3.52/1.69	WORST_CASE(?, O(1))
3.52/1.70	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.52/1.70	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.52/1.70	
3.52/1.70	
3.52/1.70	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.52/1.70	
3.52/1.70	(0) CpxIntTrs
3.52/1.70	(1) Koat Proof [FINISHED, 19 ms]
3.52/1.70	(2) BOUNDS(1, 1)
3.52/1.70	
3.52/1.70	
3.52/1.70	----------------------------------------
3.52/1.70	
3.52/1.70	(0)
3.52/1.70	Obligation:
3.52/1.70	Complexity Int TRS consisting of the following rules:
3.52/1.70	f0(A, B) -> Com_1(f0(A, A)) :|: 0 >= A + 1 && B >= 0 && B <= 0
3.52/1.70	f0(A, B) -> Com_1(f0(A, A)) :|: A >= 1 && B >= 0 && B <= 0
3.52/1.70	start(A, B) -> Com_1(f0(A, B)) :|: TRUE
3.52/1.70	
3.52/1.70	The start-symbols are:[start_2]
3.52/1.70	
3.52/1.70	
3.52/1.70	----------------------------------------
3.52/1.70	
3.52/1.70	(1) Koat Proof (FINISHED)
3.52/1.70	YES(?, 3)
3.52/1.70	
3.52/1.70	
3.52/1.70	
3.52/1.70	Initial complexity problem:
3.52/1.70	
3.52/1.70	1:	T:
3.52/1.70	
3.52/1.70			(Comp: ?, Cost: 1)    f0(ar_0, ar_1) -> Com_1(f0(ar_0, ar_0)) [ 0 >= ar_0 + 1 /\ ar_1 = 0 ]
3.52/1.70	
3.52/1.70			(Comp: ?, Cost: 1)    f0(ar_0, ar_1) -> Com_1(f0(ar_0, ar_0)) [ ar_0 >= 1 /\ ar_1 = 0 ]
3.52/1.70	
3.52/1.70			(Comp: ?, Cost: 1)    start(ar_0, ar_1) -> Com_1(f0(ar_0, ar_1))
3.52/1.70	
3.52/1.70			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(start(ar_0, ar_1)) [ 0 <= 0 ]
3.52/1.70	
3.52/1.70		start location:	koat_start
3.52/1.70	
3.52/1.70		leaf cost:	0
3.52/1.70	
3.52/1.70	
3.52/1.70	
3.52/1.70	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.52/1.70	
3.52/1.70	2:	T:
3.52/1.70	
3.52/1.70			(Comp: 1, Cost: 1)    f0(ar_0, ar_1) -> Com_1(f0(ar_0, ar_0)) [ 0 >= ar_0 + 1 /\ ar_1 = 0 ]
3.52/1.70	
3.52/1.70			(Comp: 1, Cost: 1)    f0(ar_0, ar_1) -> Com_1(f0(ar_0, ar_0)) [ ar_0 >= 1 /\ ar_1 = 0 ]
3.52/1.70	
3.52/1.70			(Comp: 1, Cost: 1)    start(ar_0, ar_1) -> Com_1(f0(ar_0, ar_1))
3.52/1.70	
3.52/1.70			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(start(ar_0, ar_1)) [ 0 <= 0 ]
3.52/1.70	
3.52/1.70		start location:	koat_start
3.52/1.70	
3.52/1.70		leaf cost:	0
3.52/1.70	
3.52/1.70	
3.52/1.70	
3.52/1.70	Complexity upper bound 3
3.52/1.70	
3.52/1.70	
3.52/1.70	
3.52/1.70	Time: 0.017 sec (SMT: 0.016 sec)
3.52/1.70	
3.52/1.70	
3.52/1.70	----------------------------------------
3.52/1.70	
3.52/1.70	(2)
3.52/1.70	BOUNDS(1, 1)
3.60/1.71	EOF