3.46/1.64	WORST_CASE(?, O(1))
3.46/1.65	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.46/1.65	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.46/1.65	
3.46/1.65	
3.46/1.65	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.46/1.65	
3.46/1.65	(0) CpxIntTrs
3.46/1.65	(1) Koat Proof [FINISHED, 22 ms]
3.46/1.65	(2) BOUNDS(1, 1)
3.46/1.65	
3.46/1.65	
3.46/1.65	----------------------------------------
3.46/1.65	
3.46/1.65	(0)
3.46/1.65	Obligation:
3.46/1.65	Complexity Int TRS consisting of the following rules:
3.46/1.65	f4(A, B) -> Com_1(f300(A, C)) :|: 0 >= A + 1
3.46/1.65	f4(A, B) -> Com_1(f300(1 + A, C)) :|: A >= 0
3.46/1.65	
3.46/1.65	The start-symbols are:[f4_2]
3.46/1.65	
3.46/1.65	
3.46/1.65	----------------------------------------
3.46/1.65	
3.46/1.65	(1) Koat Proof (FINISHED)
3.46/1.65	YES(?, 2)
3.46/1.65	
3.46/1.65	
3.46/1.65	
3.46/1.65	Initial complexity problem:
3.46/1.65	
3.46/1.65	1:	T:
3.46/1.65	
3.46/1.65			(Comp: ?, Cost: 1)    f4(ar_0, ar_1) -> Com_1(f300(ar_0, c)) [ 0 >= ar_0 + 1 ]
3.46/1.65	
3.46/1.65			(Comp: ?, Cost: 1)    f4(ar_0, ar_1) -> Com_1(f300(ar_0 + 1, c)) [ ar_0 >= 0 ]
3.46/1.65	
3.46/1.65			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(f4(ar_0, ar_1)) [ 0 <= 0 ]
3.46/1.65	
3.46/1.65		start location:	koat_start
3.46/1.65	
3.46/1.65		leaf cost:	0
3.46/1.65	
3.46/1.65	
3.46/1.65	
3.46/1.65	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.46/1.65	
3.46/1.65	2:	T:
3.46/1.65	
3.46/1.65			(Comp: 1, Cost: 1)    f4(ar_0, ar_1) -> Com_1(f300(ar_0, c)) [ 0 >= ar_0 + 1 ]
3.46/1.65	
3.46/1.65			(Comp: 1, Cost: 1)    f4(ar_0, ar_1) -> Com_1(f300(ar_0 + 1, c)) [ ar_0 >= 0 ]
3.46/1.65	
3.46/1.65			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(f4(ar_0, ar_1)) [ 0 <= 0 ]
3.46/1.65	
3.46/1.65		start location:	koat_start
3.46/1.65	
3.46/1.65		leaf cost:	0
3.46/1.65	
3.46/1.65	
3.46/1.65	
3.46/1.65	Complexity upper bound 2
3.46/1.65	
3.46/1.65	
3.46/1.65	
3.46/1.65	Time: 0.022 sec (SMT: 0.021 sec)
3.46/1.65	
3.46/1.65	
3.46/1.65	----------------------------------------
3.46/1.65	
3.46/1.65	(2)
3.46/1.65	BOUNDS(1, 1)
3.46/1.67	EOF