YES

Problem 1: 

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

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 a(b(x:S)) -> a(c(b(x: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:
 a(b(x:S)) -> a(c(b(x:S)))

Problem 1: 

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

The problem is finite.