3.21/1.50	WORST_CASE(?, O(1))
3.21/1.50	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.21/1.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.21/1.50	
3.21/1.50	
3.21/1.50	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.21/1.50	
3.21/1.50	(0) CpxTRS
3.21/1.50	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.21/1.50	(2) BOUNDS(1, 1)
3.21/1.50	
3.21/1.50	
3.21/1.50	----------------------------------------
3.21/1.50	
3.21/1.50	(0)
3.21/1.50	Obligation:
3.21/1.50	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.21/1.50	
3.21/1.50	
3.21/1.50	The TRS R consists of the following rules:
3.21/1.50	
3.21/1.50	   first(0, X) -> nil
3.21/1.50	   first(s(X), cons(Y)) -> cons(Y)
3.21/1.50	   from(X) -> cons(X)
3.21/1.50	
3.21/1.50	S is empty.
3.21/1.50	Rewrite Strategy: INNERMOST
3.21/1.50	----------------------------------------
3.21/1.50	
3.21/1.50	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.21/1.50	Constant runtime complexity proven by termination of constructor-based narrowing.
3.21/1.50	
3.21/1.50	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.21/1.50	
3.21/1.50	from(x0) ->^* cons(x0)
3.21/1.50	
3.21/1.50	first(s(x0), cons(x1)) ->^* cons(x1)
3.21/1.50	
3.21/1.50	first(0, x0) ->^* nil
3.21/1.50	
3.21/1.50	
3.21/1.50	
3.21/1.50	
3.21/1.50	----------------------------------------
3.21/1.50	
3.21/1.50	(2)
3.21/1.50	BOUNDS(1, 1)
3.30/1.54	EOF