3.43/1.69	WORST_CASE(?, O(1))
3.56/1.69	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.56/1.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.56/1.69	
3.56/1.69	
3.56/1.69	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.56/1.69	
3.56/1.69	(0) CpxIntTrs
3.56/1.69	(1) Koat Proof [FINISHED, 6 ms]
3.56/1.69	(2) BOUNDS(1, 1)
3.56/1.69	
3.56/1.69	
3.56/1.69	----------------------------------------
3.56/1.69	
3.56/1.69	(0)
3.56/1.69	Obligation:
3.56/1.69	Complexity Int TRS consisting of the following rules:
3.56/1.69	eval(A) -> Com_1(eval(-(2) + 2 * B)) :|: 2 * B >= 0 && A >= 1 + 2 * B && A <= 1 + 2 * B
3.56/1.69	start(A) -> Com_1(eval(A)) :|: TRUE
3.56/1.69	
3.56/1.69	The start-symbols are:[start_1]
3.56/1.69	
3.56/1.69	
3.56/1.69	----------------------------------------
3.56/1.69	
3.56/1.69	(1) Koat Proof (FINISHED)
3.56/1.69	YES(?, 2)
3.56/1.69	
3.56/1.69	
3.56/1.69	
3.56/1.69	Initial complexity problem:
3.56/1.69	
3.56/1.69	1:	T:
3.56/1.69	
3.56/1.69			(Comp: ?, Cost: 1)    eval(ar_0) -> Com_1(eval(2*b - 2)) [ 2*b >= 0 /\ ar_0 = 2*b + 1 ]
3.56/1.69	
3.56/1.69			(Comp: ?, Cost: 1)    start(ar_0) -> Com_1(eval(ar_0))
3.56/1.69	
3.56/1.69			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(start(ar_0)) [ 0 <= 0 ]
3.56/1.69	
3.56/1.69		start location:	koat_start
3.56/1.69	
3.56/1.69		leaf cost:	0
3.56/1.69	
3.56/1.69	
3.56/1.69	
3.56/1.69	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.56/1.69	
3.56/1.69	2:	T:
3.56/1.69	
3.56/1.69			(Comp: 1, Cost: 1)    eval(ar_0) -> Com_1(eval(2*b - 2)) [ 2*b >= 0 /\ ar_0 = 2*b + 1 ]
3.56/1.69	
3.56/1.69			(Comp: 1, Cost: 1)    start(ar_0) -> Com_1(eval(ar_0))
3.56/1.69	
3.56/1.69			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(start(ar_0)) [ 0 <= 0 ]
3.56/1.69	
3.56/1.69		start location:	koat_start
3.56/1.69	
3.56/1.69		leaf cost:	0
3.56/1.69	
3.56/1.69	
3.56/1.69	
3.56/1.69	Complexity upper bound 2
3.56/1.69	
3.56/1.69	
3.56/1.69	
3.56/1.69	Time: 0.029 sec (SMT: 0.029 sec)
3.56/1.69	
3.56/1.69	
3.56/1.69	----------------------------------------
3.56/1.69	
3.56/1.69	(2)
3.56/1.69	BOUNDS(1, 1)
3.59/1.71	EOF