NO

Problem 1: 

(VAR v_NonEmpty:S M:S N:S X:S)
(RULES
and(tt) -> X:S
plus(N:S,0) -> N:S
plus(N:S,s(M:S)) -> s(plus(N:S,M:S))
x(N:S,0) -> 0
x(N:S,s(M:S)) -> plus(x(N:S,M:S),N:S)
)

Problem 1: 

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

The problem is infinite.