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	n129.star.cs.uiowa.edu
space	ABC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	23.0476 seconds
cpu usage	32.3035
user time	31.704
system time	0.599501
max virtual memory	1.8584252E7
max residence set size	268300.0

stage attributes

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

output

32.21/23.02 WORST_CASE(Omega(n^3), O(n^3)) 32.21/23.03 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 32.21/23.03 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 32.21/23.03 32.21/23.03 32.21/23.03 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^3, nat(2 * Arg_1 + 2 * Arg_2 + -2 *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)). 32.21/23.03 32.21/23.03 (0) CpxIntTrs 32.21/23.03 (1) Koat2 Proof [FINISHED, 5096 ms] 32.21/23.03 (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)) 32.21/23.03 (3) Loat Proof [FINISHED, 21.5 s] 32.21/23.03 (4) BOUNDS(n^3, INF) 32.21/23.03 32.21/23.03 32.21/23.03 ---------------------------------------- 32.21/23.03 32.21/23.03 (0) 32.21/23.03 Obligation: 32.21/23.03 Complexity Int TRS consisting of the following rules: 32.21/23.03 evalfstart(A, B, C, D, E, F) -> Com_1(evalfentryin(A, B, C, D, E, F)) :|: TRUE 32.21/23.03 evalfentryin(A, B, C, D, E, F) -> Com_1(evalfbb7in(B, C, D, A, E, F)) :|: TRUE 32.21/23.03 evalfbb7in(A, B, C, D, E, F) -> Com_1(evalfbb5in(A, B, C, D, B, F)) :|: A >= D 32.21/23.03 evalfbb7in(A, B, C, D, E, F) -> Com_1(evalfreturnin(A, B, C, D, E, F)) :|: D >= A + 1 32.21/23.03 evalfbb5in(A, B, C, D, E, F) -> Com_1(evalfbb1in(A, B, C, D, E, F)) :|: C >= E 32.21/23.03 evalfbb5in(A, B, C, D, E, F) -> Com_1(evalfbb6in(A, B, C, D, E, F)) :|: E >= C + 1 32.21/23.03 evalfbb1in(A, B, C, D, E, F) -> Com_1(evalfbb3in(A, B, C, D, E, D - E)) :|: TRUE 32.21/23.03 evalfbb3in(A, B, C, D, E, F) -> Com_1(evalfbb2in(A, B, C, D, E, F)) :|: D + E >= F 32.21/23.03 evalfbb3in(A, B, C, D, E, F) -> Com_1(evalfbb4in(A, B, C, D, E, F)) :|: F >= D + E + 1 32.21/23.03 evalfbb2in(A, B, C, D, E, F) -> Com_1(evalfbb3in(A, B, C, D, E, F + 1)) :|: TRUE 32.21/23.03 evalfbb4in(A, B, C, D, E, F) -> Com_1(evalfbb5in(A, B, C, D, E + 1, F)) :|: TRUE 32.21/23.03 evalfbb6in(A, B, C, D, E, F) -> Com_1(evalfbb7in(A, B, C, D + 1, E, F)) :|: TRUE 32.21/23.03 evalfreturnin(A, B, C, D, E, F) -> Com_1(evalfstop(A, B, C, D, E, F)) :|: TRUE 32.21/23.03 32.21/23.03 The start-symbols are:[evalfstart_6] 32.21/23.03 32.21/23.03 32.21/23.03 ---------------------------------------- 32.21/23.03 32.21/23.03 (1) Koat2 Proof (FINISHED) 32.21/23.03 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)}) 32.21/23.03 32.21/23.03 32.21/23.03 32.21/23.03 Initial Complexity Problem: 32.21/23.03 32.21/23.03 Start: evalfstart 32.21/23.03 32.21/23.03 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5 32.21/23.03 32.21/23.03 Temp_Vars: 32.21/23.03 32.21/23.03 Locations: evalfbb1in, evalfbb2in, evalfbb3in, evalfbb4in, evalfbb5in, evalfbb6in, evalfbb7in, evalfentryin, evalfreturnin, evalfstart, evalfstop 32.21/23.03 32.21/23.03 Transitions: 32.21/23.03 32.21/23.03 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 32.21/23.03 32.21/23.03 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 32.21/23.03 32.21/23.03 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 32.21/23.03 32.21/23.03 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 32.21/23.03 32.21/23.03 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 32.21/23.03 32.21/23.03 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 32.21/23.03 32.21/23.03 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 32.21/23.03 32.21/23.03 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 32.21/23.03 32.21/23.03 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 32.21/23.03 32.21/23.03 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 32.21/23.03 32.21/23.03 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):|: 32.21/23.03 32.21/23.03 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 32.21/23.03 32.21/23.03 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):|: 32.21/23.03 32.21/23.03 32.21/23.03 32.21/23.03 Timebounds: 32.21/23.03 32.21/23.03 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)} 32.21/23.03 32.21/23.03 6: evalfbb1in->evalfbb3in: max([0, (1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)]) {O(n^2)} 32.21/23.03 32.21/23.03 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)} 32.21/23.03 32.21/23.03 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)} 32.21/23.03 32.21/23.03 8: evalfbb3in->evalfbb4in: max([0, (1+2*Arg_1+-2*Arg_0)*(3+3*Arg_3+-3*Arg_2)]) {O(n^2)} 32.21/23.03 32.21/23.03 10: evalfbb4in->evalfbb5in: max([0, (1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)]) {O(n^2)} 32.21/23.03 32.21/23.03 4: evalfbb5in->evalfbb1in: max([0, (1+2*Arg_1+-2*Arg_0)*(1+Arg_3-Arg_2)]) {O(n^2)} 32.21/23.03 32.21/23.03 5: evalfbb5in->evalfbb6in: max([0, 1+2*Arg_1+-2*Arg_0]) {O(n)} popout

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all output return to Complexity_ITS 2019-03-21 04.46