3.13/1.52	WORST_CASE(?, O(1))
3.23/1.53	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.23/1.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.23/1.53	
3.23/1.53	
3.23/1.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.23/1.53	
3.23/1.53	(0) CpxTRS
3.23/1.53	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.23/1.53	(2) BOUNDS(1, 1)
3.23/1.53	
3.23/1.53	
3.23/1.53	----------------------------------------
3.23/1.53	
3.23/1.53	(0)
3.23/1.53	Obligation:
3.23/1.53	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.23/1.53	
3.23/1.53	
3.23/1.53	The TRS R consists of the following rules:
3.23/1.53	
3.23/1.53	   f(0) -> cons(0, n__f(s(0)))
3.23/1.53	   f(s(0)) -> f(p(s(0)))
3.23/1.53	   p(s(0)) -> 0
3.23/1.53	   f(X) -> n__f(X)
3.23/1.53	   activate(n__f(X)) -> f(X)
3.23/1.53	   activate(X) -> X
3.23/1.53	
3.23/1.53	S is empty.
3.23/1.53	Rewrite Strategy: FULL
3.23/1.53	----------------------------------------
3.23/1.53	
3.23/1.53	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.23/1.53	Constant runtime complexity proven by termination of constructor-based narrowing.
3.23/1.53	
3.23/1.53	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.23/1.53	
3.23/1.53	activate(n__f(x0)) ->^* n__f(x0)
3.23/1.53	
3.23/1.53	activate(n__f(s(0))) ->^* n__f(0)
3.23/1.53	
3.23/1.53	activate(n__f(s(0))) ->^* cons(0, n__f(s(0)))
3.23/1.53	
3.23/1.53	activate(n__f(0)) ->^* cons(0, n__f(s(0)))
3.23/1.53	
3.23/1.53	f(x0) ->^* n__f(x0)
3.23/1.53	
3.23/1.53	f(s(0)) ->^* n__f(0)
3.23/1.53	
3.23/1.53	f(s(0)) ->^* cons(0, n__f(s(0)))
3.23/1.53	
3.23/1.53	f(0) ->^* cons(0, n__f(s(0)))
3.23/1.53	
3.23/1.53	p(s(0)) ->^* 0
3.23/1.53	
3.23/1.53	
3.23/1.53	
3.23/1.53	
3.23/1.53	----------------------------------------
3.23/1.53	
3.23/1.53	(2)
3.23/1.53	BOUNDS(1, 1)
3.23/1.57	EOF