Complexity_ITS 2019-03-21 04.46 pair #429990968

details
property	value
status	complete
benchmark	wcet1.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n081.star.cs.uiowa.edu
space	SAS10
run statistics
property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.92557 seconds
cpu usage	6.93854
user time	6.5317
system time	0.406844
max virtual memory	1.8828036E7
max residence set size	236000.0
stage attributes
key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))
output
6.71/2.88	WORST_CASE(Omega(n^1), O(n^1))
6.71/2.89	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.71/2.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.71/2.89	
6.71/2.89	
6.71/2.89	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
6.71/2.89	
6.71/2.89	(0) CpxIntTrs
6.71/2.89	(1) Koat Proof [FINISHED, 715 ms]
6.71/2.89	(2) BOUNDS(1, n^1)
6.71/2.89	(3) Loat Proof [FINISHED, 1211 ms]
6.71/2.89	(4) BOUNDS(n^1, INF)
6.71/2.89	
6.71/2.89	
6.71/2.89	----------------------------------------
6.71/2.89	
6.71/2.89	(0)
6.71/2.89	Obligation:
6.71/2.89	Complexity Int TRS consisting of the following rules:
6.71/2.89	start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, 0, F, D, H)) :|: 0 >= A && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H
6.71/2.89	start(A, B, C, D, E, F, G, H) -> Com_1(cut(A, B, C, D, 0, F, D - 1, H)) :|: A >= 2 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H
6.71/2.89	start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, 0, F, D - 1, H)) :|: D >= 1 && D <= 1 && B >= C && B <= C && A >= 1 && A <= 1 && E >= F && E <= F && G >= H && G <= H
6.71/2.89	start(A, B, C, D, E, F, G, H) -> Com_1(cut(A, 0, C, D, 1, F, D - 1, H)) :|: A >= 2 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H
6.71/2.89	start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, 0, C, D, 0, F, D - 1, H)) :|: D >= 1 && D <= 1 && B >= C && B <= C && A >= 1 && A <= 1 && E >= F && E <= F && G >= H && G <= H
6.71/2.89	cut(A, B, C, D, E, F, G, H) -> Com_1(cut(A, B, C, D, E - 1, F, G - 1, H)) :|: G >= 2 && E >= 2 && G >= 1 && E >= 0 && A >= G + 1 && A >= G + E && D >= A && D <= A
6.71/2.89	cut(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E - 1, F, G - 1, H)) :|: E >= 2 && E >= 0 && A >= 2 && A >= 1 + E && G >= 1 && G <= 1 && D >= A && D <= A
6.71/2.89	cut(A, B, C, D, E, F, G, H) -> Com_1(cut(A, B, C, D, 0, F, G - 1, H)) :|: G >= 2 && 1 >= E && G >= 1 && E >= 0 && A >= G + 1 && A >= G + E && D >= A && D <= A
6.71/2.89	cut(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, 0, F, G - 1, H)) :|: 1 >= E && E >= 0 && A >= 2 && A >= 1 + E && G >= 1 && G <= 1 && D >= A && D <= A
6.71/2.89	cut(A, B, C, D, E, F, G, H) -> Com_1(cut(A, E, C, D, 1 + E, F, G - 1, H)) :|: G >= 2 && A >= E + 2 && G >= 1 && E >= 0 && A >= G + 1 && A >= G + E && D >= A && D <= A
6.71/2.89	cut(A, B, C, D, E, F, G, H) -> Com_1(stop(A, E, C, D, 1 + E, F, G - 1, H)) :|: A >= E + 2 && E >= 0 && A >= 2 && A >= 1 + E && G >= 1 && G <= 1 && D >= A && D <= A
6.71/2.89	cut(A, B, C, D, E, F, G, H) -> Com_1(cut(A, E, C, D, 0, F, G - 1, H)) :|: G >= 2 && E + 1 >= A && G >= 1 && E >= 0 && A >= G + 1 && A >= G + E && D >= A && D <= A
6.71/2.89	cut(A, B, C, D, E, F, G, H) -> Com_1(stop(A, E, C, D, 0, F, G - 1, H)) :|: A >= 1 && A >= 2 && G >= 1 && G <= 1 && E + 1 >= A && E + 1 <= A && D >= A && D <= A
6.71/2.89	start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, A, F, F, H, H)) :|: TRUE
6.71/2.89	
6.71/2.89	The start-symbols are:[start0_8]
6.71/2.89	
6.71/2.89	
6.71/2.89	----------------------------------------
6.71/2.89	
6.71/2.89	(1) Koat Proof (FINISHED)
6.71/2.89	YES(?, 3*ar_0 + 10)
6.71/2.89	
6.71/2.89	
6.71/2.89	
6.71/2.89	Initial complexity problem:
6.71/2.89	
6.71/2.89	1:	T:
6.71/2.89	
6.71/2.89			(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, 0, ar_5, ar_3, ar_7)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ]
