3.31/1.62	WORST_CASE(?, O(1))
3.31/1.63	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.31/1.63	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.31/1.63	
3.31/1.63	
3.31/1.63	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.31/1.63	
3.31/1.63	(0) CpxIntTrs
3.31/1.63	(1) Koat Proof [FINISHED, 25 ms]
3.31/1.63	(2) BOUNDS(1, 1)
3.31/1.63	
3.31/1.63	
3.31/1.63	----------------------------------------
3.31/1.63	
3.31/1.63	(0)
3.31/1.63	Obligation:
3.31/1.63	Complexity Int TRS consisting of the following rules:
3.31/1.63	eval(A) -> Com_1(eval(2 * B)) :|: 2 * B >= 0 && A >= 1 + 2 * B && A <= 1 + 2 * B
3.31/1.63	start(A) -> Com_1(eval(A)) :|: TRUE
3.31/1.63	
3.31/1.63	The start-symbols are:[start_1]
3.31/1.63	
3.31/1.63	
3.31/1.63	----------------------------------------
3.31/1.63	
3.31/1.63	(1) Koat Proof (FINISHED)
3.31/1.63	YES(?, 2)
3.31/1.63	
3.31/1.63	
3.31/1.63	
3.31/1.63	Initial complexity problem:
3.31/1.63	
3.31/1.63	1:	T:
3.31/1.63	
3.31/1.63			(Comp: ?, Cost: 1)    eval(ar_0) -> Com_1(eval(2*b)) [ 2*b >= 0 /\ ar_0 = 2*b + 1 ]
3.31/1.63	
3.31/1.63			(Comp: ?, Cost: 1)    start(ar_0) -> Com_1(eval(ar_0))
3.31/1.63	
3.31/1.63			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(start(ar_0)) [ 0 <= 0 ]
3.31/1.63	
3.31/1.63		start location:	koat_start
3.31/1.63	
3.31/1.63		leaf cost:	0
3.31/1.63	
3.31/1.63	
3.31/1.63	
3.31/1.63	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.31/1.63	
3.31/1.63	2:	T:
3.31/1.63	
3.31/1.63			(Comp: 1, Cost: 1)    eval(ar_0) -> Com_1(eval(2*b)) [ 2*b >= 0 /\ ar_0 = 2*b + 1 ]
3.31/1.63	
3.31/1.63			(Comp: 1, Cost: 1)    start(ar_0) -> Com_1(eval(ar_0))
3.31/1.63	
3.31/1.63			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(start(ar_0)) [ 0 <= 0 ]
3.31/1.63	
3.31/1.63		start location:	koat_start
3.31/1.63	
3.31/1.63		leaf cost:	0
3.31/1.63	
3.31/1.63	
3.31/1.63	
3.31/1.63	Complexity upper bound 2
3.31/1.63	
3.31/1.63	
3.31/1.63	
3.31/1.63	Time: 0.023 sec (SMT: 0.023 sec)
3.31/1.63	
3.31/1.63	
3.31/1.63	----------------------------------------
3.31/1.63	
3.31/1.63	(2)
3.31/1.63	BOUNDS(1, 1)
3.53/1.70	EOF