details

property	value
status	complete
benchmark	ex13.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n002.star.cs.uiowa.edu
space	ABC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	23.057238102 seconds
cpu usage	32.220900849
max memory	3.36457728E8

stage attributes

key	value
output-size	36060
starexec-result	WORST_CASE(Omega(n^3), O(n^3))

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^3), O(n^3)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^3, nat(2 * Arg_1 + 2 * Arg_2 + -2 * Arg_5) + nat(1 + -1 * Arg_0 + Arg_1) + nat(2 + -6 * Arg_0 + -8 * Arg_0 * Arg_1 + 8 * Arg_0 * Arg_1 * Arg_2 + -8 * Arg_0 * Arg_1 * Arg_3 + 6 * Arg_0 * Arg_2 + 8 * Arg_3 * Arg_0 * Arg_2 + -14 * Arg_0 * Arg_3 + -8 * Arg_3^2 * Arg_0 + 4 * Arg_0^2 + -4 * Arg_0^2 * Arg_2 + 4 * Arg_0^2 * Arg_3 + 6 * Arg_1 + -6 * Arg_1 * Arg_2 + -8 * Arg_3 * Arg_1 * Arg_2 + 14 * Arg_1 * Arg_3 + 8 * Arg_3^2 * Arg_1 + 4 * Arg_1^2 + -4 * Arg_1^2 * Arg_2 + 4 * Arg_1^2 * Arg_3 + -2 * Arg_2 + -4 * Arg_3 * Arg_2 + 6 * Arg_3 + 4 * Arg_3^2) + nat(1 + -2 * Arg_0 + 2 * Arg_1) + nat(6 + -12 * Arg_0 + 12 * Arg_0 * Arg_2 + -12 * Arg_0 * Arg_3 + 12 * Arg_1 + -12 * Arg_1 * Arg_2 + 12 * Arg_1 * Arg_3 + -6 * Arg_2 + 6 * Arg_3) + max(4, 5 + -2 * Arg_0 + 2 * Arg_1)). (0) CpxIntTrs (1) Koat2 Proof [FINISHED, 5004 ms] (2) BOUNDS(1, nat(2 * Arg_1 + 2 * Arg_2 + -2 * Arg_5) + nat(1 + -1 * Arg_0 + Arg_1) + nat(2 + -6 * Arg_0 + -8 * Arg_0 * Arg_1 + 8 * Arg_0 * Arg_1 * Arg_2 + -8 * Arg_0 * Arg_1 * Arg_3 + 6 * Arg_0 * Arg_2 + 8 * Arg_3 * Arg_0 * Arg_2 + -14 * Arg_0 * Arg_3 + -8 * Arg_3^2 * Arg_0 + 4 * Arg_0^2 + -4 * Arg_0^2 * Arg_2 + 4 * Arg_0^2 * Arg_3 + 6 * Arg_1 + -6 * Arg_1 * Arg_2 + -8 * Arg_3 * Arg_1 * Arg_2 + 14 * Arg_1 * Arg_3 + 8 * Arg_3^2 * Arg_1 + 4 * Arg_1^2 + -4 * Arg_1^2 * Arg_2 + 4 * Arg_1^2 * Arg_3 + -2 * Arg_2 + -4 * Arg_3 * Arg_2 + 6 * Arg_3 + 4 * Arg_3^2) + nat(1 + -2 * Arg_0 + 2 * Arg_1) + nat(6 + -12 * Arg_0 + 12 * Arg_0 * Arg_2 + -12 * Arg_0 * Arg_3 + 12 * Arg_1 + -12 * Arg_1 * Arg_2 + 12 * Arg_1 * Arg_3 + -6 * Arg_2 + 6 * Arg_3) + max(4, 5 + -2 * Arg_0 + 2 * Arg_1)) (3) Loat Proof [FINISHED, 21.5 s] (4) BOUNDS(n^3, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalfstart(A, B, C, D, E, F) -> Com_1(evalfentryin(A, B, C, D, E, F)) :|: TRUE evalfentryin(A, B, C, D, E, F) -> Com_1(evalfbb7in(B, C, D, A, E, F)) :|: TRUE evalfbb7in(A, B, C, D, E, F) -> Com_1(evalfbb5in(A, B, C, D, B, F)) :|: A >= D evalfbb7in(A, B, C, D, E, F) -> Com_1(evalfreturnin(A, B, C, D, E, F)) :|: D >= A + 1 evalfbb5in(A, B, C, D, E, F) -> Com_1(evalfbb1in(A, B, C, D, E, F)) :|: C >= E evalfbb5in(A, B, C, D, E, F) -> Com_1(evalfbb6in(A, B, C, D, E, F)) :|: E >= C + 1 evalfbb1in(A, B, C, D, E, F) -> Com_1(evalfbb3in(A, B, C, D, E, D - E)) :|: TRUE evalfbb3in(A, B, C, D, E, F) -> Com_1(evalfbb2in(A, B, C, D, E, F)) :|: D + E >= F evalfbb3in(A, B, C, D, E, F) -> Com_1(evalfbb4in(A, B, C, D, E, F)) :|: F >= D + E + 1 evalfbb2in(A, B, C, D, E, F) -> Com_1(evalfbb3in(A, B, C, D, E, F + 1)) :|: TRUE evalfbb4in(A, B, C, D, E, F) -> Com_1(evalfbb5in(A, B, C, D, E + 1, F)) :|: TRUE evalfbb6in(A, B, C, D, E, F) -> Com_1(evalfbb7in(A, B, C, D + 1, E, F)) :|: TRUE evalfreturnin(A, B, C, D, E, F) -> Com_1(evalfstop(A, B, C, D, E, F)) :|: TRUE The start-symbols are:[evalfstart_6] ---------------------------------------- (1) Koat2 Proof (FINISHED) YES( ?, 4+max([0, 1+2*Arg_1+-2*Arg_0])+max([0, Arg_1+Arg_2-Arg_5])+max([0, 1+Arg_1-Arg_0])+max([0, (1+Arg_1-Arg_0+2*Arg_3)*(1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)])+max([0, 