2.89/1.62	WORST_CASE(?, O(1))
3.22/1.63	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.22/1.63	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.22/1.63	
3.22/1.63	
3.22/1.63	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.22/1.63	
3.22/1.63	(0) CpxTRS
3.22/1.63	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.22/1.63	(2) BOUNDS(1, 1)
3.22/1.63	
3.22/1.63	
3.22/1.63	----------------------------------------
3.22/1.63	
3.22/1.63	(0)
3.22/1.63	Obligation:
3.22/1.63	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.22/1.63	
3.22/1.63	
3.22/1.63	The TRS R consists of the following rules:
3.22/1.63	
3.22/1.63	   f(n__f(n__a)) -> f(n__g(f(n__a)))
3.22/1.63	   f(X) -> n__f(X)
3.22/1.63	   a -> n__a
3.22/1.63	   g(X) -> n__g(X)
3.22/1.63	   activate(n__f(X)) -> f(X)
3.22/1.63	   activate(n__a) -> a
3.22/1.63	   activate(n__g(X)) -> g(X)
3.22/1.63	   activate(X) -> X
3.22/1.63	
3.22/1.63	S is empty.
3.22/1.63	Rewrite Strategy: INNERMOST
3.22/1.63	----------------------------------------
3.22/1.63	
3.22/1.63	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.22/1.63	Constant runtime complexity proven by termination of constructor-based narrowing.
3.22/1.63	
3.22/1.63	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.22/1.63	
3.22/1.63	g(x0) ->^* n__g(x0)
3.22/1.63	
3.22/1.63	activate(n__g(x0)) ->^* n__g(x0)
3.22/1.63	
3.22/1.63	activate(n__a) ->^* n__a
3.22/1.63	
3.22/1.63	activate(n__f(x0)) ->^* n__f(x0)
3.22/1.63	
3.22/1.63	activate(n__f(n__f(n__a))) ->^* n__f(n__g(n__f(n__a)))
3.22/1.63	
3.22/1.63	f(x0) ->^* n__f(x0)
3.22/1.63	
3.22/1.63	f(n__f(n__a)) ->^* n__f(n__g(n__f(n__a)))
3.22/1.63	
3.22/1.63	a ->^* n__a
3.22/1.63	
3.22/1.63	
3.22/1.63	
3.22/1.63	
3.22/1.63	----------------------------------------
3.22/1.63	
3.22/1.63	(2)
3.22/1.63	BOUNDS(1, 1)
3.22/1.66	EOF