NO

Problem 1: 

(VAR v_NonEmpty:S M:S N:S)
(RULES
U11(tt) -> U12(tt)
U12(tt) -> s(plus(N:S,M:S))
U21(tt) -> U22(tt)
U22(tt) -> plus(x(N:S,M:S),N:S)
plus(N:S,0) -> N:S
plus(N:S,s(M:S)) -> U11(tt)
x(N:S,0) -> 0
x(N:S,s(M:S)) -> U21(tt)
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 U11(tt) -> U12(tt)
 U12(tt) -> s(plus(N:S,M:S))
 U21(tt) -> U22(tt)
 U22(tt) -> plus(x(N:S,M:S),N:S)
 plus(N:S,0) -> N:S
 plus(N:S,s(M:S)) -> U11(tt)
 x(N:S,0) -> 0
 x(N:S,s(M:S)) -> U21(tt)
-> The system has extra variables.

The problem is infinite.