YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
ap(ap(ff,x:S),x:S) -> ap(ap(x:S,ap(ff,x:S)),ap(ap(cons,x:S),nil))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 ap(ap(ff,x:S),x:S) -> ap(ap(x:S,ap(ff,x:S)),ap(ap(cons,x:S),nil))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 AP(ap(ff,x:S),x:S) -> AP(ap(x:S,ap(ff,x:S)),ap(ap(cons,x:S),nil))
 AP(ap(ff,x:S),x:S) -> AP(x:S,ap(ff,x:S))
-> Rules:
 ap(ap(ff,x:S),x:S) -> ap(ap(x:S,ap(ff,x:S)),ap(ap(cons,x:S),nil))

Problem 1: 

SCC Processor:
-> Pairs:
 AP(ap(ff,x:S),x:S) -> AP(ap(x:S,ap(ff,x:S)),ap(ap(cons,x:S),nil))
 AP(ap(ff,x:S),x:S) -> AP(x:S,ap(ff,x:S))
-> Rules:
 ap(ap(ff,x:S),x:S) -> ap(ap(x:S,ap(ff,x:S)),ap(ap(cons,x:S),nil))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.