2.98/1.59	WORST_CASE(?, O(1))
2.98/1.60	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.98/1.60	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.98/1.60	
2.98/1.60	
2.98/1.60	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.98/1.60	
2.98/1.60	(0) CpxTRS
2.98/1.60	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
2.98/1.60	(2) BOUNDS(1, 1)
2.98/1.60	
2.98/1.60	
2.98/1.60	----------------------------------------
2.98/1.60	
2.98/1.60	(0)
2.98/1.60	Obligation:
2.98/1.60	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.98/1.60	
2.98/1.60	
2.98/1.60	The TRS R consists of the following rules:
2.98/1.60	
2.98/1.60	   f(0) -> cons(0, n__f(s(0)))
2.98/1.60	   f(s(0)) -> f(p(s(0)))
2.98/1.60	   p(s(X)) -> X
2.98/1.60	   f(X) -> n__f(X)
2.98/1.60	   activate(n__f(X)) -> f(X)
2.98/1.60	   activate(X) -> X
2.98/1.60	
2.98/1.60	S is empty.
2.98/1.60	Rewrite Strategy: INNERMOST
2.98/1.60	----------------------------------------
2.98/1.60	
2.98/1.60	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
2.98/1.60	Constant runtime complexity proven by termination of constructor-based narrowing.
2.98/1.60	
2.98/1.60	The maximal most general narrowing sequences give rise to the following rewrite sequences:
2.98/1.60	
2.98/1.60	activate(n__f(x0)) ->^* n__f(x0)
2.98/1.60	
2.98/1.60	activate(n__f(s(0))) ->^* n__f(0)
2.98/1.60	
2.98/1.60	activate(n__f(s(0))) ->^* cons(0, n__f(s(0)))
2.98/1.60	
2.98/1.60	activate(n__f(0)) ->^* cons(0, n__f(s(0)))
2.98/1.60	
2.98/1.60	f(x0) ->^* n__f(x0)
2.98/1.60	
2.98/1.60	f(s(0)) ->^* n__f(0)
2.98/1.60	
2.98/1.60	f(s(0)) ->^* cons(0, n__f(s(0)))
2.98/1.60	
2.98/1.60	f(0) ->^* cons(0, n__f(s(0)))
2.98/1.60	
2.98/1.60	p(x0) ->^* p(x0)
2.98/1.60	
2.98/1.60	
2.98/1.60	
2.98/1.60	
2.98/1.60	----------------------------------------
2.98/1.60	
2.98/1.60	(2)
2.98/1.60	BOUNDS(1, 1)
3.27/1.63	EOF