details

property	value
status	complete
benchmark	sipmabubble.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n127.star.cs.uiowa.edu
space	SAS10

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	10.3228 seconds
cpu usage	21.1991
user time	20.6607
system time	0.538436
max virtual memory	1.8545744E7
max residence set size	233224.0

stage attributes

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

output

21.04/9.94 WORST_CASE(Omega(n^2), O(n^2)) 21.04/9.95 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 21.04/9.95 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 21.04/9.95 21.04/9.95 21.04/9.95 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). 21.04/9.95 21.04/9.95 (0) CpxIntTrs 21.04/9.95 (1) Koat Proof [FINISHED, 524 ms] 21.04/9.95 (2) BOUNDS(1, n^2) 21.04/9.95 (3) Loat Proof [FINISHED, 8303 ms] 21.04/9.95 (4) BOUNDS(n^2, INF) 21.04/9.95 21.04/9.95 21.04/9.95 ---------------------------------------- 21.04/9.95 21.04/9.95 (0) 21.04/9.95 Obligation: 21.04/9.95 Complexity Int TRS consisting of the following rules: 21.04/9.95 start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, D, H)) :|: 0 >= A + 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H 21.04/9.95 start(A, B, C, D, E, F, G, H) -> Com_1(lbl142(A, B, C, D, 0, F, D - 1, H)) :|: D >= 0 && D <= 0 && B >= C && B <= C && A >= 0 && A <= 0 && E >= F && E <= F && G >= H && G <= H 21.04/9.95 start(A, B, C, D, E, F, G, H) -> Com_1(lbl91(A, I, C, D, 0, F, D, H)) :|: A >= 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H 21.04/9.95 start(A, B, C, D, E, F, G, H) -> Com_1(lbl131(A, B, C, D, 1, F, D, H)) :|: A >= 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H 21.04/9.95 lbl142(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= 0 && G + 1 >= 0 && G + 1 <= 0 && E >= 0 && E <= 0 && D >= A && D <= A 21.04/9.95 lbl142(A, B, C, D, E, F, G, H) -> Com_1(lbl142(A, B, C, D, 0, F, G - 1, H)) :|: A >= 1 && G >= 0 && G <= 0 && E >= 1 && E <= 1 && D >= A && D <= A 21.04/9.95 lbl142(A, B, C, D, E, F, G, H) -> Com_1(lbl91(A, I, C, D, 0, F, G, H)) :|: E >= 2 && E >= 0 && A >= E && G + 1 >= E && G + 1 <= E && D >= A && D <= A 21.04/9.95 lbl142(A, B, C, D, E, F, G, H) -> Com_1(lbl131(A, B, C, D, 1, F, G, H)) :|: E >= 2 && E >= 0 && A >= E && G + 1 >= E && G + 1 <= E && D >= A && D <= A 21.04/9.95 lbl131(A, B, C, D, E, F, G, H) -> Com_1(lbl142(A, B, C, D, E, F, G - 1, H)) :|: G >= 1 && A >= G && E >= G && E <= G && D >= A && D <= A 21.04/9.95 lbl131(A, B, C, D, E, F, G, H) -> Com_1(lbl91(A, I, C, D, E, F, G, H)) :|: G >= E + 1 && G >= E && E >= 1 && A >= G && D >= A && D <= A 21.04/9.95 lbl131(A, B, C, D, E, F, G, H) -> Com_1(lbl131(A, B, C, D, 1 + E, F, G, H)) :|: G >= E + 1 && G >= E && E >= 1 && A >= G && D >= A && D <= A 21.04/9.95 lbl91(A, B, C, D, E, F, G, H) -> Com_1(lbl131(A, B, C, D, 1 + E, F, G, H)) :|: E >= 0 && G >= E + 1 && A >= G && D >= A && D <= A 21.04/9.95 start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, A, F, F, H, H)) :|: TRUE 21.04/9.95 21.04/9.95 The start-symbols are:[start0_8] 21.04/9.95 21.04/9.95 21.04/9.95 ---------------------------------------- 21.04/9.95 21.04/9.95 (1) Koat Proof (FINISHED) 21.04/9.95 YES(?, 62*ar_0 + 24*ar_0^2 + 41) 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Initial complexity problem: 21.04/9.95 21.04/9.95 1: T: 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_3, ar_7)) [ 0 >= ar_0 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\ ar_1 = ar_2 /\ ar_0 = 0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 0 /\ ar_6 + 1 = 0 /\ ar_4 = 0 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\ ar_6 = 0 /\ ar_4 = 1 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\ ar_0 >= ar_6 /\ ar_4 = ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\ ar_6 >= ar_4 + 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5, ar_7, ar_7)) 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] 21.04/9.95 21.04/9.95 start location: koat_start 21.04/9.95 21.04/9.95 leaf cost: 0 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Repeatedly propagating knowledge in problem 1 produces the following problem: 21.04/9.95 21.04/9.95 2: T: 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_3, ar_7)) [ 0 >= ar_0 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\ ar_1 = ar_2 /\ ar_0 = 0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 0 /\ ar_6 + 1 = 0 /\ ar_4 = 0 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\ ar_6 = 0 /\ ar_4 = 1 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] popout

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all output return to Complexity_ITS 2019-03-21 04.46