3.47/1.65	WORST_CASE(?, O(1))
3.47/1.66	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.47/1.66	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.47/1.66	
3.47/1.66	
3.47/1.66	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.47/1.66	
3.47/1.66	(0) CpxIntTrs
3.47/1.66	(1) Koat Proof [FINISHED, 8 ms]
3.47/1.66	(2) BOUNDS(1, 1)
3.47/1.66	
3.47/1.66	
3.47/1.66	----------------------------------------
3.47/1.66	
3.47/1.66	(0)
3.47/1.66	Obligation:
3.47/1.66	Complexity Int TRS consisting of the following rules:
3.47/1.66	eval(A, B) -> Com_1(eval(B, A)) :|: A >= B + 1
3.47/1.66	start(A, B) -> Com_1(eval(A, B)) :|: TRUE
3.47/1.66	
3.47/1.66	The start-symbols are:[start_2]
3.47/1.66	
3.47/1.66	
3.47/1.66	----------------------------------------
3.47/1.66	
3.47/1.66	(1) Koat Proof (FINISHED)
3.47/1.66	YES(?, 2)
3.47/1.66	
3.47/1.66	
3.47/1.66	
3.47/1.66	Initial complexity problem:
3.47/1.66	
3.47/1.66	1:	T:
3.47/1.66	
3.47/1.66			(Comp: ?, Cost: 1)    eval(ar_0, ar_1) -> Com_1(eval(ar_1, ar_0)) [ ar_0 >= ar_1 + 1 ]
3.47/1.66	
3.47/1.66			(Comp: ?, Cost: 1)    start(ar_0, ar_1) -> Com_1(eval(ar_0, ar_1))
3.47/1.66	
3.47/1.66			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(start(ar_0, ar_1)) [ 0 <= 0 ]
3.47/1.66	
3.47/1.66		start location:	koat_start
3.47/1.66	
3.47/1.66		leaf cost:	0
3.47/1.66	
3.47/1.66	
3.47/1.66	
3.47/1.66	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.47/1.66	
3.47/1.66	2:	T:
3.47/1.66	
3.47/1.66			(Comp: 1, Cost: 1)    eval(ar_0, ar_1) -> Com_1(eval(ar_1, ar_0)) [ ar_0 >= ar_1 + 1 ]
3.47/1.66	
3.47/1.66			(Comp: 1, Cost: 1)    start(ar_0, ar_1) -> Com_1(eval(ar_0, ar_1))
3.47/1.66	
3.47/1.66			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(start(ar_0, ar_1)) [ 0 <= 0 ]
3.47/1.66	
3.47/1.66		start location:	koat_start
3.47/1.66	
3.47/1.66		leaf cost:	0
3.47/1.66	
3.47/1.66	
3.47/1.66	
3.47/1.66	Complexity upper bound 2
3.47/1.66	
3.47/1.66	
3.47/1.66	
3.47/1.66	Time: 0.010 sec (SMT: 0.010 sec)
3.47/1.66	
3.47/1.66	
3.47/1.66	----------------------------------------
3.47/1.66	
3.47/1.66	(2)
3.47/1.66	BOUNDS(1, 1)
3.47/1.68	EOF