details

property	value
status	complete
benchmark	perfect.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n054.star.cs.uiowa.edu
space	SAS10

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	9.40279 seconds
cpu usage	10.7123
user time	10.2982
system time	0.41408
max virtual memory	1.8756744E7
max residence set size	236460.0

stage attributes

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

output

10.63/6.20 WORST_CASE(?, O(n^2)) 10.67/6.22 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 10.67/6.22 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.67/6.22 10.67/6.22 10.67/6.22 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 2 * max(1, -3 + 2 * Arg_0) * nat(-1 + Arg_0) + max(4, -4 + 4 * Arg_0) + max(4 + 2 * Arg_0, 8)). 10.67/6.22 10.67/6.22 (0) CpxIntTrs 10.67/6.22 (1) Koat2 Proof [FINISHED, 4504 ms] 10.67/6.22 (2) BOUNDS(1, 2 * max(1, -3 + 2 * Arg_0) * nat(-1 + Arg_0) + max(4, -4 + 4 * Arg_0) + max(4 + 2 * Arg_0, 8)) 10.67/6.22 10.67/6.22 10.67/6.22 ---------------------------------------- 10.67/6.22 10.67/6.22 (0) 10.67/6.22 Obligation: 10.67/6.22 Complexity Int TRS consisting of the following rules: 10.67/6.22 start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 1 >= A && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A 10.67/6.22 start(A, B, C, D, E, F, G, H) -> Com_1(lbl111(A, H, C, 1, E, H - 1, G, H)) :|: A >= 2 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A 10.67/6.22 lbl16(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= 2 && A >= B + 1 && F >= 0 && F <= 0 && H >= A && H <= A && D >= A && D <= A 10.67/6.22 lbl111(A, B, C, D, E, F, G, H) -> Com_1(lbl111(A, B, C, D - F, E, F, G, H)) :|: D >= F && A >= F + 1 && A >= F + D && A >= B && F >= 1 && D >= 0 && H >= A && H <= A 10.67/6.22 lbl111(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, B, C, H, E, F - 1, G, H)) :|: F >= D + 1 && 0 >= D + 1 && A >= F + 1 && A >= F + D && A >= B && F >= 1 && D >= 0 && H >= A && H <= A 10.67/6.22 lbl111(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, B, C, H, E, F - 1, G, H)) :|: F >= D + 1 && D >= 1 && A >= F + 1 && A >= F + D && A >= B && F >= 1 && D >= 0 && H >= A && H <= A 10.67/6.22 lbl111(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, B - F, C, H, E, F - 1, G, H)) :|: F >= 1 && A >= F + 1 && A >= F && A >= B && D >= 0 && D <= 0 && H >= A && H <= A 10.67/6.22 lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl16(A, B, C, D, E, F, G, H)) :|: A >= 2 && A >= B && A >= B + 1 && F >= 0 && F <= 0 && H >= A && H <= A && D >= A && D <= A 10.67/6.22 lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl111(A, B, C, D - F, E, F, G, H)) :|: F >= 1 && A >= F && F >= 0 && A >= F + 2 && A >= B && A + F >= B + 1 && H >= A && H <= A && D >= A && D <= A 10.67/6.22 lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, B, C, H, E, F - 1, G, H)) :|: F >= A + 1 && A >= 1 && F >= 0 && A >= F + 2 && A >= B && A + F >= B + 1 && H >= A && H <= A && D >= A && D <= A 10.67/6.22 lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, B, C, H, E, F - 1, G, H)) :|: F >= 1 && 0 >= A + 1 && F >= 0 && A >= F + 2 && A >= B && A + F >= B + 1 && H >= A && H <= A && D >= A && D <= A 10.67/6.22 lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, B - F, C, H, E, F - 1, G, H)) :|: F >= 1 && F >= 0 && 0 >= F + 2 && 0 >= B && F >= B + 1 && D >= 0 && D <= 0 && H >= 0 && H <= 0 && A >= 0 && A <= 0 10.67/6.22 start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, E, E, G, G, A)) :|: TRUE 10.67/6.22 10.67/6.22 The start-symbols are:[start0_8] 10.67/6.22 10.67/6.22 10.67/6.22 ---------------------------------------- 10.67/6.22 10.67/6.22 (1) Koat2 Proof (FINISHED) 10.67/6.22 YES( ?, 5+2+max([1, -1+2*(-1+Arg_0)])*max([0, -1+Arg_0])+max([2, 2*(-1+Arg_0)])+max([1, -1+2*(-1+Arg_0)])*max([0, -1+Arg_0])+max([1, -1+2*(-1+Arg_0)])+max([2, 2*(-1+Arg_0)]) {O(n^2)}) 10.67/6.22 10.67/6.22 10.67/6.22 10.67/6.22 Initial Complexity Problem: 10.67/6.22 10.67/6.22 Start: start0 10.67/6.22 10.67/6.22 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7 10.67/6.22 10.67/6.22 Temp_Vars: 10.67/6.22 10.67/6.22 Locations: lbl111, lbl16, lbl82, start, start0, stop 10.67/6.22 10.67/6.22 Transitions: 10.67/6.22 10.67/6.22 lbl111(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl111(Arg_0,Arg_1,Arg_2,Arg_3-Arg_5,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_7 <= Arg_0 && 2 <= Arg_7 && 3 <= Arg_5+Arg_7 && 1+Arg_5 <= Arg_7 && 1+Arg_3 <= Arg_7 && Arg_1 <= Arg_7 && 4 <= Arg_0+Arg_7 && Arg_0 <= Arg_7 && 1+Arg_5 <= Arg_0 && 1 <= Arg_5 && 3 <= Arg_0+Arg_5 && 1+Arg_3 <= Arg_0 && Arg_1 <= Arg_0 && 2 <= Arg_0 && Arg_5 <= Arg_3 && Arg_5+1 <= Arg_0 && Arg_5+Arg_3 <= Arg_0 && Arg_1 <= Arg_0 && 1 <= Arg_5 && 0 <= Arg_3 && Arg_7 <= Arg_0 && Arg_0 <= Arg_7 10.67/6.22 10.67/6.22 lbl111(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl82(Arg_0,Arg_1,Arg_2,Arg_7,Arg_4,Arg_5-1,Arg_6,Arg_7):|:Arg_7 <= Arg_0 && 2 <= Arg_7 && 3 <= Arg_5+Arg_7 && 1+Arg_5 <= Arg_7 && 1+Arg_3 <= Arg_7 && Arg_1 <= Arg_7 && 4 <= Arg_0+Arg_7 && Arg_0 <= Arg_7 && 1+Arg_5 <= Arg_0 && 1 <= Arg_5 && 3 <= Arg_0+Arg_5 && 1+Arg_3 <= Arg_0 && Arg_1 <= Arg_0 && 2 <= Arg_0 && Arg_3+1 <= Arg_5 && 1 <= Arg_3 && Arg_5+1 <= Arg_0 && Arg_5+Arg_3 <= Arg_0 && Arg_1 <= Arg_0 && 1 <= Arg_5 && 0 <= Arg_3 && Arg_7 <= Arg_0 && Arg_0 <= Arg_7 10.67/6.22 10.67/6.22 lbl111(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl82(Arg_0,Arg_1-Arg_5,Arg_2,Arg_7,Arg_4,Arg_5-1,Arg_6,Arg_7):|:Arg_7 <= Arg_0 && 2 <= Arg_7 && 3 <= Arg_5+Arg_7 && 1+Arg_5 <= Arg_7 && 1+Arg_3 <= Arg_7 && Arg_1 <= Arg_7 && 4 <= Arg_0+Arg_7 && Arg_0 <= Arg_7 && 1+Arg_5 <= Arg_0 && 1 <= Arg_5 && 3 <= Arg_0+Arg_5 && 1+Arg_3 <= Arg_0 && Arg_1 <= Arg_0 && 2 <= Arg_0 && 1 <= Arg_5 && Arg_5+1 <= Arg_0 && Arg_5 <= Arg_0 && Arg_1 <= Arg_0 && Arg_3 <= 0 && 0 <= Arg_3 && Arg_7 <= Arg_0 && Arg_0 <= Arg_7 10.67/6.22 10.67/6.22 lbl16(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_7 <= Arg_3 && Arg_7 <= Arg_0 && 2 <= Arg_7 && 2 <= Arg_5+Arg_7 && 2+Arg_5 <= Arg_7 && 4 <= Arg_3+Arg_7 && Arg_3 <= Arg_7 && 1+Arg_1 <= Arg_7 && 4 <= Arg_0+Arg_7 && Arg_0 <= Arg_7 && Arg_5 <= 0 && 2+Arg_5 <= Arg_3 && 2+Arg_5 <= Arg_0 && 0 <= Arg_5 && 2 <= Arg_3+Arg_5 && 2 <= Arg_0+Arg_5 && Arg_3 <= Arg_0 && 2 <= Arg_3 && 1+Arg_1 <= Arg_3 && 4 <= Arg_0+Arg_3 && Arg_0 <= Arg_3 && 1+Arg_1 <= Arg_0 && 2 <= Arg_0 && 2 <= Arg_0 && Arg_1+1 <= Arg_0 && Arg_5 <= 0 && 0 <= Arg_5 && Arg_7 <= Arg_0 && Arg_0 <= Arg_7 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 10.67/6.22 