YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
+(0,y:S) -> y:S
+(s(x:S),y:S) -> +(x:S,s(y:S))
+(s(x:S),y:S) -> s(+(x:S,y:S))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 +#(s(x:S),y:S) -> +#(x:S,s(y:S))
 +#(s(x:S),y:S) -> +#(x:S,y:S)
-> Rules:
 +(0,y:S) -> y:S
 +(s(x:S),y:S) -> +(x:S,s(y:S))
 +(s(x:S),y:S) -> s(+(x:S,y:S))

Problem 1: 

SCC Processor:
-> Pairs:
 +#(s(x:S),y:S) -> +#(x:S,s(y:S))
 +#(s(x:S),y:S) -> +#(x:S,y:S)
-> Rules:
 +(0,y:S) -> y:S
 +(s(x:S),y:S) -> +(x:S,s(y:S))
 +(s(x:S),y:S) -> s(+(x:S,y:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 +#(s(x:S),y:S) -> +#(x:S,s(y:S))
 +#(s(x:S),y:S) -> +#(x:S,y:S)
->->-> Rules:
 +(0,y:S) -> y:S
 +(s(x:S),y:S) -> +(x:S,s(y:S))
 +(s(x:S),y:S) -> s(+(x:S,y:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 +#(s(x:S),y:S) -> +#(x:S,s(y:S))
 +#(s(x:S),y:S) -> +#(x:S,y:S)
-> Rules:
 +(0,y:S) -> y:S
 +(s(x:S),y:S) -> +(x:S,s(y:S))
 +(s(x:S),y:S) -> s(+(x:S,y:S))
->Projection:
 pi(+#) = 1

Problem 1: 

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

The problem is finite.