NO

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S)
(RULES
diff(X:S,Y:S) -> if(leq(X:S,Y:S))
if(ffalse) -> Y:S
if(ttrue) -> X:S
leq(0,Y:S) -> ttrue
leq(s(X:S),0) -> ffalse
leq(s(X:S),s(Y:S)) -> leq(X:S,Y:S)
p(0) -> 0
p(s(X:S)) -> X:S
)

Problem 1: 

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

The problem is infinite.