3.26/1.83	WORST_CASE(?, O(1))
3.26/1.83	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.26/1.83	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.26/1.83	
3.26/1.83	
3.26/1.83	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.26/1.83	
3.26/1.83	(0) CpxTRS
3.26/1.83	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.26/1.83	(2) BOUNDS(1, 1)
3.26/1.83	
3.26/1.83	
3.26/1.83	----------------------------------------
3.26/1.83	
3.26/1.83	(0)
3.26/1.83	Obligation:
3.26/1.83	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.26/1.83	
3.26/1.83	
3.26/1.83	The TRS R consists of the following rules:
3.26/1.83	
3.26/1.83	   zeros -> cons(0, n__zeros)
3.26/1.83	   tail(cons(X, XS)) -> activate(XS)
3.26/1.83	   zeros -> n__zeros
3.26/1.83	   activate(n__zeros) -> zeros
3.26/1.83	   activate(X) -> X
3.26/1.83	
3.26/1.83	S is empty.
3.26/1.83	Rewrite Strategy: INNERMOST
3.26/1.83	----------------------------------------
3.26/1.83	
3.26/1.83	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.26/1.83	Constant runtime complexity proven by termination of constructor-based narrowing.
3.26/1.83	
3.26/1.83	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.26/1.83	
3.26/1.83	activate(n__zeros) ->^* n__zeros
3.26/1.83	
3.26/1.83	activate(n__zeros) ->^* cons(0, n__zeros)
3.26/1.83	
3.26/1.83	zeros ->^* n__zeros
3.26/1.83	
3.26/1.83	zeros ->^* cons(0, n__zeros)
3.26/1.83	
3.26/1.83	tail(cons(x0, n__zeros)) ->^* n__zeros
3.26/1.83	
3.26/1.83	tail(cons(x0, n__zeros)) ->^* cons(0, n__zeros)
3.26/1.83	
3.26/1.83	
3.26/1.83	
3.26/1.83	
3.26/1.83	----------------------------------------
3.26/1.83	
3.26/1.83	(2)
3.26/1.83	BOUNDS(1, 1)
3.36/1.90	EOF