YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.