YES

Problem 1: 

(VAR X)
(STRATEGY CONTEXTSENSITIVE
(c)
(f 2)
(b)
)
(RULES
c -> b
f(b,X,c) -> f(X,c,X)
)

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 F(b,X,c) -> C
 F(b,X,c) -> F(X,c,X)
-> Rules:
 c -> b
 f(b,X,c) -> f(X,c,X)
-> Unhiding rules:
 Empty
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.