3.13/1.58	WORST_CASE(?, O(1))
3.13/1.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.13/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.13/1.59	
3.13/1.59	
3.13/1.59	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.13/1.59	
3.13/1.59	(0) CpxIntTrs
3.13/1.59	(1) Koat Proof [FINISHED, 0 ms]
3.13/1.59	(2) BOUNDS(1, 1)
3.13/1.59	
3.13/1.59	
3.13/1.59	----------------------------------------
3.13/1.59	
3.13/1.59	(0)
3.13/1.59	Obligation:
3.13/1.59	Complexity Int TRS consisting of the following rules:
3.13/1.59	f0(A) -> Com_1(f6(0)) :|: TRUE
3.13/1.59	
3.13/1.59	The start-symbols are:[f0_1]
3.13/1.59	
3.13/1.59	
3.13/1.59	----------------------------------------
3.13/1.59	
3.13/1.59	(1) Koat Proof (FINISHED)
3.13/1.59	YES(?, 1)
3.13/1.59	
3.13/1.59	
3.13/1.59	
3.13/1.59	Initial complexity problem:
3.13/1.59	
3.13/1.59	1:	T:
3.13/1.59	
3.13/1.59			(Comp: ?, Cost: 1)    f0(ar_0) -> Com_1(f6(0))
3.13/1.59	
3.13/1.59			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.13/1.59	
3.13/1.59		start location:	koat_start
3.13/1.59	
3.13/1.59		leaf cost:	0
3.13/1.59	
3.13/1.59	
3.13/1.59	
3.13/1.59	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.13/1.59	
3.13/1.59	2:	T:
3.13/1.59	
3.13/1.59			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f6(0))
3.13/1.59	
3.13/1.59			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.13/1.59	
3.13/1.59		start location:	koat_start
3.13/1.59	
3.13/1.59		leaf cost:	0
3.13/1.59	
3.13/1.59	
3.13/1.59	
3.13/1.59	Complexity upper bound 1
3.13/1.59	
3.13/1.59	
3.13/1.59	
3.13/1.59	Time: 0.004 sec (SMT: 0.004 sec)
3.13/1.59	
3.13/1.59	
3.13/1.59	----------------------------------------
3.13/1.59	
3.13/1.59	(2)
3.13/1.59	BOUNDS(1, 1)
3.36/1.64	EOF