0.00/0.26	YES
0.00/0.26	
0.00/0.26	Problem 1: 
0.00/0.26	
0.00/0.26	(VAR v_NonEmpty:S X:S X1:S X2:S XS:S)
0.00/0.26	(RULES
0.00/0.26	a__tail(cons(X:S,XS:S)) -> mark(XS:S)
0.00/0.26	a__tail(X:S) -> tail(X:S)
0.00/0.26	a__zeros -> cons(0,zeros)
0.00/0.26	a__zeros -> zeros
0.00/0.26	mark(0) -> 0
0.00/0.26	mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.26	mark(tail(X:S)) -> a__tail(mark(X:S))
0.00/0.26	mark(zeros) -> a__zeros
0.00/0.26	) 
0.00/0.26	(STRATEGY INNERMOST)
0.00/0.26	
0.00/0.26	Problem 1: 
0.00/0.26	
0.00/0.26	Dependency Pairs Processor:
0.00/0.26	-> Pairs:
0.00/0.26	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
0.00/0.26	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.26	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
0.00/0.26	 MARK(tail(X:S)) -> MARK(X:S)
0.00/0.26	 MARK(zeros) -> A__ZEROS
0.00/0.26	-> Rules:
0.00/0.26	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
0.00/0.26	 a__tail(X:S) -> tail(X:S)
0.00/0.26	 a__zeros -> cons(0,zeros)
0.00/0.26	 a__zeros -> zeros
0.00/0.26	 mark(0) -> 0
0.00/0.26	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.26	 mark(tail(X:S)) -> a__tail(mark(X:S))
0.00/0.26	 mark(zeros) -> a__zeros
0.00/0.26	
0.00/0.26	Problem 1: 
0.00/0.26	
0.00/0.26	SCC Processor:
0.00/0.26	-> Pairs:
0.00/0.26	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
0.00/0.26	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.26	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
0.00/0.26	 MARK(tail(X:S)) -> MARK(X:S)
0.00/0.26	 MARK(zeros) -> A__ZEROS
0.00/0.26	-> Rules:
0.00/0.26	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
0.00/0.26	 a__tail(X:S) -> tail(X:S)
0.00/0.26	 a__zeros -> cons(0,zeros)
0.00/0.26	 a__zeros -> zeros
0.00/0.26	 mark(0) -> 0
0.00/0.26	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.26	 mark(tail(X:S)) -> a__tail(mark(X:S))
0.00/0.26	 mark(zeros) -> a__zeros
0.00/0.26	->Strongly Connected Components:
0.00/0.26	->->Cycle:
0.00/0.26	->->-> Pairs:
0.00/0.26	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
0.00/0.26	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.26	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
0.00/0.26	 MARK(tail(X:S)) -> MARK(X:S)
0.00/0.26	->->-> Rules:
0.00/0.26	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
0.00/0.26	 a__tail(X:S) -> tail(X:S)
0.00/0.26	 a__zeros -> cons(0,zeros)
0.00/0.26	 a__zeros -> zeros
0.00/0.26	 mark(0) -> 0
0.00/0.26	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.26	 mark(tail(X:S)) -> a__tail(mark(X:S))
0.00/0.26	 mark(zeros) -> a__zeros
0.00/0.26	
0.00/0.26	Problem 1: 
0.00/0.26	
0.00/0.26	Reduction Pairs Processor:
0.00/0.26	-> Pairs:
0.00/0.26	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
0.00/0.26	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.26	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
0.00/0.26	 MARK(tail(X:S)) -> MARK(X:S)
0.00/0.26	-> Rules:
0.00/0.26	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
0.00/0.26	 a__tail(X:S) -> tail(X:S)
0.00/0.26	 a__zeros -> cons(0,zeros)
0.00/0.26	 a__zeros -> zeros
0.00/0.26	 mark(0) -> 0
0.00/0.26	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.26	 mark(tail(X:S)) -> a__tail(mark(X:S))
0.00/0.26	 mark(zeros) -> a__zeros
