3.33/1.60	WORST_CASE(?, O(1))
3.33/1.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.33/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.33/1.61	
3.33/1.61	
3.33/1.61	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.33/1.61	
3.33/1.61	(0) CpxIntTrs
3.33/1.61	(1) Koat Proof [FINISHED, 26 ms]
3.33/1.61	(2) BOUNDS(1, 1)
3.33/1.61	
3.33/1.61	
3.33/1.61	----------------------------------------
3.33/1.61	
3.33/1.61	(0)
3.33/1.61	Obligation:
3.33/1.61	Complexity Int TRS consisting of the following rules:
3.33/1.61	eval(A) -> Com_1(eval(2 * C - 1)) :|: 2 * C >= 2 * B && 1 + 2 * B >= 2 * C && 2 * C >= 1 && A >= 2 * C && A <= 2 * C
3.33/1.61	start(A) -> Com_1(eval(A)) :|: TRUE
3.33/1.61	
3.33/1.61	The start-symbols are:[start_1]
3.33/1.61	
3.33/1.61	
3.33/1.61	----------------------------------------
3.33/1.61	
3.33/1.61	(1) Koat Proof (FINISHED)
3.33/1.61	YES(?, 2)
3.33/1.61	
3.33/1.61	
3.33/1.61	
3.33/1.61	Initial complexity problem:
3.33/1.61	
3.33/1.61	1:	T:
3.33/1.61	
3.33/1.61			(Comp: ?, Cost: 1)    eval(ar_0) -> Com_1(eval(2*b - 1)) [ 2*b >= 2*c /\ 2*c + 1 >= 2*b /\ 2*b >= 1 /\ ar_0 = 2*b ]
3.33/1.61	
3.33/1.61			(Comp: ?, Cost: 1)    start(ar_0) -> Com_1(eval(ar_0))
3.33/1.61	
3.33/1.61			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(start(ar_0)) [ 0 <= 0 ]
3.33/1.61	
3.33/1.61		start location:	koat_start
3.33/1.61	
3.33/1.61		leaf cost:	0
3.33/1.61	
3.33/1.61	
3.33/1.61	
3.33/1.61	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.33/1.61	
3.33/1.61	2:	T:
3.33/1.61	
3.33/1.61			(Comp: 1, Cost: 1)    eval(ar_0) -> Com_1(eval(2*b - 1)) [ 2*b >= 2*c /\ 2*c + 1 >= 2*b /\ 2*b >= 1 /\ ar_0 = 2*b ]
3.33/1.61	
3.33/1.61			(Comp: 1, Cost: 1)    start(ar_0) -> Com_1(eval(ar_0))
3.33/1.61	
3.33/1.61			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(start(ar_0)) [ 0 <= 0 ]
3.33/1.61	
3.33/1.61		start location:	koat_start
3.33/1.61	
3.33/1.61		leaf cost:	0
3.33/1.61	
3.33/1.61	
3.33/1.61	
3.33/1.61	Complexity upper bound 2
3.33/1.61	
3.33/1.61	
3.33/1.61	
3.33/1.61	Time: 0.025 sec (SMT: 0.024 sec)
3.33/1.61	
3.33/1.61	
3.33/1.61	----------------------------------------
3.33/1.61	
3.33/1.61	(2)
3.33/1.61	BOUNDS(1, 1)
3.33/1.63	EOF