0.00/0.20	YES
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	(VAR v_NonEmpty:S X:S X1:S X2:S Y:S Z:S)
0.00/0.20	(RULES
0.00/0.20	a__add(0,X:S) -> mark(X:S)
0.00/0.20	a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	a__from(X:S) -> from(X:S)
0.00/0.20	a__fst(0,Z:S) -> nil
0.00/0.20	a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	a__len(nil) -> 0
0.00/0.20	a__len(X:S) -> len(X:S)
0.00/0.20	mark(0) -> 0
0.00/0.20	mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	mark(nil) -> nil
0.00/0.20	mark(s(X:S)) -> s(X:S)
0.00/0.20	) 
0.00/0.20	(STRATEGY INNERMOST)
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Dependency Pairs Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A__ADD(0,X:S) -> MARK(X:S)
0.00/0.20	 A__FROM(X:S) -> MARK(X:S)
0.00/0.20	 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> A__ADD(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.20	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(len(X:S)) -> A__LEN(mark(X:S))
0.00/0.20	 MARK(len(X:S)) -> MARK(X:S)
0.00/0.20	-> Rules:
0.00/0.20	 a__add(0,X:S) -> mark(X:S)
0.00/0.20	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	 a__from(X:S) -> from(X:S)
0.00/0.20	 a__fst(0,Z:S) -> nil
0.00/0.20	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	 a__len(nil) -> 0
0.00/0.20	 a__len(X:S) -> len(X:S)
0.00/0.20	 mark(0) -> 0
0.00/0.20	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	 mark(nil) -> nil
0.00/0.20	 mark(s(X:S)) -> s(X:S)
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A__ADD(0,X:S) -> MARK(X:S)
0.00/0.20	 A__FROM(X:S) -> MARK(X:S)
0.00/0.20	 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> A__ADD(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.20	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(len(X:S)) -> A__LEN(mark(X:S))
0.00/0.20	 MARK(len(X:S)) -> MARK(X:S)
0.00/0.20	-> Rules:
0.00/0.20	 a__add(0,X:S) -> mark(X:S)
0.00/0.20	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	 a__from(X:S) -> from(X:S)
0.00/0.20	 a__fst(0,Z:S) -> nil
0.00/0.20	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	 a__len(nil) -> 0
0.00/0.20	 a__len(X:S) -> len(X:S)
0.00/0.20	 mark(0) -> 0
0.00/0.20	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	 mark(nil) -> nil
0.00/0.20	 mark(s(X:S)) -> s(X:S)
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 A__ADD(0,X:S) -> MARK(X:S)
0.00/0.20	 A__FROM(X:S) -> MARK(X:S)
0.00/0.20	 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> A__ADD(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.20	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(len(X:S)) -> MARK(X:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a__add(0,X:S) -> mark(X:S)
0.00/0.20	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	 a__from(X:S) -> from(X:S)
0.00/0.20	 a__fst(0,Z:S) -> nil
0.00/0.20	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	 a__len(nil) -> 0
0.00/0.20	 a__len(X:S) -> len(X:S)
0.00/0.20	 mark(0) -> 0
0.00/0.20	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	 mark(nil) -> nil
0.00/0.20	 mark(s(X:S)) -> s(X:S)
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pairs Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A__ADD(0,X:S) -> MARK(X:S)
0.00/0.20	 A__FROM(X:S) -> MARK(X:S)
0.00/0.20	 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> A__ADD(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.20	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(len(X:S)) -> MARK(X:S)
0.00/0.20	-> Rules:
0.00/0.20	 a__add(0,X:S) -> mark(X:S)
0.00/0.20	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	 a__from(X:S) -> from(X:S)
0.00/0.20	 a__fst(0,Z:S) -> nil
0.00/0.20	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	 a__len(nil) -> 0
0.00/0.20	 a__len(X:S) -> len(X:S)
0.00/0.20	 mark(0) -> 0
0.00/0.20	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	 mark(nil) -> nil
0.00/0.20	 mark(s(X:S)) -> s(X:S)
0.00/0.20	-> Usable rules:
0.00/0.20	 a__add(0,X:S) -> mark(X:S)
0.00/0.20	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	 a__from(X:S) -> from(X:S)
0.00/0.20	 a__fst(0,Z:S) -> nil
0.00/0.20	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	 a__len(nil) -> 0
0.00/0.20	 a__len(X:S) -> len(X:S)
0.00/0.20	 mark(0) -> 0
