3.09/1.58	WORST_CASE(?, O(1))
3.09/1.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.09/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.09/1.59	
3.09/1.59	
3.09/1.59	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.09/1.59	
3.09/1.59	(0) CpxTRS
3.09/1.59	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.09/1.59	(2) BOUNDS(1, 1)
3.09/1.59	
3.09/1.59	
3.09/1.59	----------------------------------------
3.09/1.59	
3.09/1.59	(0)
3.09/1.59	Obligation:
3.09/1.59	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.09/1.59	
3.09/1.59	
3.09/1.59	The TRS R consists of the following rules:
3.09/1.59	
3.09/1.59	   f(X) -> if(X, c, n__f(true))
3.09/1.59	   if(true, X, Y) -> X
3.09/1.59	   if(false, X, Y) -> activate(Y)
3.09/1.59	   f(X) -> n__f(X)
3.09/1.59	   activate(n__f(X)) -> f(X)
3.09/1.59	   activate(X) -> X
3.09/1.59	
3.09/1.59	S is empty.
3.09/1.59	Rewrite Strategy: INNERMOST
3.09/1.59	----------------------------------------
3.09/1.59	
3.09/1.59	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.09/1.59	Constant runtime complexity proven by termination of constructor-based narrowing.
3.09/1.59	
3.09/1.59	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.09/1.59	
3.09/1.59	activate(n__f(x0)) ->^* n__f(x0)
3.09/1.59	
3.09/1.59	activate(n__f(false)) ->^* n__f(true)
3.09/1.59	
3.09/1.59	activate(n__f(false)) ->^* n__f(true)
3.09/1.59	
3.09/1.59	activate(n__f(false)) ->^* c
3.09/1.59	
3.09/1.59	activate(n__f(true)) ->^* c
3.09/1.59	
3.09/1.59	if(false, x0, n__f(x1)) ->^* n__f(x1)
3.09/1.59	
3.09/1.59	if(false, x0, n__f(false)) ->^* n__f(true)
3.09/1.59	
3.09/1.59	if(false, x0, n__f(false)) ->^* n__f(true)
3.09/1.59	
3.09/1.59	if(false, x0, n__f(false)) ->^* c
3.09/1.59	
3.09/1.59	if(false, x0, n__f(true)) ->^* c
3.09/1.59	
3.09/1.59	f(x0) ->^* n__f(x0)
3.09/1.59	
3.09/1.59	f(false) ->^* n__f(true)
3.09/1.59	
3.09/1.59	f(false) ->^* n__f(true)
3.09/1.59	
3.09/1.59	f(false) ->^* c
3.09/1.59	
3.09/1.59	f(true) ->^* c
3.09/1.59	
3.09/1.59	
3.09/1.59	
3.09/1.59	
3.09/1.59	----------------------------------------
3.09/1.59	
3.09/1.59	(2)
3.09/1.59	BOUNDS(1, 1)
3.09/1.62	EOF