3.28/1.74	WORST_CASE(?, O(1))
3.28/1.75	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.28/1.75	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.28/1.75	
3.28/1.75	
3.28/1.75	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.28/1.75	
3.28/1.75	(0) CpxIntTrs
3.28/1.75	(1) Koat Proof [FINISHED, 0 ms]
3.28/1.75	(2) BOUNDS(1, 1)
3.28/1.75	
3.28/1.75	
3.28/1.75	----------------------------------------
3.28/1.75	
3.28/1.75	(0)
3.28/1.75	Obligation:
3.28/1.75	Complexity Int TRS consisting of the following rules:
3.28/1.75	f0(A, B, C) -> Com_1(f8(2, 1, 2)) :|: TRUE
3.28/1.75	
3.28/1.75	The start-symbols are:[f0_3]
3.28/1.75	
3.28/1.75	
3.28/1.75	----------------------------------------
3.28/1.75	
3.28/1.75	(1) Koat Proof (FINISHED)
3.28/1.75	YES(?, 1)
3.28/1.75	
3.28/1.75	
3.28/1.75	
3.28/1.75	Initial complexity problem:
3.28/1.75	
3.28/1.75	1:	T:
3.28/1.75	
3.28/1.75			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f8(2, 1, 2))
3.28/1.75	
3.28/1.75			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.28/1.75	
3.28/1.75		start location:	koat_start
3.28/1.75	
3.28/1.75		leaf cost:	0
3.28/1.75	
3.28/1.75	
3.28/1.75	
3.28/1.75	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.28/1.75	
3.28/1.75	2:	T:
3.28/1.75	
3.28/1.75			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f8(2, 1, 2))
3.28/1.75	
3.28/1.75			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.28/1.75	
3.28/1.75		start location:	koat_start
3.28/1.75	
3.28/1.75		leaf cost:	0
3.28/1.75	
3.28/1.75	
3.28/1.75	
3.28/1.75	Complexity upper bound 1
3.28/1.75	
3.28/1.75	
3.28/1.75	
3.28/1.75	Time: 0.007 sec (SMT: 0.007 sec)
3.28/1.75	
3.28/1.75	
3.28/1.75	----------------------------------------
3.28/1.75	
3.28/1.75	(2)
3.28/1.75	BOUNDS(1, 1)
3.28/1.77	EOF