0.00/0.20	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	 mark(nil) -> nil
0.00/0.20	 mark(s(X:S)) -> s(X:S)
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a__add](X1,X2) = X1 + 2.X2 + 2
0.00/0.20	[a__from](X) = 2.X + 2
0.00/0.20	[a__fst](X1,X2) = X1 + 2.X2 + 2
0.00/0.20	[a__len](X) = X + 2
0.00/0.20	[mark](X) = 2.X + 1
0.00/0.20	[0] = 2
0.00/0.20	[add](X1,X2) = X1 + 2.X2 + 2
0.00/0.20	[cons](X1,X2) = X1 + 1
0.00/0.20	[fSNonEmpty] = 0
0.00/0.20	[from](X) = 2.X + 2
0.00/0.20	[fst](X1,X2) = X1 + 2.X2 + 2
0.00/0.20	[len](X) = X + 2
0.00/0.20	[nil] = 0
0.00/0.20	[s](X) = 2
0.00/0.20	[A__ADD](X1,X2) = X1 + 2.X2 + 2
0.00/0.20	[A__FROM](X) = 2.X + 1
0.00/0.20	[A__FST](X1,X2) = X1 + 2.X2 + 2
0.00/0.20	[A__LEN](X) = 0
0.00/0.20	[MARK](X) = 2.X + 1
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A__FROM(X:S) -> MARK(X:S)
0.00/0.20	 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> A__ADD(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.20	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(len(X:S)) -> MARK(X:S)
0.00/0.20	-> Rules:
0.00/0.20	 a__add(0,X:S) -> mark(X:S)
0.00/0.20	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	 a__from(X:S) -> from(X:S)
0.00/0.20	 a__fst(0,Z:S) -> nil
0.00/0.20	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	 a__len(nil) -> 0
0.00/0.20	 a__len(X:S) -> len(X:S)
0.00/0.20	 mark(0) -> 0
0.00/0.20	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	 mark(nil) -> nil
0.00/0.20	 mark(s(X:S)) -> s(X:S)
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 A__FROM(X:S) -> MARK(X:S)
0.00/0.20	 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.20	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(len(X:S)) -> MARK(X:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a__add(0,X:S) -> mark(X:S)
0.00/0.20	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	 a__from(X:S) -> from(X:S)
0.00/0.20	 a__fst(0,Z:S) -> nil
0.00/0.20	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	 a__len(nil) -> 0
0.00/0.20	 a__len(X:S) -> len(X:S)
0.00/0.20	 mark(0) -> 0
0.00/0.20	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	 mark(nil) -> nil
0.00/0.20	 mark(s(X:S)) -> s(X:S)
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pairs Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A__FROM(X:S) -> MARK(X:S)
0.00/0.20	 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.20	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(len(X:S)) -> MARK(X:S)
0.00/0.20	-> Rules:
0.00/0.20	 a__add(0,X:S) -> mark(X:S)
0.00/0.20	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	 a__from(X:S) -> from(X:S)
0.00/0.20	 a__fst(0,Z:S) -> nil
0.00/0.20	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	 a__len(nil) -> 0
0.00/0.20	 a__len(X:S) -> len(X:S)
0.00/0.20	 mark(0) -> 0
0.00/0.20	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	 mark(nil) -> nil
0.00/0.20	 mark(s(X:S)) -> s(X:S)
0.00/0.20	-> Usable rules:
0.00/0.20	 a__add(0,X:S) -> mark(X:S)
0.00/0.20	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	 a__from(X:S) -> from(X:S)
0.00/0.20	 a__fst(0,Z:S) -> nil
0.00/0.20	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	 a__len(nil) -> 0
0.00/0.20	 a__len(X:S) -> len(X:S)
0.00/0.20	 mark(0) -> 0
0.00/0.20	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	 mark(nil) -> nil
0.00/0.20	 mark(s(X:S)) -> s(X:S)
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a__add](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.20	[a__from](X) = 2.X + 2
0.00/0.20	[a__fst](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.20	[a__len](X) = 2.X + 2
0.00/0.20	[mark](X) = 2.X
0.00/0.20	[0] = 2
0.00/0.20	[add](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.20	[cons](X1,X2) = X1 + 2
0.00/0.20	[fSNonEmpty] = 0
0.00/0.20	[from](X) = 2.X + 2
0.00/0.20	[fst](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.20	[len](X) = 2.X + 2
0.00/0.20	[nil] = 0
0.00/0.20	[s](X) = 2
0.00/0.20	[A__ADD](X1,X2) = 0
0.00/0.20	[A__FROM](X) = 2.X + 1
0.00/0.20	[A__FST](X1,X2) = X1 + 2.X2
0.00/0.20	[A__LEN](X) = 0
0.00/0.20	[MARK](X) = 2.X
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(from(X:S)) -> A__FROM(mark(X:S))
