Complexity_ITS 2019-03-21 04.46 pair #429990990

details
property	value
status	complete
benchmark	speedpldi2.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n055.star.cs.uiowa.edu
space	SAS10
run statistics
property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.04422 seconds
cpu usage	6.71386
user time	6.36016
system time	0.3537
max virtual memory	1.8748364E7
max residence set size	233652.0
stage attributes
key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))
output
6.51/3.00	WORST_CASE(Omega(n^1), O(n^1))
6.51/3.02	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.51/3.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.51/3.02	
6.51/3.02	
6.51/3.02	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
6.51/3.02	
6.51/3.02	(0) CpxIntTrs
6.51/3.02	(1) Koat Proof [FINISHED, 401 ms]
6.51/3.02	(2) BOUNDS(1, n^1)
6.51/3.02	(3) Loat Proof [FINISHED, 1200 ms]
6.51/3.02	(4) BOUNDS(n^1, INF)
6.51/3.02	
6.51/3.02	
6.51/3.02	----------------------------------------
6.51/3.02	
6.51/3.02	(0)
6.51/3.02	Obligation:
6.51/3.02	Complexity Int TRS consisting of the following rules:
6.51/3.02	start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 0 >= A && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
6.51/3.02	start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 0 >= G + 1 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
6.51/3.02	start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, 0, C, F, E, F, G, H)) :|: A >= 1 && F >= 0 && F <= 0 && B >= C && B <= C && D >= E && D <= E && G >= 0 && G <= 0 && H >= A && H <= A
6.51/3.02	start(A, B, C, D, E, F, G, H) -> Com_1(lM1(A, 1, C, F - 1, E, F, G, H)) :|: A >= 1 && G >= 1 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
6.51/3.02	lM1(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= B && G >= B && B >= 1 && D >= 0 && D <= 0 && H >= A && H <= A && F >= G && F <= G
6.51/3.02	lM1(A, B, C, D, E, F, G, H) -> Com_1(lZZ1(A, 0, C, D, E, F, G, H)) :|: D >= 1 && G >= D + A && A >= 1 && D >= 0 && B >= A && B <= A && H >= A && H <= A && F >= G && F <= G
6.51/3.02	lM1(A, B, C, D, E, F, G, H) -> Com_1(lM1(A, 1 + B, C, D - 1, E, F, G, H)) :|: A >= B + 1 && D >= 1 && A >= B && G >= D + B && B >= 1 && D >= 0 && H >= A && H <= A && F >= G && F <= G
6.51/3.02	lZZ1(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 0 >= D && G >= A + D && A >= 2 && D >= 1 && B >= 0 && B <= 0 && H >= A && H <= A && F >= G && F <= G
6.51/3.02	lZZ1(A, B, C, D, E, F, G, H) -> Com_1(lZZ1(A, 0, C, D, E, F, G, H)) :|: D >= 1 && 0 >= A && G >= A + D && A >= 2 && B >= 0 && B <= 0 && H >= A && H <= A && F >= G && F <= G
6.51/3.02	lZZ1(A, B, C, D, E, F, G, H) -> Com_1(lM1(A, 1 + B, C, D - 1, E, F, G, H)) :|: A >= 1 && D >= 1 && G >= A + D && A >= 2 && B >= 0 && B <= 0 && H >= A && H <= A && F >= G && F <= G
6.51/3.02	start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, E, E, G, G, A)) :|: TRUE
6.51/3.02	
6.51/3.02	The start-symbols are:[start0_8]
6.51/3.02	
6.51/3.02	
6.51/3.02	----------------------------------------
6.51/3.02	
6.51/3.02	(1) Koat Proof (FINISHED)
6.51/3.02	YES(?, 6*ar_6 + 9)
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Initial complexity problem:
6.51/3.02	
6.51/3.02	1:	T:
6.51/3.02	
6.51/3.02			(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_6, ar_7)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(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_6, ar_7)) [ 0 >= ar_6 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(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_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_5 = 0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_6 = 0 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_6 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(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 >= ar_1 /\ ar_6 >= ar_1 /\ ar_1 >= 1 /\ ar_3 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\ ar_6 >= ar_3 + ar_0 /\ ar_0 >= 1 /\ ar_3 >= 0 /\ ar_1 = ar_0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\ ar_3 >= 1 /\ ar_0 >= ar_1 /\ ar_6 >= ar_3 + ar_1 /\ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lZZ1(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)) [ 0 >= ar_3 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_3 >= 1 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\ 0 >= ar_0 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(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_4, ar_4, ar_6, ar_6, ar_0))
6.51/3.02	
6.51/3.02			(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 ]
6.51/3.02	
6.51/3.02		start location:	koat_start
6.51/3.02	
6.51/3.02		leaf cost:	0
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Testing for reachability in the complexity graph removes the following transitions from problem 1:
6.51/3.02	
6.51/3.02		lZZ1(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)) [ 0 >= ar_3 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_3 >= 1 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02		lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\ 0 >= ar_0 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02	We thus obtain the following problem:
6.51/3.02	
6.51/3.02	2:	T:
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\ ar_3 >= 1 /\ ar_0 >= ar_1 /\ ar_6 >= ar_3 + ar_1 /\ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\ ar_6 >= ar_3 + ar_0 /\ ar_0 >= 1 /\ ar_3 >= 0 /\ ar_1 = ar_0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(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 >= ar_1 /\ ar_6 >= ar_1 /\ ar_1 >= 1 /\ ar_3 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_6 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(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_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_5 = 0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_6 = 0 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(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_6, ar_7)) [ 0 >= ar_6 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(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_6, ar_7)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
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