YES

Problem 1: 

(VAR X)
(STRATEGY CONTEXTSENSITIVE
(f 1)
(g)
(h 1)
)
(RULES
f(X) -> g(h(f(X)))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(X) -> g(h(f(X)))
-> The context-sensitive term rewriting system is an orthogonal system. Therefore, innermost cs-termination implies cs-termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 Empty
-> Rules:
 f(X) -> g(h(f(X)))
-> Unhiding Rules:
 Empty

Problem 1: 

Basic Processor:
-> Pairs:
 Empty
-> Rules:
 f(X) -> g(h(f(X)))
-> Unhiding rules:
 Empty
-> Result:
 Set P is empty

The problem is finite.