1.48/1.61	WORST_CASE(?, O(1))
1.48/1.62	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1.48/1.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1.48/1.62	
1.48/1.62	
1.48/1.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
1.48/1.62	
1.48/1.62	(0) CpxTRS
1.48/1.62	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
1.48/1.62	(2) BOUNDS(1, 1)
1.48/1.62	
1.48/1.62	
1.48/1.62	----------------------------------------
1.48/1.62	
1.48/1.62	(0)
1.48/1.62	Obligation:
1.48/1.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
1.48/1.62	
1.48/1.62	
1.48/1.62	The TRS R consists of the following rules:
1.48/1.62	
1.48/1.62	   f(n__f(n__a)) -> f(n__g(f(n__a)))
1.48/1.62	   f(X) -> n__f(X)
1.48/1.62	   a -> n__a
1.48/1.62	   g(X) -> n__g(X)
1.48/1.62	   activate(n__f(X)) -> f(X)
1.48/1.62	   activate(n__a) -> a
1.48/1.62	   activate(n__g(X)) -> g(X)
1.48/1.62	   activate(X) -> X
1.48/1.62	
1.48/1.62	S is empty.
1.48/1.62	Rewrite Strategy: FULL
1.48/1.62	----------------------------------------
1.48/1.62	
1.48/1.62	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
1.48/1.62	Constant runtime complexity proven by termination of constructor-based narrowing.
1.48/1.62	
1.48/1.62	The maximal most general narrowing sequences give rise to the following rewrite sequences:
1.48/1.62	
1.48/1.62	g(x0) ->^* n__g(x0)
1.48/1.62	
1.48/1.62	activate(n__g(x0)) ->^* n__g(x0)
1.48/1.62	
1.48/1.62	activate(n__a) ->^* n__a
1.48/1.62	
1.48/1.62	activate(n__f(x0)) ->^* n__f(x0)
1.48/1.62	
1.48/1.62	activate(n__f(n__f(n__a))) ->^* n__f(n__g(n__f(n__a)))
1.48/1.62	
1.48/1.62	f(x0) ->^* n__f(x0)
1.48/1.62	
1.48/1.62	f(n__f(n__a)) ->^* n__f(n__g(n__f(n__a)))
1.48/1.62	
1.48/1.62	a ->^* n__a
1.48/1.62	
1.48/1.62	
1.48/1.62	
1.48/1.62	
1.48/1.62	----------------------------------------
1.48/1.62	
1.48/1.62	(2)
1.48/1.62	BOUNDS(1, 1)
3.53/1.64	EOF