details

property	value
status	complete
benchmark	loops.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	WTC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.71925 seconds
cpu usage	5.78228
user time	5.47086
system time	0.311428
max virtual memory	1.8706048E7
max residence set size	220892.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^2))

output

5.64/2.68 WORST_CASE(?, O(n^2)) 5.64/2.69 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 5.64/2.69 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.64/2.69 5.64/2.69 5.64/2.69 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(1, 1 + 3 * Arg_0) + nat(2 + 2 * Arg_0) + nat(3 * Arg_0 * max(1, Arg_0)) + nat(3 * Arg_0 * max(3 * Arg_0, 6)) + nat(Arg_0) + max(1, 1 + 2 * Arg_0) + max(5, 5 + 6 * Arg_0)). 5.64/2.69 5.64/2.69 (0) CpxIntTrs 5.64/2.69 (1) Koat2 Proof [FINISHED, 1046 ms] 5.64/2.69 (2) BOUNDS(1, max(1, 1 + 3 * Arg_0) + nat(2 + 2 * Arg_0) + nat(3 * Arg_0 * max(1, Arg_0)) + nat(3 * Arg_0 * max(3 * Arg_0, 6)) + nat(Arg_0) + max(1, 1 + 2 * Arg_0) + max(5, 5 + 6 * Arg_0)) 5.64/2.69 5.64/2.69 5.64/2.69 ---------------------------------------- 5.64/2.69 5.64/2.69 (0) 5.64/2.69 Obligation: 5.64/2.69 Complexity Int TRS consisting of the following rules: 5.64/2.69 evalloopsstart(A, B) -> Com_1(evalloopsentryin(A, B)) :|: TRUE 5.64/2.69 evalloopsentryin(A, B) -> Com_1(evalloopsbb6in(A, B)) :|: A >= 0 5.64/2.69 evalloopsentryin(A, B) -> Com_1(evalloopsreturnin(A, B)) :|: 0 >= A + 1 5.64/2.69 evalloopsbb6in(A, B) -> Com_1(evalloopsbb1in(A, B)) :|: A >= 0 5.64/2.69 evalloopsbb6in(A, B) -> Com_1(evalloopsreturnin(A, B)) :|: 0 >= A + 1 5.64/2.69 evalloopsbb1in(A, B) -> Com_1(evalloopsbb4in(A, 1)) :|: A >= 2 5.64/2.69 evalloopsbb1in(A, B) -> Com_1(evalloopsbb5in(A, C)) :|: 1 >= A 5.64/2.69 evalloopsbb4in(A, B) -> Com_1(evalloopsbb3in(A, B)) :|: A >= B + 1 5.64/2.69 evalloopsbb4in(A, B) -> Com_1(evalloopsbb5in(A, B)) :|: B >= A 5.64/2.69 evalloopsbb3in(A, B) -> Com_1(evalloopsbb4in(A, 2 * B)) :|: TRUE 5.64/2.69 evalloopsbb5in(A, B) -> Com_1(evalloopsbb6in(A - 1, B)) :|: TRUE 5.64/2.69 evalloopsreturnin(A, B) -> Com_1(evalloopsstop(A, B)) :|: TRUE 5.64/2.69 5.64/2.69 The start-symbols are:[evalloopsstart_2] 5.64/2.69 5.64/2.69 5.64/2.69 ---------------------------------------- 5.64/2.69 5.64/2.69 (1) Koat2 Proof (FINISHED) 5.64/2.69 YES( ?, 5+2*max([0, 3*Arg_0])+max([1, 1+3*Arg_0])+max([0, 1+Arg_0])+max([0, 1+Arg_0])+max([0, 3*Arg_0*max([1, Arg_0])])+max([0, 3*Arg_0*max([6, 3*max([1, Arg_0])])])+max([0, Arg_0])+max([1, 1+2*Arg_0]) {O(n^2)}) 5.64/2.69 5.64/2.69 5.64/2.69 5.64/2.69 Initial Complexity Problem: 5.64/2.69 5.64/2.69 Start: evalloopsstart 5.64/2.69 5.64/2.69 Program_Vars: Arg_0, Arg_1 5.64/2.69 5.64/2.69 