NO

Problem 1: 

(VAR v_NonEmpty:S)
(RULES
c -> d
g -> h
h -> g
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 G -> H
 H -> G
-> Rules:
 c -> d
 g -> h
 h -> g

Problem 1: 

SCC Processor:
-> Pairs:
 G -> H
 H -> G
-> Rules:
 c -> d
 g -> h
 h -> g
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G -> H
 H -> G
->->-> Rules:
 c -> d
 g -> h
 h -> g

Problem 1: 

Infinite Processor:
-> Pairs:
 G -> H
 H -> G
-> Rules:
 c -> d
 g -> h
 h -> g
-> Pairs in cycle:
 G -> H
 H -> G

The problem is infinite.