1+2*Arg_1+-2*Arg_0])+max([0, (1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)])+max([0, (1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)])+max([0, (1+Arg_1-Arg_0+2*Arg_3)*(1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)])+max([0, (1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)])+max([0, Arg_1+Arg_2-Arg_5])+max([0, (1+2*Arg_1+-2*Arg_0)*(3+3*Arg_3+-3*Arg_2)]) {O(n^3)}) Initial Complexity Problem: Start: evalfstart Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5 Temp_Vars: Locations: evalfbb1in, evalfbb2in, evalfbb3in, evalfbb4in, evalfbb5in, evalfbb6in, evalfbb7in, evalfentryin, evalfreturnin, evalfstart, evalfstop Transitions: evalfbb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_3-Arg_4):|:Arg_4 <= Arg_2 && Arg_1 <= Arg_4 && Arg_3 <= Arg_0 && Arg_1 <= Arg_2 evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5+1):|:Arg_4 <= Arg_2 && Arg_1 <= Arg_4 && Arg_3 <= Arg_0 && Arg_1 <= Arg_2 evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalfbb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4 <= Arg_2 && Arg_1 <= Arg_4 && Arg_3 <= Arg_0 && Arg_1 <= Arg_2 && Arg_5 <= Arg_3+Arg_4 evalfbb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4 <= Arg_2 && Arg_1 <= Arg_4 && Arg_3 <= Arg_0 && Arg_1 <= Arg_2 && Arg_3+Arg_4+1 <= Arg_5 evalfbb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5):|:Arg_4 <= Arg_2 && Arg_1 <= Arg_4 && Arg_3 <= Arg_0 && Arg_1 <= Arg_2 evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalfbb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1 <= Arg_4 && Arg_3 <= Arg_0 && Arg_4 <= Arg_2 evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1 <= Arg_4 && Arg_3 <= Arg_0 && Arg_2+1 <= Arg_4 evalfbb6in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3+1,Arg_4,Arg_5):|:1+Arg_2 <= Arg_4 && Arg_1 <= Arg_4 && Arg_3 <= Arg_0 evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalfbb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_1,Arg_5):|:Arg_3 <= Arg_0 evalfbb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0+1 <= Arg_3 evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalfbb7in(Arg_1,Arg_2,Arg_3,Arg_0,Arg_4,Arg_5):|: evalfreturnin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalfstop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1+Arg_0 <= Arg_3 evalfstart(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalfentryin(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|: Timebounds: Overall timebound: 4+max([0, 1+2*Arg_1+-2*Arg_0])+max([0, Arg_1+Arg_2-Arg_5])+max([0, 1+Arg_1-Arg_0])+max([0, (1+Arg_1-Arg_0+2*Arg_3)*(1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)])+max([0, 1+2*Arg_1+-2*Arg_0])+max([0, (1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)])+max([0, (1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)])+max([0, (1+Arg_1-Arg_0+2*Arg_3)*(1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)])+max([0, (1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)])+max([0, Arg_1+Arg_2-Arg_5])+max([0, (1+2*Arg_1+-2*Arg_0)*(3+3*Arg_3+-3*Arg_2)]) {O(n^3)} 6: evalfbb1in->evalfbb3in: max([0, (1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)]) {O(n^2)} 9: evalfbb2in->evalfbb3in: max([0, (1+Arg_1-Arg_0+2*Arg_3)*(1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)])+max([0, Arg_1+Arg_2-Arg_5]) {O(n^3)} 7: evalfbb3in->evalfbb2in: max([0, (1+Arg_1-Arg_0+2*Arg_3)*(1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)])+max([0, Arg_1+Arg_2-Arg_5]) {O(n^3)} 8: evalfbb3in->evalfbb4in: max([0, (1+2*Arg_1+-2*Arg_0)*(3+3*Arg_3+-3*Arg_2)]) {O(n^2)} popout

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all output return to Compl Integ Trans Syste 26843