NO

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S)
(RULES
div(0) -> 0
div(s(X:S)) -> if(geq)
geq -> geq
geq -> ffalse
geq -> ttrue
if(ffalse) -> Y:S
if(ttrue) -> X:S
minus -> minus
minus -> 0
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 div(0) -> 0
 div(s(X:S)) -> if(geq)
 geq -> geq
 geq -> ffalse
 geq -> ttrue
 if(ffalse) -> Y:S
 if(ttrue) -> X:S
 minus -> minus
 minus -> 0
-> The system has extra variables.

The problem is infinite.