YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
f(f(x:S)) -> f(c(f(x:S)))
f(f(x:S)) -> f(d(f(x:S)))
g(c(1)) -> g(d(h(0)))
g(c(h(0))) -> g(d(1))
g(c(x:S)) -> x:S
g(d(x:S)) -> x:S
g(h(x:S)) -> g(x:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(f(x:S)) -> F(c(f(x:S)))
 F(f(x:S)) -> F(d(f(x:S)))
 G(c(1)) -> G(d(h(0)))
 G(c(h(0))) -> G(d(1))
 G(h(x:S)) -> G(x:S)
-> Rules:
 f(f(x:S)) -> f(c(f(x:S)))
 f(f(x:S)) -> f(d(f(x:S)))
 g(c(1)) -> g(d(h(0)))
 g(c(h(0))) -> g(d(1))
 g(c(x:S)) -> x:S
 g(d(x:S)) -> x:S
 g(h(x:S)) -> g(x:S)

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(x:S)) -> F(c(f(x:S)))
 F(f(x:S)) -> F(d(f(x:S)))
 G(c(1)) -> G(d(h(0)))
 G(c(h(0))) -> G(d(1))
 G(h(x:S)) -> G(x:S)
-> Rules:
 f(f(x:S)) -> f(c(f(x:S)))
 f(f(x:S)) -> f(d(f(x:S)))
 g(c(1)) -> g(d(h(0)))
 g(c(h(0))) -> g(d(1))
 g(c(x:S)) -> x:S
 g(d(x:S)) -> x:S
 g(h(x:S)) -> g(x:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(h(x:S)) -> G(x:S)
->->-> Rules:
 f(f(x:S)) -> f(c(f(x:S)))
 f(f(x:S)) -> f(d(f(x:S)))
 g(c(1)) -> g(d(h(0)))
 g(c(h(0))) -> g(d(1))
 g(c(x:S)) -> x:S
 g(d(x:S)) -> x:S
 g(h(x:S)) -> g(x:S)

Problem 1: 

Subterm Processor:
-> Pairs:
 G(h(x:S)) -> G(x:S)
-> Rules:
 f(f(x:S)) -> f(c(f(x:S)))
 f(f(x:S)) -> f(d(f(x:S)))
 g(c(1)) -> g(d(h(0)))
 g(c(h(0))) -> g(d(1))
 g(c(x:S)) -> x:S
 g(d(x:S)) -> x:S
 g(h(x:S)) -> g(x:S)
->Projection:
 pi(G) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(f(x:S)) -> f(c(f(x:S)))
 f(f(x:S)) -> f(d(f(x:S)))
 g(c(1)) -> g(d(h(0)))
 g(c(h(0))) -> g(d(1))
 g(c(x:S)) -> x:S
 g(d(x:S)) -> x:S
 g(h(x:S)) -> g(x:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.