YES

Problem 1: 

(VAR v_NonEmpty:S X:S X1:S X2:S Y:S)
(RULES
a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
a__from(X:S) -> from(X:S)
a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S))
a__length(nil) -> 0
a__length(X:S) -> length(X:S)
a__length1(X:S) -> a__length(X:S)
a__length1(X:S) -> length1(X:S)
mark(0) -> 0
mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
mark(from(X:S)) -> a__from(mark(X:S))
mark(length(X:S)) -> a__length(X:S)
mark(length1(X:S)) -> a__length1(X:S)
mark(nil) -> nil
mark(s(X:S)) -> s(mark(X:S))
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A__FROM(X:S) -> MARK(X:S)
 A__LENGTH(cons(X:S,Y:S)) -> A__LENGTH1(Y:S)
 A__LENGTH1(X:S) -> A__LENGTH(X: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(length(X:S)) -> A__LENGTH(X:S)
 MARK(length1(X:S)) -> A__LENGTH1(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S))
 a__length(nil) -> 0
 a__length(X:S) -> length(X:S)
 a__length1(X:S) -> a__length(X:S)
 a__length1(X:S) -> length1(X:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(length(X:S)) -> a__length(X:S)
 mark(length1(X:S)) -> a__length1(X:S)
 mark(nil) -> nil
 mark(s(X:S)) -> s(mark(X:S))

Problem 1: 

SCC Processor:
-> Pairs:
 A__FROM(X:S) -> MARK(X:S)
 A__LENGTH(cons(X:S,Y:S)) -> A__LENGTH1(Y:S)
 A__LENGTH1(X:S) -> A__LENGTH(X: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(length(X:S)) -> A__LENGTH(X:S)
 MARK(length1(X:S)) -> A__LENGTH1(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S))
 a__length(nil) -> 0
 a__length(X:S) -> length(X:S)
 a__length1(X:S) -> a__length(X:S)
 a__length1(X:S) -> length1(X:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(length(X:S)) -> a__length(X:S)
 mark(length1(X:S)) -> a__length1(X:S)
 mark(nil) -> nil
 mark(s(X:S)) -> s(mark(X:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__LENGTH(cons(X:S,Y:S)) -> A__LENGTH1(Y:S)
 A__LENGTH1(X:S) -> A__LENGTH(X:S)
->->-> Rules:
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S))
 a__length(nil) -> 0
 a__length(X:S) -> length(X:S)
 a__length1(X:S) -> a__length(X:S)
 a__length1(X:S) -> length1(X:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(length(X:S)) -> a__length(X:S)
 mark(length1(X:S)) -> a__length1(X:S)
 mark(nil) -> nil
 mark(s(X:S)) -> s(mark(X:S))
->->Cycle:
->->-> Pairs:
 A__FROM(X:S) -> MARK(X: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(s(X:S)) -> MARK(X:S)
->->-> Rules:
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S))
 a__length(nil) -> 0
 a__length(X:S) -> length(X:S)
 a__length1(X:S) -> a__length(X:S)
 a__length1(X:S) -> length1(X:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(length(X:S)) -> a__length(X:S)
 mark(length1(X:S)) -> a__length1(X:S)
 mark(nil) -> nil
 mark(s(X:S)) -> s(mark(X:S))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 A__LENGTH(cons(X:S,Y:S)) -> A__LENGTH1(Y:S)
 A__LENGTH1(X:S) -> A__LENGTH(X:S)
-> Rules:
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S))
 a__length(nil) -> 0
 a__length(X:S) -> length(X:S)
 a__length1(X:S) -> a__length(X:S)
 a__length1(X:S) -> length1(X:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(length(X:S)) -> a__length(X:S)
 mark(length1(X:S)) -> a__length1(X:S)
 mark(nil) -> nil
 mark(s(X:S)) -> s(mark(X:S))
->Projection:
 pi(A__LENGTH) = 1
 pi(A__LENGTH1) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 A__LENGTH1(X:S) -> A__LENGTH(X:S)
-> Rules:
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S))
 a__length(nil) -> 0
 a__length(X:S) -> length(X:S)
 a__length1(X:S) -> a__length(X:S)
 a__length1(X:S) -> length1(X:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(length(X:S)) -> a__length(X:S)
 mark(length1(X:S)) -> a__length1(X:S)
 mark(nil) -> nil
 mark(s(X:S)) -> s(mark(X:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Reduction Pairs Processor:
-> Pairs:
 A__FROM(X:S) -> MARK(X: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(s(X:S)) -> MARK(X:S)
-> Rules:
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S))
 a__length(nil) -> 0
 a__length(X:S) -> length(X:S)
 a__length1(X:S) -> a__length(X:S)
 a__length1(X:S) -> length1(X:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(length(X:S)) -> a__length(X:S)
 mark(length1(X:S)) -> a__length1(X:S)
 mark(nil) -> nil
 mark(s(X:S)) -> s(mark(X:S))
-> Usable rules:
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S))
 a__length(nil) -> 0
 a__length(X:S) -> length(X:S)
 a__length1(X:S) -> a__length(X:S)
 a__length1(X:S) -> length1(X:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(length(X:S)) -> a__length(X:S)
 mark(length1(X:S)) -> a__length1(X:S)
 mark(nil) -> nil
 mark(s(X:S)) -> s(mark(X:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__from](X) = 2.X + 2
[a__length](X) = 0
[a__length1](X) = 0
[mark](X) = 2.X
[0] = 0
[cons](X1,X2) = X1 + 2
[fSNonEmpty] = 0
[from](X) = 2.X + 2
[length](X) = 0
[length1](X) = 0
[nil] = 2
[s](X) = 2.X
[A__FROM](X) = 2.X + 2
[A__LENGTH](X) = 0
[A__LENGTH1](X) = 0
[MARK](X) = 2.X

