3.16/1.61	WORST_CASE(?, O(1))
3.16/1.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.16/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.16/1.61	
3.16/1.61	
3.16/1.61	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.16/1.61	
3.16/1.61	(0) CpxIntTrs
3.16/1.61	(1) Koat Proof [FINISHED, 18 ms]
3.16/1.61	(2) BOUNDS(1, 1)
3.16/1.61	
3.16/1.61	
3.16/1.61	----------------------------------------
3.16/1.61	
3.16/1.61	(0)
3.16/1.61	Obligation:
3.16/1.61	Complexity Int TRS consisting of the following rules:
3.16/1.61	f0(A, B) -> Com_1(f1(3000, B)) :|: TRUE
3.16/1.61	f1(A, B) -> Com_1(f1(A, B + 1000)) :|: B + 889 >= 0 && 1999 >= A
3.16/1.61	
3.16/1.61	The start-symbols are:[f0_2]
3.16/1.61	
3.16/1.61	
3.16/1.61	----------------------------------------
3.16/1.61	
3.16/1.61	(1) Koat Proof (FINISHED)
3.16/1.61	YES(?, 1)
3.16/1.61	
3.16/1.61	
3.16/1.61	
3.16/1.61	Initial complexity problem:
3.16/1.61	
3.16/1.61	1:	T:
3.16/1.61	
3.16/1.61			(Comp: ?, Cost: 1)    f0(ar_0, ar_1) -> Com_1(f1(3000, ar_1))
3.16/1.61	
3.16/1.61			(Comp: ?, Cost: 1)    f1(ar_0, ar_1) -> Com_1(f1(ar_0, ar_1 + 1000)) [ ar_1 + 889 >= 0 /\ 1999 >= ar_0 ]
3.16/1.61	
3.16/1.61			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(f0(ar_0, ar_1)) [ 0 <= 0 ]
3.16/1.61	
3.16/1.61		start location:	koat_start
3.16/1.61	
3.16/1.61		leaf cost:	0
3.16/1.61	
3.16/1.61	
3.16/1.61	
3.16/1.61	Testing for reachability in the complexity graph removes the following transition from problem 1:
3.16/1.61	
3.16/1.61		f1(ar_0, ar_1) -> Com_1(f1(ar_0, ar_1 + 1000)) [ ar_1 + 889 >= 0 /\ 1999 >= ar_0 ]
3.16/1.61	
3.16/1.61	We thus obtain the following problem:
3.16/1.61	
3.16/1.61	2:	T:
3.16/1.61	
3.16/1.61			(Comp: ?, Cost: 1)    f0(ar_0, ar_1) -> Com_1(f1(3000, ar_1))
3.16/1.61	
3.16/1.61			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(f0(ar_0, ar_1)) [ 0 <= 0 ]
3.16/1.61	
3.16/1.61		start location:	koat_start
3.16/1.61	
3.16/1.61		leaf cost:	0
3.16/1.61	
3.16/1.61	
3.16/1.61	
3.16/1.61	Repeatedly propagating knowledge in problem 2 produces the following problem:
3.16/1.61	
3.16/1.61	3:	T:
3.16/1.61	
3.16/1.61			(Comp: 1, Cost: 1)    f0(ar_0, ar_1) -> Com_1(f1(3000, ar_1))
3.16/1.61	
3.16/1.61			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(f0(ar_0, ar_1)) [ 0 <= 0 ]
3.16/1.61	
3.16/1.61		start location:	koat_start
3.16/1.61	
3.16/1.61		leaf cost:	0
3.16/1.61	
3.16/1.61	
3.16/1.61	
3.16/1.61	Complexity upper bound 1
3.16/1.61	
3.16/1.61	
3.16/1.61	
3.16/1.61	Time: 0.008 sec (SMT: 0.007 sec)
3.16/1.61	
3.16/1.61	
3.16/1.61	----------------------------------------
3.16/1.61	
3.16/1.61	(2)
3.16/1.61	BOUNDS(1, 1)
3.42/1.65	EOF