0.00/0.46	YES
0.00/0.46	
0.00/0.46	Problem 1: 
0.00/0.46	
0.00/0.46	(VAR v_NonEmpty:S X:S X1:S X2:S Y:S Z:S)
0.00/0.46	(RULES
0.00/0.46	a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	a__from(X:S) -> from(X:S)
0.00/0.46	mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	) 
0.00/0.46	(STRATEGY INNERMOST)
0.00/0.46	
0.00/0.46	Problem 1: 
0.00/0.46	
0.00/0.46	Dependency Pairs Processor:
0.00/0.46	-> Pairs:
0.00/0.46	 A__2ND(cons(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
0.00/0.46	 A__FROM(X:S) -> MARK(X:S)
0.00/0.46	 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
0.00/0.46	 MARK(2nd(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.46	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.46	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.46	-> Rules:
0.00/0.46	 a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	 a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	 a__from(X:S) -> from(X:S)
0.00/0.46	 mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	
0.00/0.46	Problem 1: 
0.00/0.46	
0.00/0.46	SCC Processor:
0.00/0.46	-> Pairs:
0.00/0.46	 A__2ND(cons(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
0.00/0.46	 A__FROM(X:S) -> MARK(X:S)
0.00/0.46	 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
0.00/0.46	 MARK(2nd(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.46	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.46	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.46	-> Rules:
0.00/0.46	 a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	 a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	 a__from(X:S) -> from(X:S)
0.00/0.46	 mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	->Strongly Connected Components:
0.00/0.46	->->Cycle:
0.00/0.46	->->-> Pairs:
0.00/0.46	 A__2ND(cons(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
0.00/0.46	 A__FROM(X:S) -> MARK(X:S)
0.00/0.46	 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
0.00/0.46	 MARK(2nd(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.46	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.46	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.46	->->-> Rules:
0.00/0.46	 a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	 a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	 a__from(X:S) -> from(X:S)
0.00/0.46	 mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	
0.00/0.46	Problem 1: 
0.00/0.46	
0.00/0.46	Reduction Pairs Processor:
0.00/0.46	-> Pairs:
0.00/0.46	 A__2ND(cons(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
0.00/0.46	 A__FROM(X:S) -> MARK(X:S)
0.00/0.46	 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
0.00/0.46	 MARK(2nd(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.46	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.46	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.46	-> Rules:
0.00/0.46	 a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	 a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	 a__from(X:S) -> from(X:S)
0.00/0.46	 mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	-> Usable rules:
0.00/0.46	 a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	 a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	 a__from(X:S) -> from(X:S)
0.00/0.46	 mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	->Interpretation type:
0.00/0.46	 Linear
0.00/0.46	->Coefficients:
0.00/0.46	 All rationals
0.00/0.46	->Dimension:
0.00/0.46	 1
0.00/0.46	->Bound:
0.00/0.46	 2
0.00/0.46	->Interpretation:
0.00/0.46	 
0.00/0.46	[a__2nd](X) = 2.X + 2
0.00/0.46	[a__from](X) = 2.X + 2
0.00/0.46	[mark](X) = X
0.00/0.46	[2nd](X) = 2.X + 2
0.00/0.46	[cons](X1,X2) = X1 + 1/2.X2 + 1/2
0.00/0.46	[fSNonEmpty] = 0
0.00/0.46	[from](X) = 2.X + 2
0.00/0.46	[s](X) = X + 1/2
0.00/0.46	[A__2ND](X) = 2.X + 1/2
0.00/0.46	[A__FROM](X) = X + 2
0.00/0.46	[MARK](X) = X + 1
0.00/0.46	
0.00/0.46	Problem 1: 
0.00/0.46	
0.00/0.46	SCC Processor:
0.00/0.46	-> Pairs:
0.00/0.46	 A__FROM(X:S) -> MARK(X:S)
0.00/0.46	 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
0.00/0.46	 MARK(2nd(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.46	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.46	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.46	-> Rules:
