NO

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S)
(RULES
add(0,X:S) -> X:S
add(s(X:S),Y:S) -> s(add(X:S,Y:S))
fact(X:S) -> if(zero(X:S))
if(ffalse) -> Y:S
if(ttrue) -> X:S
p(s(X:S)) -> X:S
prod(0,X:S) -> 0
prod(s(X:S),Y:S) -> add(Y:S,prod(X:S,Y:S))
zero(0) -> ttrue
zero(s(X:S)) -> ffalse
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 add(0,X:S) -> X:S
 add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 fact(X:S) -> if(zero(X:S))
 if(ffalse) -> Y:S
 if(ttrue) -> X:S
 p(s(X:S)) -> X:S
 prod(0,X:S) -> 0
 prod(s(X:S),Y:S) -> add(Y:S,prod(X:S,Y:S))
 zero(0) -> ttrue
 zero(s(X:S)) -> ffalse
-> The system has extra variables.

The problem is infinite.