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_0 >= 2 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ]
6.71/2.89	
6.71/2.89			(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, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 1 /\ ar_1 = ar_2 /\ ar_0 = 1 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ]
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(cut(ar_0, 0, ar_2, ar_3, 1, ar_5, ar_3 - 1, ar_7)) [ ar_0 >= 2 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ]
6.71/2.89	
6.71/2.89			(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, 0, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 1 /\ ar_1 = ar_2 /\ ar_0 = 1 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ]
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 2 /\ ar_4 >= 2 /\ ar_6 >= 1 /\ ar_4 >= 0 /\ ar_0 >= ar_6 + 1 /\ ar_0 >= ar_6 + ar_4 /\ ar_3 = ar_0 ]
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    cut(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 - 1, ar_5, ar_6 - 1, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= 2 /\ ar_0 >= ar_4 + 1 /\ ar_6 = 1 /\ ar_3 = ar_0 ]
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 2 /\ 1 >= ar_4 /\ ar_6 >= 1 /\ ar_4 >= 0 /\ ar_0 >= ar_6 + 1 /\ ar_0 >= ar_6 + ar_4 /\ ar_3 = ar_0 ]
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    cut(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, 0, ar_5, ar_6 - 1, ar_7)) [ 1 >= ar_4 /\ ar_4 >= 0 /\ ar_0 >= 2 /\ ar_0 >= ar_4 + 1 /\ ar_6 = 1 /\ ar_3 = ar_0 ]
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(cut(ar_0, ar_4, ar_2, ar_3, ar_4 + 1, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 2 /\ ar_0 >= ar_4 + 2 /\ ar_6 >= 1 /\ ar_4 >= 0 /\ ar_0 >= ar_6 + 1 /\ ar_0 >= ar_6 + ar_4 /\ ar_3 = ar_0 ]
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_4, ar_2, ar_3, ar_4 + 1, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= ar_4 + 2 /\ ar_4 >= 0 /\ ar_0 >= 2 /\ ar_0 >= ar_4 + 1 /\ ar_6 = 1 /\ ar_3 = ar_0 ]
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(cut(ar_0, ar_4, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 2 /\ ar_4 + 1 >= ar_0 /\ ar_6 >= 1 /\ ar_4 >= 0 /\ ar_0 >= ar_6 + 1 /\ ar_0 >= ar_6 + ar_4 /\ ar_3 = ar_0 ]
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_4, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\ ar_0 >= 2 /\ ar_6 = 1 /\ ar_4 + 1 = ar_0 /\ ar_3 = ar_0 ]
6.71/2.89	
6.71/2.89			(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))
6.71/2.89	
6.71/2.89			(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 ]
6.71/2.89	
6.71/2.89		start location:	koat_start
6.71/2.89	
6.71/2.89		leaf cost:	0
6.71/2.89	
6.71/2.89	
6.71/2.89	
6.71/2.89	Testing for reachability in the complexity graph removes the following transition from problem 1:
6.71/2.89	
6.71/2.89		cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(cut(ar_0, ar_4, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 2 /\ ar_4 + 1 >= ar_0 /\ ar_6 >= 1 /\ ar_4 >= 0 /\ ar_0 >= ar_6 + 1 /\ ar_0 >= ar_6 + ar_4 /\ ar_3 = ar_0 ]
6.71/2.89	
6.71/2.89	We thus obtain the following problem:
6.71/2.89	
6.71/2.89	2:	T:
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    cut(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 - 1, ar_5, ar_6 - 1, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= 2 /\ ar_0 >= ar_4 + 1 /\ ar_6 = 1 /\ ar_3 = ar_0 ]
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 2 /\ ar_4 >= 2 /\ ar_6 >= 1 /\ ar_4 >= 0 /\ ar_0 >= ar_6 + 1 /\ ar_0 >= ar_6 + ar_4 /\ ar_3 = ar_0 ]
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_4, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\ ar_0 >= 2 /\ ar_6 = 1 /\ ar_4 + 1 = ar_0 /\ ar_3 = ar_0 ]
6.71/2.89	
6.71/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_4, ar_2, ar_3, ar_4 + 1, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= ar_4 + 2 /\ ar_4 >= 0 /\ ar_0 >= 2 /\ ar_0 >= ar_4 + 1 /\ ar_6 = 1 /\ ar_3 = ar_0 ]
6.71/2.89
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