NO

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
ap(ap(g,x:S),y:S) -> y:S
ap(f,x:S) -> ap(f,app(g,x:S))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 AP(f,x:S) -> AP(f,app(g,x:S))
-> Rules:
 ap(ap(g,x:S),y:S) -> y:S
 ap(f,x:S) -> ap(f,app(g,x:S))

Problem 1: 

Infinite Processor:
-> Pairs:
 AP(f,x:S) -> AP(f,app(g,x:S))
-> Rules:
 ap(ap(g,x:S),y:S) -> y:S
 ap(f,x:S) -> ap(f,app(g,x:S))
-> Pairs in cycle:
 AP(f,x:S) -> AP(f,app(g,x:S))

The problem is infinite.