0.00/0.20	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(len(X:S)) -> MARK(X:S)
0.00/0.20	-> Rules:
0.00/0.20	 a__add(0,X:S) -> mark(X:S)
0.00/0.20	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	 a__from(X:S) -> from(X:S)
0.00/0.20	 a__fst(0,Z:S) -> nil
0.00/0.20	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	 a__len(nil) -> 0
0.00/0.20	 a__len(X:S) -> len(X:S)
0.00/0.20	 mark(0) -> 0
0.00/0.20	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	 mark(nil) -> nil
0.00/0.20	 mark(s(X:S)) -> s(X:S)
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(len(X:S)) -> MARK(X:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a__add(0,X:S) -> mark(X:S)
0.00/0.20	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	 a__from(X:S) -> from(X:S)
0.00/0.20	 a__fst(0,Z:S) -> nil
0.00/0.20	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	 a__len(nil) -> 0
0.00/0.20	 a__len(X:S) -> len(X:S)
0.00/0.20	 mark(0) -> 0
0.00/0.20	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	 mark(nil) -> nil
0.00/0.20	 mark(s(X:S)) -> s(X:S)
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pairs Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(len(X:S)) -> MARK(X:S)
0.00/0.20	-> Rules:
0.00/0.20	 a__add(0,X:S) -> mark(X:S)
0.00/0.20	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	 a__from(X:S) -> from(X:S)
0.00/0.20	 a__fst(0,Z:S) -> nil
0.00/0.20	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	 a__len(nil) -> 0
0.00/0.20	 a__len(X:S) -> len(X:S)
0.00/0.20	 mark(0) -> 0
0.00/0.20	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	 mark(nil) -> nil
0.00/0.20	 mark(s(X:S)) -> s(X:S)
0.00/0.20	-> Usable rules:
0.00/0.20	 a__add(0,X:S) -> mark(X:S)
0.00/0.20	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.20	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.20	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.20	 a__from(X:S) -> from(X:S)
0.00/0.20	 a__fst(0,Z:S) -> nil
0.00/0.20	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.20	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.20	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.20	 a__len(nil) -> 0
0.00/0.20	 a__len(X:S) -> len(X:S)
0.00/0.20	 mark(0) -> 0
0.00/0.20	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.20	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.20	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.20	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.20	 mark(nil) -> nil
0.00/0.20	 mark(s(X:S)) -> s(X:S)
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a__add](X1,X2) = X1 + 2.X2
0.00/0.20	[a__from](X) = 2.X + 2
0.00/0.20	[a__fst](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.20	[a__len](X) = 2.X + 2
0.00/0.20	[mark](X) = 2.X
0.00/0.20	[0] = 1
0.00/0.20	[add](X1,X2) = X1 + 2.X2
0.00/0.20	[cons](X1,X2) = X1 + 1
0.00/0.20	[fSNonEmpty] = 0
0.00/0.20	[from](X) = 2.X + 2
0.00/0.20	[fst](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.20	[len](X) = 2.X + 1
0.00/0.20	[nil] = 0
0.00/0.20	[s](X) = 2
0.00/0.20	[A__ADD](X1,X2) = 0
0.00/0.20	[A__FROM](X) = 0
0.00/0.20	[A__FST](X1,X2) = X1 + X2 + 2
0.00/0.20	[A__LEN](X) = 0
0.00/0.20	[MARK](X) = X + 2
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.20	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.20	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.20	 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
0.00/0.21	 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.21	 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.21	 MARK(len(X:S)) -> MARK(X:S)
0.00/0.21	-> Rules:
0.00/0.21	 a__add(0,X:S) -> mark(X:S)
0.00/0.21	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.21	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.21	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.21	 a__from(X:S) -> from(X:S)
0.00/0.21	 a__fst(0,Z:S) -> nil
0.00/0.21	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.21	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.21	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.21	 a__len(nil) -> 0
0.00/0.21	 a__len(X:S) -> len(X:S)
0.00/0.21	 mark(0) -> 0