0.00/0.46	 a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	 a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	 a__from(X:S) -> from(X:S)
0.00/0.46	 mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	->Strongly Connected Components:
0.00/0.46	->->Cycle:
0.00/0.46	->->-> Pairs:
0.00/0.46	 A__FROM(X:S) -> MARK(X:S)
0.00/0.46	 MARK(2nd(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.46	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.46	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.46	->->-> Rules:
0.00/0.46	 a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	 a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	 a__from(X:S) -> from(X:S)
0.00/0.46	 mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	
0.00/0.46	Problem 1: 
0.00/0.46	
0.00/0.46	Reduction Pairs Processor:
0.00/0.46	-> Pairs:
0.00/0.46	 A__FROM(X:S) -> MARK(X:S)
0.00/0.46	 MARK(2nd(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.46	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.46	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.46	-> Rules:
0.00/0.46	 a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	 a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	 a__from(X:S) -> from(X:S)
0.00/0.46	 mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	-> Usable rules:
0.00/0.46	 a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	 a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	 a__from(X:S) -> from(X:S)
0.00/0.46	 mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	->Interpretation type:
0.00/0.46	 Linear
0.00/0.46	->Coefficients:
0.00/0.46	 All rationals
0.00/0.46	->Dimension:
0.00/0.46	 1
0.00/0.46	->Bound:
0.00/0.46	 2
0.00/0.46	->Interpretation:
0.00/0.46	 
0.00/0.46	[a__2nd](X) = 2.X + 2
0.00/0.46	[a__from](X) = 2.X + 1/2
0.00/0.46	[mark](X) = X
0.00/0.46	[2nd](X) = 2.X + 2
0.00/0.46	[cons](X1,X2) = X1 + 1/2.X2
0.00/0.46	[fSNonEmpty] = 0
0.00/0.46	[from](X) = 2.X + 1/2
0.00/0.46	[s](X) = X
0.00/0.46	[A__2ND](X) = 0
0.00/0.46	[A__FROM](X) = X + 1/2
0.00/0.46	[MARK](X) = X
0.00/0.46	
0.00/0.46	Problem 1: 
0.00/0.46	
0.00/0.46	SCC Processor:
0.00/0.46	-> Pairs:
0.00/0.46	 MARK(2nd(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.46	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.46	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.46	-> Rules:
0.00/0.46	 a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	 a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	 a__from(X:S) -> from(X:S)
0.00/0.46	 mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	->Strongly Connected Components:
0.00/0.46	->->Cycle:
0.00/0.46	->->-> Pairs:
0.00/0.46	 MARK(2nd(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.46	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.46	->->-> Rules:
0.00/0.46	 a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	 a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	 a__from(X:S) -> from(X:S)
0.00/0.46	 mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	
0.00/0.46	Problem 1: 
0.00/0.46	
0.00/0.46	Subterm Processor:
0.00/0.46	-> Pairs:
0.00/0.46	 MARK(2nd(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.46	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.46	-> Rules:
0.00/0.46	 a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	 a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	 a__from(X:S) -> from(X:S)
0.00/0.46	 mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	->Projection:
0.00/0.46	 pi(MARK) = 1
0.00/0.46	
0.00/0.46	Problem 1: 
0.00/0.46	
0.00/0.46	SCC Processor:
0.00/0.46	-> Pairs:
0.00/0.46	 Empty
0.00/0.46	-> Rules:
0.00/0.46	 a__2nd(cons(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
0.00/0.46	 a__2nd(X:S) -> 2nd(X:S)
0.00/0.46	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.46	 a__from(X:S) -> from(X:S)
0.00/0.46	 mark(2nd(X:S)) -> a__2nd(mark(X:S))
0.00/0.46	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.46	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.46	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.46	->Strongly Connected Components:
0.00/0.46	 There is no strongly connected component
0.00/0.46	
0.00/0.46	The problem is finite.
0.00/0.46	EOF