3.31/1.58	YES
3.31/1.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.31/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.31/1.59	
3.31/1.59	
3.31/1.59	Termination w.r.t. Q of the given QTRS could be proven:
3.31/1.59	
3.31/1.59	(0) QTRS
3.31/1.59	(1) QTRSRRRProof [EQUIVALENT, 27 ms]
3.31/1.59	(2) QTRS
3.31/1.59	(3) RisEmptyProof [EQUIVALENT, 0 ms]
3.31/1.59	(4) YES
3.31/1.59	
3.31/1.59	
3.31/1.59	----------------------------------------
3.31/1.59	
3.31/1.59	(0)
3.31/1.59	Obligation:
3.31/1.59	Q restricted rewrite system:
3.31/1.59	The TRS R consists of the following rules:
3.31/1.59	
3.31/1.59	   app(nil, YS) -> YS
3.31/1.59	   app(cons(X), YS) -> cons(X)
3.31/1.59	   from(X) -> cons(X)
3.31/1.59	   zWadr(nil, YS) -> nil
3.31/1.59	   zWadr(XS, nil) -> nil
3.31/1.59	   zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))
3.31/1.59	   prefix(L) -> cons(nil)
3.31/1.59	
3.31/1.59	The set Q consists of the following terms:
3.31/1.59	
3.31/1.59	   app(nil, x0)
3.31/1.59	   app(cons(x0), x1)
3.31/1.59	   from(x0)
3.31/1.59	   zWadr(nil, x0)
3.31/1.59	   zWadr(x0, nil)
3.31/1.59	   zWadr(cons(x0), cons(x1))
3.31/1.59	   prefix(x0)
3.31/1.59	
3.31/1.59	
3.31/1.59	----------------------------------------
3.31/1.59	
3.31/1.59	(1) QTRSRRRProof (EQUIVALENT)
3.31/1.59	Used ordering:
3.31/1.59	Knuth-Bendix order [KBO] with precedence:nil > zWadr_2 > from_1 > prefix_1 > cons_1 > app_2
3.31/1.59	
3.31/1.59	and weight map:
3.31/1.59	
3.31/1.59	   nil=2
3.31/1.59	   cons_1=1
3.31/1.59	   from_1=1
3.31/1.59	   prefix_1=2
3.31/1.59	   app_2=0
3.31/1.59	   zWadr_2=0
3.31/1.59	
3.31/1.59	The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.31/1.59	
3.31/1.59	   app(nil, YS) -> YS
3.31/1.59	   app(cons(X), YS) -> cons(X)
3.31/1.59	   from(X) -> cons(X)
3.31/1.59	   zWadr(nil, YS) -> nil
3.31/1.59	   zWadr(XS, nil) -> nil
3.31/1.59	   zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X)))
3.31/1.59	   prefix(L) -> cons(nil)
3.31/1.59	
3.31/1.59	
3.31/1.59	
3.31/1.59	
3.31/1.59	----------------------------------------
3.31/1.59	
3.31/1.59	(2)
3.31/1.59	Obligation:
3.31/1.59	Q restricted rewrite system:
3.31/1.59	R is empty.
3.31/1.59	The set Q consists of the following terms:
3.31/1.59	
3.31/1.59	   app(nil, x0)
3.31/1.59	   app(cons(x0), x1)
3.31/1.59	   from(x0)
3.31/1.59	   zWadr(nil, x0)
3.31/1.59	   zWadr(x0, nil)
3.31/1.59	   zWadr(cons(x0), cons(x1))
3.31/1.59	   prefix(x0)
3.31/1.59	
3.31/1.59	
3.31/1.59	----------------------------------------
3.31/1.59	
3.31/1.59	(3) RisEmptyProof (EQUIVALENT)
3.31/1.59	The TRS R is empty. Hence, termination is trivially proven.
3.31/1.59	----------------------------------------
3.31/1.59	
3.31/1.59	(4)
3.31/1.59	YES
3.31/1.62	EOF