YES

Problem 1: 

(VAR v_NonEmpty:S x1:S)
(RULES
b(b(c(a(b(c(x1:S)))))) -> a(b(b(c(b(c(a(x1:S)))))))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 b(b(c(a(b(c(x1:S)))))) -> a(b(b(c(b(c(a(x1:S)))))))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 Empty
-> Rules:
 b(b(c(a(b(c(x1:S)))))) -> a(b(b(c(b(c(a(x1:S)))))))

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 b(b(c(a(b(c(x1:S)))))) -> a(b(b(c(b(c(a(x1:S)))))))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.