NO

Problem 1: 

(VAR v_NonEmpty:S M:S N:S)
(RULES
U11(tt) -> U12(isNat)
U12(tt) -> tt
U21(tt) -> tt
U31(tt) -> N:S
U41(tt) -> U42(isNat)
U42(tt) -> s(plus(N:S,M:S))
isNat -> U11(isNat)
isNat -> U21(isNat)
isNat -> tt
plus(N:S,0) -> U31(isNat)
plus(N:S,s(M:S)) -> U41(isNat)
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 U11(tt) -> U12(isNat)
 U12(tt) -> tt
 U21(tt) -> tt
 U31(tt) -> N:S
 U41(tt) -> U42(isNat)
 U42(tt) -> s(plus(N:S,M:S))
 isNat -> U11(isNat)
 isNat -> U21(isNat)
 isNat -> tt
 plus(N:S,0) -> U31(isNat)
 plus(N:S,s(M:S)) -> U41(isNat)
-> The system has extra variables.

The problem is infinite.