YES

Problem 1: 

(VAR v_NonEmpty:S X:S X1:S X2:S Y:S Z:S)
(RULES
a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
a__2nd(X:S) -> 2nd(X:S)
a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
a__from(X:S) -> from(X:S)
mark(2nd(X:S)) -> a__2nd(mark(X:S))
mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
mark(from(X:S)) -> a__from(mark(X:S))
mark(s(X:S)) -> s(mark(X:S))
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A__2ND(cons(X:S,X1:S)) -> A__2ND(cons1(mark(X:S),mark(X1:S)))
 A__2ND(cons(X:S,X1:S)) -> MARK(X:S)
 A__2ND(cons(X:S,X1:S)) -> MARK(X1:S)
 A__2ND(cons1(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))

Problem 1: 

SCC Processor:
-> Pairs:
 A__2ND(cons(X:S,X1:S)) -> A__2ND(cons1(mark(X:S),mark(X1:S)))
 A__2ND(cons(X:S,X1:S)) -> MARK(X:S)
 A__2ND(cons(X:S,X1:S)) -> MARK(X1:S)
 A__2ND(cons1(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__2ND(cons(X:S,X1:S)) -> A__2ND(cons1(mark(X:S),mark(X1:S)))
 A__2ND(cons(X:S,X1:S)) -> MARK(X:S)
 A__2ND(cons(X:S,X1:S)) -> MARK(X1:S)
 A__2ND(cons1(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
->->-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__2ND(cons(X:S,X1:S)) -> A__2ND(cons1(mark(X:S),mark(X1:S)))
 A__2ND(cons(X:S,X1:S)) -> MARK(X:S)
 A__2ND(cons(X:S,X1:S)) -> MARK(X1:S)
 A__2ND(cons1(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
-> Usable rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[a__2nd](X) = [1 1;1 1].X + [1;1]
[a__from](X) = [1 1;1 0].X + [0;1]
[mark](X) = [1 0;0 1].X
[2nd](X) = [1 1;1 1].X + [1;1]
[cons](X1,X2) = [1 1;0 0].X1 + [0 0;1 0].X2 + [0;1]
[cons1](X1,X2) = [1 1;0 0].X1 + [1 0;0 0].X2
[fSNonEmpty] = 0
[from](X) = [1 1;1 0].X + [0;1]
[s](X) = [1 0;0 0].X
[A__2ND](X) = [1 1;1 1].X + [1;1]
[A__FROM](X) = [1 1;1 1].X + [1;1]
[MARK](X) = [1 0;1 0].X + [1;1]

Problem 1: 

SCC Processor:
-> Pairs:
 A__2ND(cons(X:S,X1:S)) -> MARK(X:S)
 A__2ND(cons(X:S,X1:S)) -> MARK(X1:S)
 A__2ND(cons1(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__2ND(cons(X:S,X1:S)) -> MARK(X:S)
 A__2ND(cons(X:S,X1:S)) -> MARK(X1:S)
 A__2ND(cons1(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
->->-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__2ND(cons(X:S,X1:S)) -> MARK(X:S)
 A__2ND(cons(X:S,X1:S)) -> MARK(X1:S)
 A__2ND(cons1(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
-> Usable rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[a__2nd](X) = [1 1;1 1].X + [1;1]
[a__from](X) = [1 1;1 1].X + [1;1]
[mark](X) = [1 0;0 1].X
[2nd](X) = [1 1;1 1].X + [1;1]
[cons](X1,X2) = [0 0;1 1].X1 + [0 1;0 0].X2 + [0;1]
[cons1](X1,X2) = [0 0;0 1].X1 + [0 0;0 1].X2 + [0;1]
[fSNonEmpty] = 0
[from](X) = [1 1;1 1].X + [1;1]
[s](X) = [0 0;1 1].X
[A__2ND](X) = [1 1;1 1].X + [0;1]
[A__FROM](X) = [1 1;1 1].X + [1;1]
[MARK](X) = [0 1;0 1].X + [0;1]

