Complexity_ITS 2019-03-21 04.46 pair #429990908

details

property	value
status	complete
benchmark	p-58.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n099.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.07698 seconds
cpu usage	3.58004
user time	3.38181
system time	0.198229
max virtual memory	3.6437256E7
max residence set size	221912.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(1))

output

3.43/1.93	WORST_CASE(?, O(1))
3.43/1.94	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
3.43/1.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.43/1.94	
3.43/1.94	
3.43/1.94	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.43/1.94	
3.43/1.94	(0) CpxIntTrs
3.43/1.94	(1) Koat Proof [FINISHED, 11 ms]
3.43/1.94	(2) BOUNDS(1, 1)
3.43/1.94	
3.43/1.94	
3.43/1.94	----------------------------------------
3.43/1.94	
3.43/1.94	(0)
3.43/1.94	Obligation:
3.43/1.94	Complexity Int TRS consisting of the following rules:
3.43/1.94	f2(A, B, C, D) -> Com_1(f2(1 + A, 1 + B, -(1) + C, D)) :|: TRUE
3.43/1.94	f1(A, B, C, D) -> Com_1(f2(A, B, C, D)) :|: A >= C && B >= 1 + A && C >= 1 + B
3.43/1.94	f1(A, B, C, D) -> Com_1(f300(A, B, C, E)) :|: C >= 1 + B && B >= 1 + A && C >= 1 + A
3.43/1.94	f1(A, B, C, D) -> Com_1(f300(A, B, C, E)) :|: B >= 1 + A && B >= C
3.43/1.94	f1(A, B, C, D) -> Com_1(f300(A, B, C, E)) :|: A >= B
3.43/1.94	
3.43/1.94	The start-symbols are:[f1_4]
3.43/1.94	
3.43/1.94	
3.43/1.94	----------------------------------------
3.43/1.94	
3.43/1.94	(1) Koat Proof (FINISHED)
3.43/1.94	YES(?, 3)
3.43/1.94	
3.43/1.94	
3.43/1.94	
3.43/1.94	Initial complexity problem:
3.43/1.94	
3.43/1.94	1:	T:
3.43/1.94	
3.43/1.94			(Comp: ?, Cost: 1)    f2(ar_0, ar_1, ar_2, ar_3) -> Com_1(f2(ar_0 + 1, ar_1 + 1, ar_2 - 1, ar_3))
3.43/1.94	
3.43/1.94			(Comp: ?, Cost: 1)    f1(ar_0, ar_1, ar_2, ar_3) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 /\ ar_1 >= ar_0 + 1 /\ ar_2 >= ar_1 + 1 ]
3.43/1.94	
3.43/1.94			(Comp: ?, Cost: 1)    f1(ar_0, ar_1, ar_2, ar_3) -> Com_1(f300(ar_0, ar_1, ar_2, e)) [ ar_2 >= ar_1 + 1 /\ ar_1 >= ar_0 + 1 /\ ar_2 >= ar_0 + 1 ]
3.43/1.94	
3.43/1.94			(Comp: ?, Cost: 1)    f1(ar_0, ar_1, ar_2, ar_3) -> Com_1(f300(ar_0, ar_1, ar_2, e)) [ ar_1 >= ar_0 + 1 /\ ar_1 >= ar_2 ]
3.43/1.94	
3.43/1.94			(Comp: ?, Cost: 1)    f1(ar_0, ar_1, ar_2, ar_3) -> Com_1(f300(ar_0, ar_1, ar_2, e)) [ ar_0 >= ar_1 ]
3.43/1.94	
3.43/1.94			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
3.43/1.94	
3.43/1.94		start location:	koat_start
3.43/1.94	
3.43/1.94		leaf cost:	0
3.43/1.94	
3.43/1.94	
3.43/1.94	
3.43/1.94	Testing for reachability in the complexity graph removes the following transitions from problem 1:
3.43/1.94	
3.43/1.94		f2(ar_0, ar_1, ar_2, ar_3) -> Com_1(f2(ar_0 + 1, ar_1 + 1, ar_2 - 1, ar_3))
3.43/1.94	
3.43/1.94		f1(ar_0, ar_1, ar_2, ar_3) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 /\ ar_1 >= ar_0 + 1 /\ ar_2 >= ar_1 + 1 ]
3.43/1.94	
3.43/1.94	We thus obtain the following problem:
3.43/1.94	
3.43/1.94	2:	T:
3.43/1.94	
3.43/1.94			(Comp: ?, Cost: 1)    f1(ar_0, ar_1, ar_2, ar_3) -> Com_1(f300(ar_0, ar_1, ar_2, e)) [ ar_0 >= ar_1 ]
3.43/1.94	
3.43/1.94			(Comp: ?, Cost: 1)    f1(ar_0, ar_1, ar_2, ar_3) -> Com_1(f300(ar_0, ar_1, ar_2, e)) [ ar_1 >= ar_0 + 1 /\ ar_1 >= ar_2 ]
3.43/1.94	
3.43/1.94			(Comp: ?, Cost: 1)    f1(ar_0, ar_1, ar_2, ar_3) -> Com_1(f300(ar_0, ar_1, ar_2, e)) [ ar_2 >= ar_1 + 1 /\ ar_1 >= ar_0 + 1 /\ ar_2 >= ar_0 + 1 ]
3.43/1.94	
3.43/1.94			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
3.43/1.94	
3.43/1.94		start location:	koat_start
3.43/1.94	
3.43/1.94		leaf cost:	0
3.43/1.94	
3.43/1.94	
3.43/1.94	
3.43/1.94	Repeatedly propagating knowledge in problem 2 produces the following problem:
3.43/1.94	
3.43/1.94	3:	T:
3.43/1.94	
3.43/1.94			(Comp: 1, Cost: 1)    f1(ar_0, ar_1, ar_2, ar_3) -> Com_1(f300(ar_0, ar_1, ar_2, e)) [ ar_0 >= ar_1 ]
3.43/1.94	
3.43/1.94			(Comp: 1, Cost: 1)    f1(ar_0, ar_1, ar_2, ar_3) -> Com_1(f300(ar_0, ar_1, ar_2, e)) [ ar_1 >= ar_0 + 1 /\ ar_1 >= ar_2 ]
3.43/1.94	
3.43/1.94			(Comp: 1, Cost: 1)    f1(ar_0, ar_1, ar_2, ar_3) -> Com_1(f300(ar_0, ar_1, ar_2, e)) [ ar_2 >= ar_1 + 1 /\ ar_1 >= ar_0 + 1 /\ ar_2 >= ar_0 + 1 ]
3.43/1.94	
3.43/1.94			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
3.43/1.94	
3.43/1.94		start location:	koat_start
3.43/1.94	
3.43/1.94		leaf cost:	0
3.43/1.94	
3.43/1.94	
3.43/1.94	
3.43/1.94	Complexity upper bound 3
3.43/1.94	
3.43/1.94

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