3.07/1.60	WORST_CASE(?, O(1))
3.07/1.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.07/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.07/1.61	
3.07/1.61	
3.07/1.61	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.07/1.61	
3.07/1.61	(0) CpxTRS
3.07/1.61	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.07/1.61	(2) BOUNDS(1, 1)
3.07/1.61	
3.07/1.61	
3.07/1.61	----------------------------------------
3.07/1.61	
3.07/1.61	(0)
3.07/1.61	Obligation:
3.07/1.61	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.07/1.61	
3.07/1.61	
3.07/1.61	The TRS R consists of the following rules:
3.07/1.61	
3.07/1.61	   f(0) -> cons(0, n__f(s(0)))
3.07/1.61	   f(s(0)) -> f(p(s(0)))
3.07/1.61	   p(s(0)) -> 0
3.07/1.61	   f(X) -> n__f(X)
3.07/1.61	   activate(n__f(X)) -> f(X)
3.07/1.61	   activate(X) -> X
3.07/1.61	
3.07/1.61	S is empty.
3.07/1.61	Rewrite Strategy: INNERMOST
3.07/1.61	----------------------------------------
3.07/1.61	
3.07/1.61	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.07/1.61	Constant runtime complexity proven by termination of constructor-based narrowing.
3.07/1.61	
3.07/1.61	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.07/1.61	
3.07/1.61	activate(n__f(x0)) ->^* n__f(x0)
3.07/1.61	
3.07/1.61	activate(n__f(s(0))) ->^* n__f(0)
3.07/1.61	
3.07/1.61	activate(n__f(s(0))) ->^* cons(0, n__f(s(0)))
3.07/1.61	
3.07/1.61	activate(n__f(0)) ->^* cons(0, n__f(s(0)))
3.07/1.61	
3.07/1.61	f(x0) ->^* n__f(x0)
3.07/1.61	
3.07/1.61	f(s(0)) ->^* n__f(0)
3.07/1.61	
3.07/1.61	f(s(0)) ->^* cons(0, n__f(s(0)))
3.07/1.61	
3.07/1.61	f(0) ->^* cons(0, n__f(s(0)))
3.07/1.61	
3.07/1.61	p(s(0)) ->^* 0
3.07/1.61	
3.07/1.61	
3.07/1.61	
3.07/1.61	
3.07/1.61	----------------------------------------
3.07/1.61	
3.07/1.61	(2)
3.07/1.61	BOUNDS(1, 1)
3.07/1.65	EOF