YES

Problem 1: 

(VAR X)
(STRATEGY CONTEXTSENSITIVE
(b)
(f 1)
(a)
)
(RULES
b -> a
f(X,X) -> f(a,b)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 Empty
-> Rules:
 b -> a
 f(X,X) -> f(a,b)
-> Unhiding Rules:
 Empty

Problem 1: 

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

The problem is finite.