3.00/1.51	WORST_CASE(?, O(1))
3.00/1.52	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.00/1.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.00/1.52	
3.00/1.52	
3.00/1.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.00/1.52	
3.00/1.52	(0) CpxTRS
3.00/1.52	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.00/1.52	(2) BOUNDS(1, 1)
3.00/1.52	
3.00/1.52	
3.00/1.52	----------------------------------------
3.00/1.52	
3.00/1.52	(0)
3.00/1.52	Obligation:
3.00/1.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.00/1.52	
3.00/1.52	
3.00/1.52	The TRS R consists of the following rules:
3.00/1.52	
3.00/1.52	   zeros -> cons(0, n__zeros)
3.00/1.52	   tail(cons(X, XS)) -> activate(XS)
3.00/1.52	   zeros -> n__zeros
3.00/1.52	   activate(n__zeros) -> zeros
3.00/1.52	   activate(X) -> X
3.00/1.52	
3.00/1.52	S is empty.
3.00/1.52	Rewrite Strategy: FULL
3.00/1.52	----------------------------------------
3.00/1.52	
3.00/1.52	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.00/1.52	Constant runtime complexity proven by termination of constructor-based narrowing.
3.00/1.52	
3.00/1.52	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.00/1.52	
3.00/1.52	activate(n__zeros) ->^* n__zeros
3.00/1.52	
3.00/1.52	activate(n__zeros) ->^* cons(0, n__zeros)
3.00/1.52	
3.00/1.52	zeros ->^* n__zeros
3.00/1.52	
3.00/1.52	zeros ->^* cons(0, n__zeros)
3.00/1.52	
3.00/1.52	tail(cons(x0, n__zeros)) ->^* n__zeros
3.00/1.52	
3.00/1.52	tail(cons(x0, n__zeros)) ->^* cons(0, n__zeros)
3.00/1.52	
3.00/1.52	
3.00/1.52	
3.00/1.52	
3.00/1.52	----------------------------------------
3.00/1.52	
3.00/1.52	(2)
3.00/1.52	BOUNDS(1, 1)
3.26/1.55	EOF