YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
f(a,f(a,x:S)) -> f(a,f(f(a,a),f(a,x:S)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(a,f(a,x:S)) -> F(f(a,a),f(a,x:S))
 F(a,f(a,x:S)) -> F(a,f(f(a,a),f(a,x:S)))
-> Rules:
 f(a,f(a,x:S)) -> f(a,f(f(a,a),f(a,x:S)))

Problem 1: 

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

The problem is finite.