YES

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S Z:S)
(RULES
f(f(X:S,Y:S),Z:S) -> f(X:S,f(Y:S,Z:S))
f(X:S,f(Y:S,Z:S)) -> f(Y:S,Y:S)
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(f(X:S,Y:S),Z:S) -> F(X:S,f(Y:S,Z:S))
 F(f(X:S,Y:S),Z:S) -> F(Y:S,Z:S)
 F(X:S,f(Y:S,Z:S)) -> F(Y:S,Y:S)
-> Rules:
 f(f(X:S,Y:S),Z:S) -> f(X:S,f(Y:S,Z:S))
 f(X:S,f(Y:S,Z:S)) -> f(Y:S,Y:S)

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(X:S,Y:S),Z:S) -> F(X:S,f(Y:S,Z:S))
 F(f(X:S,Y:S),Z:S) -> F(Y:S,Z:S)
 F(X:S,f(Y:S,Z:S)) -> F(Y:S,Y:S)
-> Rules:
 f(f(X:S,Y:S),Z:S) -> f(X:S,f(Y:S,Z:S))
 f(X:S,f(Y:S,Z:S)) -> f(Y:S,Y:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.