Problem 1: 

SCC Processor:
-> Pairs:
 A__2ND(cons(X:S,X1:S)) -> MARK(X1:S)
 A__2ND(cons1(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__2ND(cons(X:S,X1:S)) -> MARK(X1:S)
 A__2ND(cons1(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
->->-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__2ND(cons(X:S,X1:S)) -> MARK(X1:S)
 A__2ND(cons1(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
-> Usable rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[a__2nd](X) = [1 1;1 1].X + [1;1]
[a__from](X) = [0 1;1 1].X + [1;0]
[mark](X) = [1 0;0 1].X
[2nd](X) = [1 1;1 1].X + [1;1]
[cons](X1,X2) = [0 0;1 1].X1 + [0 1;0 0].X2 + [1;0]
[cons1](X1,X2) = [0 0;1 1].X1 + [0 0;0 1].X2
[fSNonEmpty] = 0
[from](X) = [0 1;1 1].X + [1;0]
[s](X) = [0 0;0 1].X
[A__2ND](X) = [1 1;1 1].X + [1;1]
[A__FROM](X) = [0 1;0 1].X + [1;0]
[MARK](X) = [0 1;0 1].X + [1;0]

Problem 1: 

SCC Processor:
-> Pairs:
 A__2ND(cons1(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__2ND(cons1(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
->->-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__2ND(cons1(X:S,cons(Y:S,Z:S))) -> MARK(Y:S)
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
-> Usable rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[a__2nd](X) = [1 1;1 1].X + [1;1]
[a__from](X) = [1 1;1 0].X + [0;1]
[mark](X) = [1 0;0 1].X
[2nd](X) = [1 1;1 1].X + [1;1]
[cons](X1,X2) = [1 1;0 0].X1 + [0 0;1 0].X2 + [0;1]
[cons1](X1,X2) = [1 0;0 1].X1 + [1 0;0 0].X2 + [1;0]
[fSNonEmpty] = 0
[from](X) = [1 1;1 0].X + [0;1]
[s](X) = [1 0;0 0].X
[A__2ND](X) = [1 1;1 1].X + [1;1]
[A__FROM](X) = [1 1;1 1].X + [1;1]
[MARK](X) = [1 0;1 0].X + [1;1]

Problem 1: 

SCC Processor:
-> Pairs:
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> A__2ND(mark(X:S))
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
->->-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__FROM(X:S) -> MARK(X:S)
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
-> Usable rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[a__2nd](X) = [1 1;1 1].X + [1;1]
[a__from](X) = [1 1;1 0].X + [1;1]
[mark](X) = [1 0;0 1].X
[2nd](X) = [1 1;1 1].X + [1;1]
[cons](X1,X2) = [1 1;0 0].X1 + [0 0;1 0].X2
[cons1](X1,X2) = [1 1;0 0].X1 + [1 0;0 0].X2
[fSNonEmpty] = 0
[from](X) = [1 1;1 0].X + [1;1]
[s](X) = [1 0;0 0].X
[A__2ND](X) = 0
[A__FROM](X) = [1 0;1 1].X + [1;0]
[MARK](X) = [1 0;1 0].X

Problem 1: 

SCC Processor:
-> Pairs:
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> A__FROM(mark(X:S))
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
->->-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 MARK(2nd(X:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S)
 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
->Projection:
 pi(MARK) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__2nd(cons(X:S,X1:S)) -> a__2nd(cons1(mark(X:S),mark(X1:S)))
 a__2nd(cons1(X:S,cons(Y:S,Z:S))) -> mark(Y:S)
 a__2nd(X:S) -> 2nd(X:S)
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 mark(2nd(X:S)) -> a__2nd(mark(X:S))
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(cons1(X1:S,X2:S)) -> cons1(mark(X1:S),mark(X2:S))
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.