YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
h(c(s(x:S),c(s(0),y:S)),z:S) -> h(y:S,c(s(0),c(x:S,z:S)))
h(x:S,c(y:S,z:S)) -> h(c(s(y:S),x:S),z:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 H(c(s(x:S),c(s(0),y:S)),z:S) -> H(y:S,c(s(0),c(x:S,z:S)))
 H(x:S,c(y:S,z:S)) -> H(c(s(y:S),x:S),z:S)
-> Rules:
 h(c(s(x:S),c(s(0),y:S)),z:S) -> h(y:S,c(s(0),c(x:S,z:S)))
 h(x:S,c(y:S,z:S)) -> h(c(s(y:S),x:S),z:S)

Problem 1: 

SCC Processor:
-> Pairs:
 H(c(s(x:S),c(s(0),y:S)),z:S) -> H(y:S,c(s(0),c(x:S,z:S)))
 H(x:S,c(y:S,z:S)) -> H(c(s(y:S),x:S),z:S)
-> Rules:
 h(c(s(x:S),c(s(0),y:S)),z:S) -> h(y:S,c(s(0),c(x:S,z:S)))
 h(x:S,c(y:S,z:S)) -> h(c(s(y:S),x:S),z:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 H(c(s(x:S),c(s(0),y:S)),z:S) -> H(y:S,c(s(0),c(x:S,z:S)))
 H(x:S,c(y:S,z:S)) -> H(c(s(y:S),x:S),z:S)
->->-> Rules:
 h(c(s(x:S),c(s(0),y:S)),z:S) -> h(y:S,c(s(0),c(x:S,z:S)))
 h(x:S,c(y:S,z:S)) -> h(c(s(y:S),x:S),z:S)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 H(c(s(x:S),c(s(0),y:S)),z:S) -> H(y:S,c(s(0),c(x:S,z:S)))
 H(x:S,c(y:S,z:S)) -> H(c(s(y:S),x:S),z:S)
-> Rules:
 h(c(s(x:S),c(s(0),y:S)),z:S) -> h(y:S,c(s(0),c(x:S,z:S)))
 h(x:S,c(y:S,z:S)) -> h(c(s(y:S),x:S),z:S)
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0] = 1/2
[c](X1,X2) = 1/2.X1 + X2
[s](X) = 1/2.X
[H](X1,X2) = X1 + 1/2.X2

Problem 1: 

SCC Processor:
-> Pairs:
 H(x:S,c(y:S,z:S)) -> H(c(s(y:S),x:S),z:S)
-> Rules:
 h(c(s(x:S),c(s(0),y:S)),z:S) -> h(y:S,c(s(0),c(x:S,z:S)))
 h(x:S,c(y:S,z:S)) -> h(c(s(y:S),x:S),z:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 H(x:S,c(y:S,z:S)) -> H(c(s(y:S),x:S),z:S)
->->-> Rules:
 h(c(s(x:S),c(s(0),y:S)),z:S) -> h(y:S,c(s(0),c(x:S,z:S)))
 h(x:S,c(y:S,z:S)) -> h(c(s(y:S),x:S),z:S)

Problem 1: 

Subterm Processor:
-> Pairs:
 H(x:S,c(y:S,z:S)) -> H(c(s(y:S),x:S),z:S)
-> Rules:
 h(c(s(x:S),c(s(0),y:S)),z:S) -> h(y:S,c(s(0),c(x:S,z:S)))
 h(x:S,c(y:S,z:S)) -> h(c(s(y:S),x:S),z:S)
->Projection:
 pi(H) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 h(c(s(x:S),c(s(0),y:S)),z:S) -> h(y:S,c(s(0),c(x:S,z:S)))
 h(x:S,c(y:S,z:S)) -> h(c(s(y:S),x:S),z:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.