3.29/1.60	WORST_CASE(?, O(1))
3.37/1.61	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
3.37/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.37/1.61	
3.37/1.61	
3.37/1.61	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.37/1.61	
3.37/1.61	(0) CpxIntTrs
3.37/1.61	(1) Koat Proof [FINISHED, 23 ms]
3.37/1.61	(2) BOUNDS(1, 1)
3.37/1.61	
3.37/1.61	
3.37/1.61	----------------------------------------
3.37/1.61	
3.37/1.61	(0)
3.37/1.61	Obligation:
3.37/1.61	Complexity Int TRS consisting of the following rules:
3.37/1.61	f8(A, B, C) -> Com_1(f12(2, 1, C)) :|: A >= 2 && A <= 2
3.37/1.61	f8(A, B, C) -> Com_1(f12(A, 0, C)) :|: 1 >= A
3.37/1.61	f8(A, B, C) -> Com_1(f12(A, 0, C)) :|: A >= 3
3.37/1.61	f0(A, B, C) -> Com_1(f12(1, 1, 1)) :|: TRUE
3.37/1.61	
3.37/1.61	The start-symbols are:[f0_3]
3.37/1.61	
3.37/1.61	
3.37/1.61	----------------------------------------
3.37/1.61	
3.37/1.61	(1) Koat Proof (FINISHED)
3.37/1.61	YES(?, 1)
3.37/1.61	
3.37/1.61	
3.37/1.61	
3.37/1.61	Initial complexity problem:
3.37/1.61	
3.37/1.61	1:	T:
3.37/1.61	
3.37/1.61			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f12(2, 1, ar_2)) [ ar_0 = 2 ]
3.37/1.61	
3.37/1.61			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f12(ar_0, 0, ar_2)) [ 1 >= ar_0 ]
3.37/1.61	
3.37/1.61			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f12(ar_0, 0, ar_2)) [ ar_0 >= 3 ]
3.37/1.61	
3.37/1.61			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f12(1, 1, 1))
3.37/1.61	
3.37/1.61			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.37/1.61	
3.37/1.61		start location:	koat_start
3.37/1.61	
3.37/1.61		leaf cost:	0
3.37/1.61	
3.37/1.61	
3.37/1.61	
3.37/1.61	Testing for reachability in the complexity graph removes the following transitions from problem 1:
3.37/1.61	
3.37/1.61		f8(ar_0, ar_1, ar_2) -> Com_1(f12(2, 1, ar_2)) [ ar_0 = 2 ]
3.37/1.61	
3.37/1.61		f8(ar_0, ar_1, ar_2) -> Com_1(f12(ar_0, 0, ar_2)) [ 1 >= ar_0 ]
3.37/1.61	
3.37/1.61		f8(ar_0, ar_1, ar_2) -> Com_1(f12(ar_0, 0, ar_2)) [ ar_0 >= 3 ]
3.37/1.61	
3.37/1.61	We thus obtain the following problem:
3.37/1.61	
3.37/1.61	2:	T:
3.37/1.61	
3.37/1.61			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f12(1, 1, 1))
3.37/1.61	
3.37/1.61			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.37/1.61	
3.37/1.61		start location:	koat_start
3.37/1.61	
3.37/1.61		leaf cost:	0
3.37/1.61	
3.37/1.61	
3.37/1.61	
3.37/1.61	Repeatedly propagating knowledge in problem 2 produces the following problem:
3.37/1.61	
3.37/1.61	3:	T:
3.37/1.61	
3.37/1.61			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f12(1, 1, 1))
3.37/1.61	
3.37/1.61			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.37/1.61	
3.37/1.61		start location:	koat_start
3.37/1.61	
3.37/1.61		leaf cost:	0
3.37/1.61	
3.37/1.61	
3.37/1.61	
3.37/1.61	Complexity upper bound 1
3.37/1.61	
3.37/1.61	
3.37/1.61	
3.37/1.61	Time: 0.007 sec (SMT: 0.007 sec)
3.37/1.61	
3.37/1.61	
3.37/1.61	----------------------------------------
3.37/1.61	
3.37/1.61	(2)
3.37/1.61	BOUNDS(1, 1)
3.38/1.63	EOF