YES

Problem 1: 

(VAR v_NonEmpty:S a:S b:S c:S k:S l:S x:S)
(RULES
f(cons(x:S,k:S),l:S) -> g(k:S,l:S,cons(x:S,k:S))
f(empty,l:S) -> l:S
g(a:S,b:S,c:S) -> f(a:S,cons(b:S,c:S))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(cons(x:S,k:S),l:S) -> g(k:S,l:S,cons(x:S,k:S))
 f(empty,l:S) -> l:S
 g(a:S,b:S,c:S) -> f(a:S,cons(b:S,c:S))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(cons(x:S,k:S),l:S) -> G(k:S,l:S,cons(x:S,k:S))
 G(a:S,b:S,c:S) -> F(a:S,cons(b:S,c:S))
-> Rules:
 f(cons(x:S,k:S),l:S) -> g(k:S,l:S,cons(x:S,k:S))
 f(empty,l:S) -> l:S
 g(a:S,b:S,c:S) -> f(a:S,cons(b:S,c:S))

Problem 1: 

SCC Processor:
-> Pairs:
 F(cons(x:S,k:S),l:S) -> G(k:S,l:S,cons(x:S,k:S))
 G(a:S,b:S,c:S) -> F(a:S,cons(b:S,c:S))
-> Rules:
 f(cons(x:S,k:S),l:S) -> g(k:S,l:S,cons(x:S,k:S))
 f(empty,l:S) -> l:S
 g(a:S,b:S,c:S) -> f(a:S,cons(b:S,c:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(cons(x:S,k:S),l:S) -> G(k:S,l:S,cons(x:S,k:S))
 G(a:S,b:S,c:S) -> F(a:S,cons(b:S,c:S))
->->-> Rules:
 f(cons(x:S,k:S),l:S) -> g(k:S,l:S,cons(x:S,k:S))
 f(empty,l:S) -> l:S
 g(a:S,b:S,c:S) -> f(a:S,cons(b:S,c:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 F(cons(x:S,k:S),l:S) -> G(k:S,l:S,cons(x:S,k:S))
 G(a:S,b:S,c:S) -> F(a:S,cons(b:S,c:S))
-> Rules:
 f(cons(x:S,k:S),l:S) -> g(k:S,l:S,cons(x:S,k:S))
 f(empty,l:S) -> l:S
 g(a:S,b:S,c:S) -> f(a:S,cons(b:S,c:S))
->Projection:
 pi(F) = 1
 pi(G) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 G(a:S,b:S,c:S) -> F(a:S,cons(b:S,c:S))
-> Rules:
 f(cons(x:S,k:S),l:S) -> g(k:S,l:S,cons(x:S,k:S))
 f(empty,l:S) -> l:S
 g(a:S,b:S,c:S) -> f(a:S,cons(b:S,c:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.