YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
a(f,a(f,x:S)) -> a(x:S,x:S)
a(h,x:S) -> a(f,a(g,a(f,x:S)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(f,a(f,x:S)) -> A(x:S,x:S)
 A(h,x:S) -> A(f,a(g,a(f,x:S)))
 A(h,x:S) -> A(f,x:S)
 A(h,x:S) -> A(g,a(f,x:S))
-> Rules:
 a(f,a(f,x:S)) -> a(x:S,x:S)
 a(h,x:S) -> a(f,a(g,a(f,x:S)))

Problem 1: 

SCC Processor:
-> Pairs:
 A(f,a(f,x:S)) -> A(x:S,x:S)
 A(h,x:S) -> A(f,a(g,a(f,x:S)))
 A(h,x:S) -> A(f,x:S)
 A(h,x:S) -> A(g,a(f,x:S))
-> Rules:
 a(f,a(f,x:S)) -> a(x:S,x:S)
 a(h,x:S) -> a(f,a(g,a(f,x:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(f,a(f,x:S)) -> A(x:S,x:S)
 A(h,x:S) -> A(f,x:S)
->->-> Rules:
 a(f,a(f,x:S)) -> a(x:S,x:S)
 a(h,x:S) -> a(f,a(g,a(f,x:S)))

Problem 1: 

Subterm Processor:
-> Pairs:
 A(f,a(f,x:S)) -> A(x:S,x:S)
 A(h,x:S) -> A(f,x:S)
-> Rules:
 a(f,a(f,x:S)) -> a(x:S,x:S)
 a(h,x:S) -> a(f,a(g,a(f,x:S)))
->Projection:
 pi(A) = 2

Problem 1: 

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

The problem is finite.