10.67/6.22 lbl82(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl111(Arg_0,Arg_1,Arg_2,Arg_3-Arg_5,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_7 <= Arg_3 && Arg_7 <= Arg_0 && 2+Arg_5 <= Arg_7 && Arg_3 <= Arg_7 && Arg_1 <= Arg_7 && Arg_0 <= Arg_7 && 2+Arg_5 <= Arg_3 && 2+Arg_5 <= Arg_0 && Arg_3 <= Arg_0 && Arg_1 <= Arg_3 && Arg_0 <= Arg_3 && Arg_1 <= Arg_0 && 1 <= Arg_5 && Arg_5 <= Arg_0 && 0 <= Arg_5 && Arg_5+2 <= Arg_0 && Arg_1 <= Arg_0 && Arg_1+1 <= Arg_0+Arg_5 && Arg_7 <= Arg_0 && Arg_0 <= Arg_7 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 10.67/6.22 10.67/6.22 lbl82(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl16(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_7 <= Arg_3 && Arg_7 <= Arg_0 && 2+Arg_5 <= Arg_7 && Arg_3 <= Arg_7 && Arg_1 <= Arg_7 && Arg_0 <= Arg_7 && 2+Arg_5 <= Arg_3 && 2+Arg_5 <= Arg_0 && Arg_3 <= Arg_0 && Arg_1 <= Arg_3 && Arg_0 <= Arg_3 && Arg_1 <= Arg_0 && 2 <= Arg_0 && Arg_1 <= Arg_0 && Arg_1+1 <= Arg_0 && Arg_5 <= 0 && 0 <= Arg_5 && Arg_7 <= Arg_0 && Arg_0 <= Arg_7 && Arg_3 <= Arg_0 && Arg_0 <= Arg_3 10.67/6.22 10.67/6.22 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl111(Arg_0,Arg_7,Arg_2,1,Arg_4,Arg_7-1,Arg_6,Arg_7):|:Arg_7 <= Arg_0 && Arg_0 <= Arg_7 && Arg_6 <= Arg_5 && Arg_5 <= Arg_6 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 2 <= Arg_0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_6 && Arg_6 <= Arg_5 && Arg_7 <= Arg_0 && Arg_0 <= Arg_7 10.67/6.22 10.67/6.22 start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_7 <= Arg_0 && Arg_0 <= Arg_7 && Arg_6 <= Arg_5 && Arg_5 <= Arg_6 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && Arg_0 <= 1 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_6 && Arg_6 <= Arg_5 && Arg_7 <= Arg_0 && Arg_0 <= Arg_7 10.67/6.22 10.67/6.22 start0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> start(Arg_0,Arg_2,Arg_2,Arg_4,Arg_4,Arg_6,Arg_6,Arg_0):|: 10.67/6.22 10.67/6.22 10.67/6.22 10.67/6.22 Timebounds: 10.67/6.22 10.67/6.22 Overall timebound: 5+2+max([1, -1+2*(-1+Arg_0)])*max([0, -1+Arg_0])+max([2, 2*(-1+Arg_0)])+max([1, -1+2*(-1+Arg_0)])*max([0, -1+Arg_0])+max([1, -1+2*(-1+Arg_0)])+max([2, 2*(-1+Arg_0)]) {O(n^2)} 10.67/6.22 10.67/6.22 3: lbl111->lbl111: 2+max([1, -1+2*(-1+Arg_0)])*max([0, -1+Arg_0])+max([1, -1+2*(-1+Arg_0)])*max([0, -1+Arg_0]) {O(n^2)} 10.67/6.22 10.67/6.22 5: lbl111->lbl82: max([2, 2*(-1+Arg_0)]) {O(n)} 10.67/6.22 10.67/6.22 6: lbl111->lbl82: max([2, 2*(-1+Arg_0)]) {O(n)} 10.67/6.22 10.67/6.22 2: lbl16->stop: 1 {O(1)} 10.67/6.22 10.67/6.22 7: lbl82->lbl16: 1 {O(1)} 10.67/6.22 10.67/6.22 8: lbl82->lbl111: max([1, -1+2*(-1+Arg_0)]) {O(n)} 10.67/6.22 10.67/6.22 0: start->stop: 1 {O(1)} 10.67/6.22 10.67/6.22 1: start->lbl111: 1 {O(1)} 10.67/6.22 10.67/6.22 12: start0->start: 1 {O(1)} 10.67/6.22 10.67/6.22 10.67/6.22 10.67/6.22 Costbounds: 10.67/6.22 10.67/6.22 Overall costbound: 5+2+max([1, -1+2*(-1+Arg_0)])*max([0, -1+Arg_0])+max([2, 2*(-1+Arg_0)])+max([1, -1+2*(-1+Arg_0)])*max([0, -1+Arg_0])+max([1, -1+2*(-1+Arg_0)])+max([2, 2*(-1+Arg_0)]) {O(n^2)} popout

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job log

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actions

all output return to Complexity_ITS 2019-03-21 04.46