details

property	value
status	complete
benchmark	gcd.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n111.star.cs.uiowa.edu
space	SAS10

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	290.207 seconds
cpu usage	296.241
user time	294.913
system time	1.32846
max virtual memory	1.8689384E7
max residence set size	305972.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

296.11/290.18 WORST_CASE(Omega(n^1), O(n^1)) 296.11/290.19 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 296.11/290.19 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 296.11/290.19 296.11/290.19 296.11/290.19 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(2, 1 + Arg_2) + nat(Arg_0) + nat(-1 + Arg_0) + max(8 + Arg_0, 8) + max(3, 3 * Arg_2) + max(-3 + 3 * Arg_2, 3) + nat(2 * Arg_2)). 296.11/290.19 296.11/290.19 (0) CpxIntTrs 296.11/290.19 (1) Koat2 Proof [FINISHED, 2743 ms] 296.11/290.19 (2) BOUNDS(1, max(2, 1 + Arg_2) + nat(Arg_0) + nat(-1 + Arg_0) + max(8 + Arg_0, 8) + max(3, 3 * Arg_2) + max(-3 + 3 * Arg_2, 3) + nat(2 * Arg_2)) 296.11/290.19 (3) Loat Proof [FINISHED, 288.4 s] 296.11/290.19 (4) BOUNDS(n^1, INF) 296.11/290.19 296.11/290.19 296.11/290.19 ---------------------------------------- 296.11/290.19 296.11/290.19 (0) 296.11/290.19 Obligation: 296.11/290.19 Complexity Int TRS consisting of the following rules: 296.11/290.19 start(A, B, C, D) -> Com_1(stop(A, B, C, D)) :|: 0 >= A && B >= C && B <= C && D >= A && D <= A 296.11/290.19 start(A, B, C, D) -> Com_1(lbl6(A, B, C, D)) :|: A >= 1 && 0 >= C && B >= C && B <= C && D >= A && D <= A 296.11/290.19 start(A, B, C, D) -> Com_1(cut(A, B, C, D)) :|: A >= 1 && D >= A && D <= A && B >= A && B <= A && C >= A && C <= A 296.11/290.19 start(A, B, C, D) -> Com_1(lbl101(A, B - D, C, D)) :|: A >= 1 && C >= A + 1 && B >= C && B <= C && D >= A && D <= A 296.11/290.19 start(A, B, C, D) -> Com_1(lbl111(A, B, C, D - B)) :|: A >= C + 1 && C >= 1 && B >= C && B <= C && D >= A && D <= A 296.11/290.19 lbl6(A, B, C, D) -> Com_1(stop(A, B, C, D)) :|: A >= 1 && 0 >= C && D >= A && D <= A && B >= C && B <= C 296.11/290.19 lbl101(A, B, C, D) -> Com_1(cut(A, B, C, D)) :|: A >= B && B >= 1 && C >= 2 * B && D >= B && D <= B 296.11/290.19 lbl101(A, B, C, D) -> Com_1(lbl101(A, B - D, C, D)) :|: B >= D + 1 && A >= D && B >= 1 && D >= 1 && C >= D + B 296.11/290.19 lbl101(A, B, C, D) -> Com_1(lbl111(A, B, C, D - B)) :|: D >= B + 1 && A >= D && B >= 1 && D >= 1 && C >= D + B 296.11/290.19 lbl111(A, B, C, D) -> Com_1(cut(A, B, C, D)) :|: C >= B && B >= 1 && A >= 2 * B && D >= B && D <= B 296.11/290.19 lbl111(A, B, C, D) -> Com_1(lbl101(A, B - D, C, D)) :|: B >= D + 1 && C >= B && B >= 1 && D >= 1 && A >= D + B 296.11/290.19 lbl111(A, B, C, D) -> Com_1(lbl111(A, B, C, D - B)) :|: D >= B + 1 && C >= B && B >= 1 && D >= 1 && A >= D + B 296.11/290.19 cut(A, B, C, D) -> Com_1(stop(A, B, C, D)) :|: A >= B && B >= 1 && C >= B && D >= B && D <= B 296.11/290.19 start0(A, B, C, D) -> Com_1(start(A, C, C, A)) :|: TRUE 296.11/290.19 296.11/290.19 The start-symbols are:[start0_4] 296.11/290.19 296.11/290.19 296.11/290.19 ---------------------------------------- 