0.00/0.21	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.21	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.21	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.21	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.21	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.21	 mark(nil) -> nil
0.00/0.21	 mark(s(X:S)) -> s(X:S)
0.00/0.21	->Strongly Connected Components:
0.00/0.21	->->Cycle:
0.00/0.21	->->-> Pairs:
0.00/0.21	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.21	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.21	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.21	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.21	 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.21	 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.21	 MARK(len(X:S)) -> MARK(X:S)
0.00/0.21	->->-> Rules:
0.00/0.21	 a__add(0,X:S) -> mark(X:S)
0.00/0.21	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.21	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.21	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.21	 a__from(X:S) -> from(X:S)
0.00/0.21	 a__fst(0,Z:S) -> nil
0.00/0.21	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.21	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.21	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.21	 a__len(nil) -> 0
0.00/0.21	 a__len(X:S) -> len(X:S)
0.00/0.21	 mark(0) -> 0
0.00/0.21	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.21	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.21	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.21	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.21	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.21	 mark(nil) -> nil
0.00/0.21	 mark(s(X:S)) -> s(X:S)
0.00/0.21	
0.00/0.21	Problem 1: 
0.00/0.21	
0.00/0.21	Subterm Processor:
0.00/0.21	-> Pairs:
0.00/0.21	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.21	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.21	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.21	 MARK(from(X:S)) -> MARK(X:S)
0.00/0.21	 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.21	 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.21	 MARK(len(X:S)) -> MARK(X:S)
0.00/0.21	-> Rules:
0.00/0.21	 a__add(0,X:S) -> mark(X:S)
0.00/0.21	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.21	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.21	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.21	 a__from(X:S) -> from(X:S)
0.00/0.21	 a__fst(0,Z:S) -> nil
0.00/0.21	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.21	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.21	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.21	 a__len(nil) -> 0
0.00/0.21	 a__len(X:S) -> len(X:S)
0.00/0.21	 mark(0) -> 0
0.00/0.21	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.21	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.21	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.21	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.21	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.21	 mark(nil) -> nil
0.00/0.21	 mark(s(X:S)) -> s(X:S)
0.00/0.21	->Projection:
0.00/0.21	 pi(MARK) = 1
0.00/0.21	
0.00/0.21	Problem 1: 
0.00/0.21	
0.00/0.21	SCC Processor:
0.00/0.21	-> Pairs:
0.00/0.21	 Empty
0.00/0.21	-> Rules:
0.00/0.21	 a__add(0,X:S) -> mark(X:S)
0.00/0.21	 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
0.00/0.21	 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
0.00/0.21	 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
0.00/0.21	 a__from(X:S) -> from(X:S)
0.00/0.21	 a__fst(0,Z:S) -> nil
0.00/0.21	 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
0.00/0.21	 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
0.00/0.21	 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
0.00/0.21	 a__len(nil) -> 0
0.00/0.21	 a__len(X:S) -> len(X:S)
0.00/0.21	 mark(0) -> 0
0.00/0.21	 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
0.00/0.21	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.21	 mark(from(X:S)) -> a__from(mark(X:S))
0.00/0.21	 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
0.00/0.21	 mark(len(X:S)) -> a__len(mark(X:S))
0.00/0.21	 mark(nil) -> nil
0.00/0.21	 mark(s(X:S)) -> s(X:S)
0.00/0.21	->Strongly Connected Components:
0.00/0.21	 There is no strongly connected component
0.00/0.21	
0.00/0.21	The problem is finite.
0.00/0.21	EOF