YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
a(a(x:S)) -> a(b(a(x:S)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(a(x:S)) -> A(b(a(x:S)))
-> Rules:
 a(a(x:S)) -> a(b(a(x:S)))

Problem 1: 

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

The problem is finite.