YES

Problem 1: 

(VAR X Y)
(STRATEGY CONTEXTSENSITIVE
(b)
(f)
(g 1)
(c)
)
(RULES
b -> c
f(X,g(X),Y) -> f(Y,Y,Y)
g(b) -> c
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 Empty
-> Rules:
 b -> c
 f(X,g(X),Y) -> f(Y,Y,Y)
 g(b) -> c
-> Unhiding Rules:
 Empty

Problem 1: 

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

The problem is finite.