0.00/0.26	-> Usable rules:
0.00/0.26	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
0.00/0.26	 a__tail(X:S) -> tail(X:S)
0.00/0.26	 a__zeros -> cons(0,zeros)
0.00/0.26	 a__zeros -> zeros
0.00/0.26	 mark(0) -> 0
0.00/0.26	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.26	 mark(tail(X:S)) -> a__tail(mark(X:S))
0.00/0.26	 mark(zeros) -> a__zeros
0.00/0.26	->Interpretation type:
0.00/0.26	 Linear
0.00/0.26	->Coefficients:
0.00/0.26	 Natural Numbers
0.00/0.26	->Dimension:
0.00/0.26	 1
0.00/0.26	->Bound:
0.00/0.26	 2
0.00/0.26	->Interpretation:
0.00/0.26	 
0.00/0.26	[a__tail](X) = 2.X
0.00/0.26	[a__zeros] = 2
0.00/0.26	[mark](X) = 2.X
0.00/0.26	[0] = 0
0.00/0.26	[cons](X1,X2) = 2.X1 + X2 + 1
0.00/0.26	[fSNonEmpty] = 0
0.00/0.26	[tail](X) = 2.X
0.00/0.26	[zeros] = 1
0.00/0.26	[A__TAIL](X) = 2.X + 1
0.00/0.26	[A__ZEROS] = 0
0.00/0.26	[MARK](X) = 2.X + 2
0.00/0.26	
0.00/0.26	Problem 1: 
0.00/0.26	
0.00/0.26	SCC Processor:
0.00/0.26	-> Pairs:
0.00/0.26	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.26	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
0.00/0.26	 MARK(tail(X:S)) -> MARK(X:S)
0.00/0.26	-> Rules:
0.00/0.26	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
0.00/0.26	 a__tail(X:S) -> tail(X:S)
0.00/0.26	 a__zeros -> cons(0,zeros)
0.00/0.26	 a__zeros -> zeros
0.00/0.26	 mark(0) -> 0
0.00/0.26	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.26	 mark(tail(X:S)) -> a__tail(mark(X:S))
0.00/0.26	 mark(zeros) -> a__zeros
0.00/0.26	->Strongly Connected Components:
0.00/0.26	->->Cycle:
0.00/0.26	->->-> Pairs:
0.00/0.26	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.26	 MARK(tail(X:S)) -> MARK(X:S)
0.00/0.26	->->-> Rules:
0.00/0.26	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
0.00/0.26	 a__tail(X:S) -> tail(X:S)
0.00/0.26	 a__zeros -> cons(0,zeros)
0.00/0.26	 a__zeros -> zeros
0.00/0.26	 mark(0) -> 0
0.00/0.26	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.26	 mark(tail(X:S)) -> a__tail(mark(X:S))
0.00/0.26	 mark(zeros) -> a__zeros
0.00/0.26	
0.00/0.26	Problem 1: 
0.00/0.26	
0.00/0.26	Subterm Processor:
0.00/0.26	-> Pairs:
0.00/0.26	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.26	 MARK(tail(X:S)) -> MARK(X:S)
0.00/0.26	-> Rules:
0.00/0.26	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
0.00/0.26	 a__tail(X:S) -> tail(X:S)
0.00/0.26	 a__zeros -> cons(0,zeros)
0.00/0.26	 a__zeros -> zeros
0.00/0.26	 mark(0) -> 0
0.00/0.26	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.26	 mark(tail(X:S)) -> a__tail(mark(X:S))
0.00/0.26	 mark(zeros) -> a__zeros
0.00/0.26	->Projection:
0.00/0.26	 pi(MARK) = 1
0.00/0.26	
0.00/0.26	Problem 1: 
0.00/0.26	
0.00/0.26	SCC Processor:
0.00/0.26	-> Pairs:
0.00/0.26	 Empty
0.00/0.26	-> Rules:
0.00/0.26	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
0.00/0.26	 a__tail(X:S) -> tail(X:S)
0.00/0.26	 a__zeros -> cons(0,zeros)
0.00/0.26	 a__zeros -> zeros
0.00/0.26	 mark(0) -> 0
0.00/0.26	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.26	 mark(tail(X:S)) -> a__tail(mark(X:S))
0.00/0.26	 mark(zeros) -> a__zeros
0.00/0.26	->Strongly Connected Components:
0.00/0.26	 There is no strongly connected component
0.00/0.26	
0.00/0.26	The problem is finite.
0.00/0.26	EOF