3.23/1.65	WORST_CASE(?, O(1))
3.23/1.66	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
3.23/1.66	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.23/1.66	
3.23/1.66	
3.23/1.66	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.23/1.66	
3.23/1.66	(0) CpxIntTrs
3.23/1.66	(1) Koat Proof [FINISHED, 0 ms]
3.23/1.66	(2) BOUNDS(1, 1)
3.23/1.66	
3.23/1.66	
3.23/1.66	----------------------------------------
3.23/1.66	
3.23/1.66	(0)
3.23/1.66	Obligation:
3.23/1.66	Complexity Int TRS consisting of the following rules:
3.23/1.66	f0(A, B) -> Com_1(f7(1, 1)) :|: TRUE
3.23/1.66	
3.23/1.66	The start-symbols are:[f0_2]
3.23/1.66	
3.23/1.66	
3.23/1.66	----------------------------------------
3.23/1.66	
3.23/1.66	(1) Koat Proof (FINISHED)
3.23/1.66	YES(?, 1)
3.23/1.66	
3.23/1.66	
3.23/1.66	
3.23/1.66	Initial complexity problem:
3.23/1.66	
3.23/1.66	1:	T:
3.23/1.66	
3.23/1.66			(Comp: ?, Cost: 1)    f0(ar_0, ar_1) -> Com_1(f7(1, 1))
3.23/1.66	
3.23/1.66			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(f0(ar_0, ar_1)) [ 0 <= 0 ]
3.23/1.66	
3.23/1.66		start location:	koat_start
3.23/1.66	
3.23/1.66		leaf cost:	0
3.23/1.66	
3.23/1.66	
3.23/1.66	
3.23/1.66	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.23/1.66	
3.23/1.66	2:	T:
3.23/1.66	
3.23/1.66			(Comp: 1, Cost: 1)    f0(ar_0, ar_1) -> Com_1(f7(1, 1))
3.23/1.66	
3.23/1.66			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(f0(ar_0, ar_1)) [ 0 <= 0 ]
3.23/1.66	
3.23/1.66		start location:	koat_start
3.23/1.66	
3.23/1.66		leaf cost:	0
3.23/1.66	
3.23/1.66	
3.23/1.66	
3.23/1.66	Complexity upper bound 1
3.23/1.66	
3.23/1.66	
3.23/1.66	
3.23/1.66	Time: 0.005 sec (SMT: 0.005 sec)
3.23/1.66	
3.23/1.66	
3.23/1.66	----------------------------------------
3.23/1.66	
3.23/1.66	(2)
3.23/1.66	BOUNDS(1, 1)
3.44/1.69	EOF