90/12.36 16.90/12.36 16.90/12.36 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^4, 3 + max(1, 1 + 3 * Arg_1 * max(1, -1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(4, -2 + 6 * Arg_1) + min(8 + -24 * Arg_1, -8), 4) + nat(-2 + 3 * Arg_1) + max(1, 1 + Arg_1)). 16.90/12.36 16.90/12.36 (0) CpxIntTrs 16.90/12.36 (1) Koat2 Proof [FINISHED, 10.5 s] 16.90/12.36 (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(4, -2 + 6 * Arg_1) + min(8 + -24 * Arg_1, -8), 4) + nat(-2 + 3 * Arg_1) + max(1, 1 + Arg_1)) 16.90/12.36 (3) Loat Proof [FINISHED, 2105 ms] 16.90/12.36 (4) BOUNDS(n^4, INF) 16.90/12.36 16.90/12.36 16.90/12.36 ---------------------------------------- 16.90/12.36 16.90/12.36 (0) 16.90/12.36 Obligation: 16.90/12.36 Complexity Int TRS consisting of the following rules: 16.90/12.36 evalfstart(A, B, C, D, E) -> Com_1(evalfentryin(A, B, C, D, E)) :|: TRUE 16.90/12.36 evalfentryin(A, B, C, D, E) -> Com_1(evalfbb10in(1, B, C, D, E)) :|: TRUE 16.90/12.36 evalfbb10in(A, B, C, D, E) -> Com_1(evalfbb8in(A, B, 1, D, E)) :|: B >= A 16.90/12.36 evalfbb10in(A, B, C, D, E) -> Com_1(evalfreturnin(A, B, C, D, E)) :|: A >= B + 1 16.90/12.36 evalfbb8in(A, B, C, D, E) -> Com_1(evalfbb6in(A, B, C, A + 1, E)) :|: A >= C 16.90/12.36 evalfbb8in(A, B, C, D, E) -> Com_1(evalfbb10in(A + 1, B, C, D, E)) :|: C >= A + 1 16.90/12.36 evalfbb6in(A, B, C, D, E) -> Com_1(evalfbb4in(A, B, C, D, 1)) :|: B >= D 16.90/12.36 evalfbb6in(A, B, C, D, E) -> Com_1(evalfbb7in(A, B, C, D, E)) :|: D >= B + 1 16.90/12.36 evalfbb4in(A, B, C, D, E) -> Com_1(evalfbb3in(A, B, C, D, E)) :|: D >= E 16.90/12.36 evalfbb4in(A, B, C, D, E) -> Com_1(evalfbb5in(A, B, C, D, E)) :|: E >= D + 1 16.90/12.36 evalfbb3in(A, B, C, D, E) -> Com_1(evalfbb4in(A, B, C, D, E + 1)) :|: TRUE 16.90/12.36 evalfbb5in(A, B, C, D, E) -> Com_1(evalfbb6in(A, B, C, D + 1, E)) :|: TRUE 16.90/12.36 evalfbb7in(A, B, C, D, E) -> Com_1(evalfbb8in(A, B, C + 1, D, E)) :|: TRUE 16.90/12.36 evalfreturnin(A, B, C, D, E) -> Com_1(evalfstop(A, B, C, D, E)) :|: TRUE 16.90/12.36 16.90/12.36 The start-symbols are:[evalfstart_5] 16.90/12.36 16.90/12.36 16.90/12.36 ---------------------------------------- 16.90/12.36 16.90/12.36 (1) Koat2 Proof (FINISHED) 16.90/12.36 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)}) 16.90/12.36 16.90/12.36 16.90/12.36 16.90/12.36 Initial Complexity Problem: 16.90/12.36 16.90/12.36 Start: evalfstart 16.90/12.36 16.90/12.36 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4 16.90/12.36 16.90/12.36 Temp_Vars: 16.90/12.36 16.90/12.36 Locations: evalfbb10in, evalfbb3in, evalfbb4in, evalfbb5in, evalfbb6in, evalfbb7in, evalfbb8in, evalfentryin, evalfreturnin, evalfstart, evalfstop 16.90/12.36 16.90/12.36 Transitions: 16.90/12.36 16.90/12.36 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 16.90/12.36 16.90/12.36 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 16.90/12.36 16.90/12.36 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 16.90/12.36 16.90/12.36 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 16.90/12.36 16.90/12.36 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 16.90/12.36 16.90/12.36 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 16.90/12.36 16.90/12.36 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 16.90/12.36 16.90/12.36 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 16.90/12.36 16.90/12.36 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 16.90/12.36 16.90/12.36 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 16.90/12.36 16.90/12.36 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 16.90/12.36 16.90/12.36 evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfbb10in(1,Arg_1,Arg_2,Arg_3,Arg_4):|: 16.90/12.36 16.90/12.36 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 16.90/12.36 16.90/12.36 evalfstart(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|: 16.90/12.36 16.90/12.36 16.90/12.36 16.90/12.36 Timebounds: 16.90/12.36 16.90/12.36 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)} 16.90/12.36 16.90/12.36 2: evalfbb10in->evalfbb8in: max([0, Arg_1]) {O(n)} 16.90/12.36 16.90/12.36 3: evalfbb10in->evalfreturnin: 1 {O(1)} 16.90/12.36 16.90/12.36 10: evalfbb3in->evalfbb4in: (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]) {O(n^5)} 16.90/12.36 16.90/12.36 8: evalfbb4in->evalfbb3in: 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]) {O(n^4)} 16.90/12.36 16.90/12.36 9: evalfbb4in->evalfbb5in: max([1, 1+(-2+3*Arg_1)*max([1, -1+3*Arg_1])])*max([0, -2+2*Arg_1]) {O(n^3)} 16.90/12.36 popout

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all output return to Complexity_ITS 2019-03-21 04.46