296.11/290.19 296.11/290.19 (1) Koat2 Proof (FINISHED) 296.11/290.19 YES( ?, 8+max([0, Arg_0])+max([3, 3*Arg_2])+max([3, 3*(-1+Arg_2)])+max([0, Arg_2])+max([2, 1+Arg_2])+max([0, Arg_2])+max([0, Arg_0])+max([0, -1+Arg_0]) {O(n)}) 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Initial Complexity Problem: 296.11/290.19 296.11/290.19 Start: start0 296.11/290.19 296.11/290.19 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3 296.11/290.19 296.11/290.19 Temp_Vars: 296.11/290.19 296.11/290.19 Locations: cut, lbl101, lbl111, lbl6, start, start0, stop 296.11/290.19 296.11/290.19 Transitions: 296.11/290.19 296.11/290.19 cut(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_3 <= Arg_0 && 1 <= Arg_3 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && Arg_1 <= Arg_3 && 2 <= Arg_0+Arg_3 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && Arg_1 <= Arg_2 && 2 <= Arg_0+Arg_2 && Arg_1 <= Arg_0 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_1 <= Arg_0 && 1 <= Arg_1 && Arg_1 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_3 296.11/290.19 296.11/290.19 lbl101(Arg_0,Arg_1,Arg_2,Arg_3) -> cut(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3 <= Arg_2 && Arg_3 <= Arg_0 && 1 <= Arg_3 && 3 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && 2 <= Arg_0+Arg_3 && 2 <= Arg_2 && 3 <= Arg_1+Arg_2 && 1+Arg_1 <= Arg_2 && 3 <= Arg_0+Arg_2 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_1 <= Arg_0 && 1 <= Arg_1 && (2)*Arg_1 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_3 296.11/290.19 296.11/290.19 lbl101(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl101(Arg_0,Arg_1-Arg_3,Arg_2,Arg_3):|:1+Arg_3 <= Arg_2 && Arg_3 <= Arg_0 && 1 <= Arg_3 && 3 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && 2 <= Arg_0+Arg_3 && 2 <= Arg_2 && 3 <= Arg_1+Arg_2 && 1+Arg_1 <= Arg_2 && 3 <= Arg_0+Arg_2 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_3+1 <= Arg_1 && Arg_3 <= Arg_0 && 1 <= Arg_1 && 1 <= Arg_3 && Arg_3+Arg_1 <= Arg_2 296.11/290.19 296.11/290.19 lbl101(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl111(Arg_0,Arg_1,Arg_2,Arg_3-Arg_1):|:1+Arg_3 <= Arg_2 && Arg_3 <= Arg_0 && 1 <= Arg_3 && 3 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && 2 <= Arg_0+Arg_3 && 2 <= Arg_2 && 3 <= Arg_1+Arg_2 && 1+Arg_1 <= Arg_2 && 3 <= Arg_0+Arg_2 && 2 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_1+1 <= Arg_3 && Arg_3 <= Arg_0 && 1 <= Arg_1 && 1 <= Arg_3 && Arg_3+Arg_1 <= Arg_2 296.11/290.19 296.11/290.19 lbl111(Arg_0,Arg_1,Arg_2,Arg_3) -> cut(Arg_0,Arg_1,Arg_2,Arg_3):|:1+Arg_3 <= Arg_0 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && Arg_1 <= Arg_2 && 3 <= Arg_0+Arg_2 && 1+Arg_1 <= Arg_0 && 1 <= Arg_1 && 3 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_1 <= Arg_2 && 1 <= Arg_1 && (2)*Arg_1 <= Arg_0 && Arg_3 <= Arg_1 && Arg_1 <= Arg_3 296.11/290.19 296.11/290.19 lbl111(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl101(Arg_0,Arg_1-Arg_3,Arg_2,Arg_3):|:1+Arg_3 <= Arg_0 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && Arg_1 <= Arg_2 && 3 <= Arg_0+Arg_2 && 1+Arg_1 <= Arg_0 && 1 <= Arg_1 && 3 