3.35/1.65	WORST_CASE(?, O(1))
3.35/1.66	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.35/1.66	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.35/1.66	
3.35/1.66	
3.35/1.66	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.35/1.66	
3.35/1.66	(0) CpxTRS
3.35/1.66	(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
3.35/1.66	(2) BOUNDS(1, 1)
3.35/1.66	
3.35/1.66	
3.35/1.66	----------------------------------------
3.35/1.66	
3.35/1.66	(0)
3.35/1.66	Obligation:
3.35/1.66	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.35/1.66	
3.35/1.66	
3.35/1.66	The TRS R consists of the following rules:
3.35/1.66	
3.35/1.66	   app(nil, YS) -> YS
3.35/1.66	   app(cons(X), YS) -> cons(X)
3.35/1.66	   from(X) -> cons(X)
3.35/1.66	   zWadr(nil, YS) -> nil
3.35/1.66	   zWadr(XS, nil) -> nil
3.35/1.66	   zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))
3.35/1.66	   prefix(L) -> cons(nil)
3.35/1.66	
3.35/1.66	S is empty.
3.35/1.66	Rewrite Strategy: INNERMOST
3.35/1.66	----------------------------------------
3.35/1.66	
3.35/1.66	(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.35/1.66	Constant runtime complexity proven by termination of constructor-based narrowing.
3.35/1.66	
3.35/1.66	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.35/1.66	
3.35/1.66	from(x0) ->^* cons(x0)
3.35/1.66	
3.35/1.66	prefix(x0) ->^* cons(nil)
3.35/1.66	
3.35/1.66	app(cons(x0), x1) ->^* cons(x0)
3.35/1.66	
3.35/1.66	zWadr(cons(x0), cons(cons(x1))) ->^* cons(cons(x1))
3.35/1.66	
3.35/1.66	zWadr(cons(x0), cons(nil)) ->^* cons(cons(x0))
3.35/1.66	
3.35/1.66	zWadr(x0, nil) ->^* nil
3.35/1.66	
3.35/1.66	zWadr(nil, x0) ->^* nil
3.35/1.66	
3.35/1.66	
3.35/1.66	
3.35/1.66	
3.35/1.66	----------------------------------------
3.35/1.66	
3.35/1.66	(2)
3.35/1.66	BOUNDS(1, 1)
3.54/1.70	EOF