3.25/1.67	WORST_CASE(?, O(1))
3.25/1.68	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.25/1.68	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.25/1.68	
3.25/1.68	
3.25/1.68	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.25/1.68	
3.25/1.68	(0) CpxIntTrs
3.25/1.68	(1) Koat Proof [FINISHED, 7 ms]
3.25/1.68	(2) BOUNDS(1, 1)
3.25/1.68	
3.25/1.68	
3.25/1.68	----------------------------------------
3.25/1.68	
3.25/1.68	(0)
3.25/1.68	Obligation:
3.25/1.68	Complexity Int TRS consisting of the following rules:
3.25/1.68	f0(A) -> Com_1(f7(B)) :|: TRUE
3.25/1.68	
3.25/1.68	The start-symbols are:[f0_1]
3.25/1.68	
3.25/1.68	
3.25/1.68	----------------------------------------
3.25/1.68	
3.25/1.68	(1) Koat Proof (FINISHED)
3.25/1.68	YES(?, 1)
3.25/1.68	
3.25/1.68	
3.25/1.68	
3.25/1.68	Initial complexity problem:
3.25/1.68	
3.25/1.68	1:	T:
3.25/1.68	
3.25/1.68			(Comp: ?, Cost: 1)    f0(ar_0) -> Com_1(f7(b))
3.25/1.68	
3.25/1.68			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.25/1.68	
3.25/1.68		start location:	koat_start
3.25/1.68	
3.25/1.68		leaf cost:	0
3.25/1.68	
3.25/1.68	
3.25/1.68	
3.25/1.68	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.25/1.68	
3.25/1.68	2:	T:
3.25/1.68	
3.25/1.68			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f7(b))
3.25/1.68	
3.25/1.68			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.25/1.68	
3.25/1.68		start location:	koat_start
3.25/1.68	
3.25/1.68		leaf cost:	0
3.25/1.68	
3.25/1.68	
3.25/1.68	
3.25/1.68	Complexity upper bound 1
3.25/1.68	
3.25/1.68	
3.25/1.68	
3.25/1.68	Time: 0.005 sec (SMT: 0.005 sec)
3.25/1.68	
3.25/1.68	
3.25/1.68	----------------------------------------
3.25/1.68	
3.25/1.68	(2)
3.25/1.68	BOUNDS(1, 1)
3.39/1.71	EOF