3.28/1.83	WORST_CASE(?, O(1))
3.28/1.84	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.28/1.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.28/1.84	
3.28/1.84	
3.28/1.84	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.28/1.84	
3.28/1.84	(0) CpxIntTrs
3.28/1.84	(1) Koat Proof [FINISHED, 0 ms]
3.28/1.84	(2) BOUNDS(1, 1)
3.28/1.84	
3.28/1.84	
3.28/1.84	----------------------------------------
3.28/1.84	
3.28/1.84	(0)
3.28/1.84	Obligation:
3.28/1.84	Complexity Int TRS consisting of the following rules:
3.28/1.84	f0(A) -> Com_1(f8(A)) :|: 0 >= B + 1
3.28/1.84	f0(A) -> Com_1(f8(A)) :|: TRUE
3.28/1.84	f0(A) -> Com_1(f8(B)) :|: TRUE
3.28/1.84	
3.28/1.84	The start-symbols are:[f0_1]
3.28/1.84	
3.28/1.84	
3.28/1.84	----------------------------------------
3.28/1.84	
3.28/1.84	(1) Koat Proof (FINISHED)
3.28/1.84	YES(?, 3)
3.28/1.84	
3.28/1.84	
3.28/1.84	
3.28/1.84	Initial complexity problem:
3.28/1.84	
3.28/1.84	1:	T:
3.28/1.84	
3.28/1.84			(Comp: ?, Cost: 1)    f0(ar_0) -> Com_1(f8(ar_0)) [ 0 >= b + 1 ]
3.28/1.84	
3.28/1.84			(Comp: ?, Cost: 1)    f0(ar_0) -> Com_1(f8(ar_0))
3.28/1.84	
3.28/1.84			(Comp: ?, Cost: 1)    f0(ar_0) -> Com_1(f8(b))
3.28/1.84	
3.28/1.84			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.28/1.84	
3.28/1.84		start location:	koat_start
3.28/1.84	
3.28/1.84		leaf cost:	0
3.28/1.84	
3.28/1.84	
3.28/1.84	
3.28/1.84	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.28/1.84	
3.28/1.84	2:	T:
3.28/1.84	
3.28/1.84			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f8(ar_0)) [ 0 >= b + 1 ]
3.28/1.84	
3.28/1.84			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f8(ar_0))
3.28/1.84	
3.28/1.84			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f8(b))
3.28/1.84	
3.28/1.84			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.28/1.84	
3.28/1.84		start location:	koat_start
3.28/1.84	
3.28/1.84		leaf cost:	0
3.28/1.84	
3.28/1.84	
3.28/1.84	
3.28/1.84	Complexity upper bound 3
3.28/1.84	
3.28/1.84	
3.28/1.84	
3.28/1.84	Time: 0.008 sec (SMT: 0.007 sec)
3.28/1.84	
3.28/1.84	
3.28/1.84	----------------------------------------
3.28/1.84	
3.28/1.84	(2)
3.28/1.84	BOUNDS(1, 1)
3.32/1.85	EOF