YES

Problem 1: 

(VAR v_NonEmpty:S X:S X1:S X2:S Y:S Z:S)
(RULES
a__add(0,X:S) -> mark(X:S)
a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
a__add(X1:S,X2:S) -> add(X1:S,X2:S)
a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
a__from(X:S) -> from(X:S)
a__fst(0,Z:S) -> nil
a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
a__len(cons(X:S,Z:S)) -> s(len(Z:S))
a__len(nil) -> 0
a__len(X:S) -> len(X:S)
mark(0) -> 0
mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
mark(from(X:S)) -> a__from(mark(X:S))
mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
mark(len(X:S)) -> a__len(mark(X:S))
mark(nil) -> nil
mark(s(X:S)) -> s(X:S)
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A__ADD(0,X:S) -> MARK(X:S)
 A__FROM(X:S) -> MARK(X:S)
 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
 MARK(add(X1:S,X2:S)) -> A__ADD(mark(X1:S),mark(X2:S))
 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
 MARK(len(X:S)) -> A__LEN(mark(X:S))
 MARK(len(X:S)) -> MARK(X:S)
-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)

Problem 1: 

SCC Processor:
-> Pairs:
 A__ADD(0,X:S) -> MARK(X:S)
 A__FROM(X:S) -> MARK(X:S)
 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
 MARK(add(X1:S,X2:S)) -> A__ADD(mark(X1:S),mark(X2:S))
 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
 MARK(len(X:S)) -> A__LEN(mark(X:S))
 MARK(len(X:S)) -> MARK(X:S)
-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__ADD(0,X:S) -> MARK(X:S)
 A__FROM(X:S) -> MARK(X:S)
 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
 MARK(add(X1:S,X2:S)) -> A__ADD(mark(X1:S),mark(X2:S))
 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
 MARK(len(X:S)) -> MARK(X:S)
->->-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__ADD(0,X:S) -> MARK(X:S)
 A__FROM(X:S) -> MARK(X:S)
 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
 MARK(add(X1:S,X2:S)) -> A__ADD(mark(X1:S),mark(X2:S))
 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
 MARK(len(X:S)) -> MARK(X:S)
-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)
-> Usable rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__add](X1,X2) = X1 + 2.X2 + 2
[a__from](X) = 2.X + 2
[a__fst](X1,X2) = X1 + 2.X2 + 2
[a__len](X) = X + 2
[mark](X) = 2.X + 1
[0] = 2
[add](X1,X2) = X1 + 2.X2 + 2
[cons](X1,X2) = X1 + 1
[fSNonEmpty] = 0
[from](X) = 2.X + 2
[fst](X1,X2) = X1 + 2.X2 + 2
[len](X) = X + 2
[nil] = 0
[s](X) = 2
[A__ADD](X1,X2) = X1 + 2.X2 + 2
[A__FROM](X) = 2.X + 1
[A__FST](X1,X2) = X1 + 2.X2 + 2
[A__LEN](X) = 0
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A__FROM(X:S) -> MARK(X:S)
 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
 MARK(add(X1:S,X2:S)) -> A__ADD(mark(X1:S),mark(X2:S))
 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
 MARK(len(X:S)) -> MARK(X:S)
-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__FROM(X:S) -> MARK(X:S)
 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
 MARK(len(X:S)) -> MARK(X:S)
->->-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__FROM(X:S) -> MARK(X:S)
 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
 MARK(len(X:S)) -> MARK(X:S)
-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)
-> Usable rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__add](X1,X2) = 2.X1 + 2.X2 + 2
[a__from](X) = 2.X + 2
[a__fst](X1,X2) = 2.X1 + 2.X2 + 2
[a__len](X) = 2.X + 2
[mark](X) = 2.X
[0] = 2
[add](X1,X2) = 2.X1 + 2.X2 + 2
[cons](X1,X2) = X1 + 2
[fSNonEmpty] = 0
[from](X) = 2.X + 2
[fst](X1,X2) = 2.X1 + 2.X2 + 2
[len](X) = 2.X + 2
[nil] = 0
[s](X) = 2
[A__ADD](X1,X2) = 0
[A__FROM](X) = 2.X + 1
[A__FST](X1,X2) = X1 + 2.X2
[A__LEN](X) = 0
[MARK](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
 MARK(len(X:S)) -> MARK(X:S)
-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
 MARK(len(X:S)) -> MARK(X:S)
->->-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__FST(s(X:S),cons(Y:S,Z:S)) -> MARK(Y:S)
 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
 MARK(len(X:S)) -> MARK(X:S)
-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)
-> Usable rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__add](X1,X2) = X1 + 2.X2
[a__from](X) = 2.X + 2
[a__fst](X1,X2) = 2.X1 + 2.X2 + 2
[a__len](X) = 2.X + 2
[mark](X) = 2.X
[0] = 1
[add](X1,X2) = X1 + 2.X2
[cons](X1,X2) = X1 + 1
[fSNonEmpty] = 0
[from](X) = 2.X + 2
[fst](X1,X2) = 2.X1 + 2.X2 + 2
[len](X) = 2.X + 1
[nil] = 0
[s](X) = 2
[A__ADD](X1,X2) = 0
[A__FROM](X) = 0
[A__FST](X1,X2) = X1 + X2 + 2
[A__LEN](X) = 0
[MARK](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(fst(X1:S,X2:S)) -> A__FST(mark(X1:S),mark(X2:S))
 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
 MARK(len(X:S)) -> MARK(X:S)
-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
 MARK(len(X:S)) -> MARK(X:S)
->->-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)

Problem 1: 

Subterm Processor:
-> Pairs:
 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X1:S)
 MARK(fst(X1:S,X2:S)) -> MARK(X2:S)
 MARK(len(X:S)) -> MARK(X:S)
-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)
->Projection:
 pi(MARK) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__add(0,X:S) -> mark(X:S)
 a__add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 a__add(X1:S,X2:S) -> add(X1:S,X2:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__fst(0,Z:S) -> nil
 a__fst(s(X:S),cons(Y:S,Z:S)) -> cons(mark(Y:S),fst(X:S,Z:S))
 a__fst(X1:S,X2:S) -> fst(X1:S,X2:S)
 a__len(cons(X:S,Z:S)) -> s(len(Z:S))
 a__len(nil) -> 0
 a__len(X:S) -> len(X:S)
 mark(0) -> 0
 mark(add(X1:S,X2:S)) -> a__add(mark(X1:S),mark(X2:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(fst(X1:S,X2:S)) -> a__fst(mark(X1:S),mark(X2:S))
 mark(len(X:S)) -> a__len(mark(X:S))
 mark(nil) -> nil
 mark(s(X:S)) -> s(X:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.