Problem 1.2: 

SCC Processor:
-> Pairs:
 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(s(X:S)) -> MARK(X:S)
-> Rules:
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S))
 a__length(nil) -> 0
 a__length(X:S) -> length(X:S)
 a__length1(X:S) -> a__length(X:S)
 a__length1(X:S) -> length1(X:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(length(X:S)) -> a__length(X:S)
 mark(length1(X:S)) -> a__length1(X:S)
 mark(nil) -> nil
 mark(s(X:S)) -> s(mark(X:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
->->-> Rules:
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S))
 a__length(nil) -> 0
 a__length(X:S) -> length(X:S)
 a__length1(X:S) -> a__length(X:S)
 a__length1(X:S) -> length1(X:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(length(X:S)) -> a__length(X:S)
 mark(length1(X:S)) -> a__length1(X:S)
 mark(nil) -> nil
 mark(s(X:S)) -> s(mark(X:S))

Problem 1.2: 

Subterm Processor:
-> Pairs:
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(from(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S))
 a__length(nil) -> 0
 a__length(X:S) -> length(X:S)
 a__length1(X:S) -> a__length(X:S)
 a__length1(X:S) -> length1(X:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(length(X:S)) -> a__length(X:S)
 mark(length1(X:S)) -> a__length1(X:S)
 mark(nil) -> nil
 mark(s(X:S)) -> s(mark(X:S))
->Projection:
 pi(MARK) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__from(X:S) -> cons(mark(X:S),from(s(X:S)))
 a__from(X:S) -> from(X:S)
 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S))
 a__length(nil) -> 0
 a__length(X:S) -> length(X:S)
 a__length1(X:S) -> a__length(X:S)
 a__length1(X:S) -> length1(X:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(from(X:S)) -> a__from(mark(X:S))
 mark(length(X:S)) -> a__length(X:S)
 mark(length1(X:S)) -> a__length1(X:S)
 mark(nil) -> nil
 mark(s(X:S)) -> s(mark(X:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.