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_3+1 <= Arg_1 && Arg_1 <= Arg_2 && 1 <= Arg_1 && 1 <= Arg_3 && Arg_3+Arg_1 <= Arg_0 296.11/290.19 296.11/290.19 lbl111(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl111(Arg_0,Arg_1,Arg_2,Arg_3-Arg_1):|:1+Arg_3 <= Arg_0 && 2 <= Arg_2+Arg_3 && 2 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && Arg_1 <= Arg_2 && 3 <= Arg_0+Arg_2 && 1+Arg_1 <= Arg_0 && 1 <= Arg_1 && 3 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_1+1 <= Arg_3 && Arg_1 <= Arg_2 && 1 <= Arg_1 && 1 <= Arg_3 && Arg_3+Arg_1 <= Arg_0 296.11/290.19 296.11/290.19 lbl6(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3 <= Arg_0 && 1 <= Arg_3 && 1+Arg_2 <= Arg_3 && 1+Arg_1 <= Arg_3 && 2 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && Arg_2 <= 0 && Arg_2 <= Arg_1 && Arg_1+Arg_2 <= 0 && 1+Arg_2 <= Arg_0 && Arg_1 <= Arg_2 && Arg_1 <= 0 && 1+Arg_1 <= Arg_0 && 1 <= Arg_0 && 1 <= Arg_0 && Arg_2 <= 0 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 296.11/290.19 296.11/290.19 start(Arg_0,Arg_1,Arg_2,Arg_3) -> cut(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 1 <= Arg_0 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_1 <= Arg_0 && Arg_0 <= Arg_1 && Arg_2 <= Arg_0 && Arg_0 <= Arg_2 296.11/290.19 296.11/290.19 start(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl101(Arg_0,Arg_1-Arg_3,Arg_2,Arg_3):|:Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 1 <= Arg_0 && Arg_0+1 <= Arg_2 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 296.11/290.19 296.11/290.19 start(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl111(Arg_0,Arg_1,Arg_2,Arg_3-Arg_1):|:Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && Arg_2+1 <= Arg_0 && 1 <= Arg_2 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 296.11/290.19 296.11/290.19 start(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl6(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 1 <= Arg_0 && Arg_2 <= 0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 296.11/290.19 296.11/290.19 start(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3 <= Arg_0 && Arg_0 <= Arg_3 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && Arg_0 <= 0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 296.11/290.19 296.11/290.19 start0(Arg_0,Arg_1,Arg_2,Arg_3) -> start(Arg_0,Arg_2,Arg_2,Arg_0):|: 296.11/290.19 296.11/290.19 296.11/290.19 296.11/290.19 Timebounds: 296.11/290.19 296.11/290.19 Overall timebound: 8+max([0, Arg_0])+max([3, 3*Arg_2])+max([3, 3*(-1+Arg_2)])+max([0, Arg_2])+max([2, 1+Arg_2])+max([0, Arg_2])+max([0, Arg_0])+max([0, -1+Arg_0]) {O(n)} 296.11/290.19 296.11/290.19 12: cut->stop: 1 {O(1)} 296.11/290.19 296.11/290.19 6: lbl101->cut: 1 {O(1)} 296.11/290.19 296.11/290.19 7: lbl101->lbl101: max([0, -1+Arg_2])+max([0, Arg_2]) {O(n)} 296.11/290.19 296.11/290.19 8: lbl101->lbl111: max([0, Arg_0])+max([0, Arg_2]) {O(n)} 296.11/290.19 296.11/290.19 9: lbl111->cut: 1 {O(1)} 296.11/290.19 popout

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

job log

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actions

all output return to Complexity_ITS 2019-03-21 04.46