2.97/1.57	WORST_CASE(?, O(1))
2.97/1.58	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.97/1.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.97/1.58	
2.97/1.58	
2.97/1.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.97/1.58	
2.97/1.58	(0) CpxTRS
2.97/1.58	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
2.97/1.58	(2) BOUNDS(1, 1)
2.97/1.58	
2.97/1.58	
2.97/1.58	----------------------------------------
2.97/1.58	
2.97/1.58	(0)
2.97/1.58	Obligation:
2.97/1.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.97/1.58	
2.97/1.58	
2.97/1.58	The TRS R consists of the following rules:
2.97/1.58	
2.97/1.58	   first(0, X) -> nil
2.97/1.58	   first(s(X), cons(Y)) -> cons(Y)
2.97/1.58	   from(X) -> cons(X)
2.97/1.58	
2.97/1.58	S is empty.
2.97/1.58	Rewrite Strategy: FULL
2.97/1.58	----------------------------------------
2.97/1.58	
2.97/1.58	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
2.97/1.58	Constant runtime complexity proven by termination of constructor-based narrowing.
2.97/1.58	
2.97/1.58	The maximal most general narrowing sequences give rise to the following rewrite sequences:
2.97/1.58	
2.97/1.58	from(x0) ->^* cons(x0)
2.97/1.58	
2.97/1.58	first(s(x0), cons(x1)) ->^* cons(x1)
2.97/1.58	
2.97/1.58	first(0, x0) ->^* nil
2.97/1.58	
2.97/1.58	
2.97/1.58	
2.97/1.58	
2.97/1.58	----------------------------------------
2.97/1.59	
2.97/1.59	(2)
2.97/1.59	BOUNDS(1, 1)
3.27/1.65	EOF