Temp_Vars: C 5.64/2.69 5.64/2.69 Locations: evalloopsbb1in, evalloopsbb3in, evalloopsbb4in, evalloopsbb5in, evalloopsbb6in, evalloopsentryin, evalloopsreturnin, evalloopsstart, evalloopsstop 5.64/2.69 5.64/2.69 Transitions: 5.64/2.69 5.64/2.69 evalloopsbb1in(Arg_0,Arg_1) -> evalloopsbb4in(Arg_0,1):|:0 <= Arg_0 && 2 <= Arg_0 5.64/2.69 5.64/2.69 evalloopsbb1in(Arg_0,Arg_1) -> evalloopsbb5in(Arg_0,C):|:0 <= Arg_0 && Arg_0 <= 1 5.64/2.69 5.64/2.69 evalloopsbb3in(Arg_0,Arg_1) -> evalloopsbb4in(Arg_0,(2)*Arg_1):|:1+Arg_1 <= Arg_0 && 1 <= Arg_1 && 3 <= Arg_0+Arg_1 && 2 <= Arg_0 5.64/2.69 5.64/2.69 evalloopsbb4in(Arg_0,Arg_1) -> evalloopsbb3in(Arg_0,Arg_1):|:1 <= Arg_1 && 3 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_1+1 <= Arg_0 5.64/2.69 5.64/2.69 evalloopsbb4in(Arg_0,Arg_1) -> evalloopsbb5in(Arg_0,Arg_1):|:1 <= Arg_1 && 3 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_0 <= Arg_1 5.64/2.69 5.64/2.69 evalloopsbb5in(Arg_0,Arg_1) -> evalloopsbb6in(Arg_0-1,Arg_1):|:0 <= Arg_0 5.64/2.69 5.64/2.69 evalloopsbb6in(Arg_0,Arg_1) -> evalloopsbb1in(Arg_0,Arg_1):|:0 <= Arg_0 5.64/2.69 5.64/2.69 evalloopsbb6in(Arg_0,Arg_1) -> evalloopsreturnin(Arg_0,Arg_1):|:Arg_0+1 <= 0 5.64/2.69 5.64/2.69 evalloopsentryin(Arg_0,Arg_1) -> evalloopsbb6in(Arg_0,Arg_1):|:0 <= Arg_0 5.64/2.69 5.64/2.69 evalloopsentryin(Arg_0,Arg_1) -> evalloopsreturnin(Arg_0,Arg_1):|:Arg_0+1 <= 0 5.64/2.69 5.64/2.69 evalloopsreturnin(Arg_0,Arg_1) -> evalloopsstop(Arg_0,Arg_1):|:1+Arg_0 <= 0 5.64/2.69 5.64/2.69 evalloopsstart(Arg_0,Arg_1) -> evalloopsentryin(Arg_0,Arg_1):|: 5.64/2.69 5.64/2.69 5.64/2.69 5.64/2.69 Timebounds: 5.64/2.69 5.64/2.69 Overall timebound: 5+2*max([0, 3*Arg_0])+max([1, 1+3*Arg_0])+max([0, 1+Arg_0])+max([0, 1+Arg_0])+max([0, 3*Arg_0*max([1, Arg_0])])+max([0, 3*Arg_0*max([6, 3*max([1, Arg_0])])])+max([0, Arg_0])+max([1, 1+2*Arg_0]) {O(n^2)} 5.64/2.69 5.64/2.69 5: evalloopsbb1in->evalloopsbb4in: max([0, 1+Arg_0]) {O(n)} 5.64/2.69 5.64/2.69 6: evalloopsbb1in->evalloopsbb5in: max([1, 1+2*Arg_0]) {O(n)} 5.64/2.69 5.64/2.69 9: evalloopsbb3in->evalloopsbb4in: max([0, 3*Arg_0*max([1, Arg_0])])+max([0, Arg_0]) {O(n^2)} 5.64/2.69 5.64/2.69 7: evalloopsbb4in->evalloopsbb3in: max([0, 3*Arg_0*max([6, 3*max([1, Arg_0])])])+max([0, 3*Arg_0]) {O(n^2)} 5.64/2.69 5.64/2.69 8: evalloopsbb4in->evalloopsbb5in: max([0, 3*Arg_0]) {O(n)} 5.64/2.69 5.64/2.69 10: evalloopsbb5in->evalloopsbb6in: max([0, 1+Arg_0]) {O(n)} 5.64/2.69 5.64/2.69 3: evalloopsbb6in->evalloopsbb1in: max([1, 1+3*Arg_0]) {O(n)} 5.64/2.69 5.64/2.69 4: evalloopsbb6in->evalloopsreturnin: 1 {O(1)} 5.64/2.69 5.64/2.69 1: evalloopsentryin->evalloopsbb6in: 1 {O(1)} 5.64/2.69 popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Complexity_ITS 2019-03-21 04.46