(VAR x y)
(RULES
minus(x,y) -> if(gt(x,y),x,y)
if(true,x,y) -> s(minus(p(x),y))
if(false,x,y) -> 0

p(0) -> 0
p(s(x)) -> x

ge(x, 0) -> true
ge(0, s(x)) -> false
ge(s(x), s(y)) -> ge(x, y)

gt(0, y) -> false
gt(s(x),0) -> true
gt(s(x), s(y)) -> gt(x, y)

div(x,y) -> if1(ge(x,y), x, y)
if1(true,x,y) -> if2(gt(y,0),x,y)
if1(false,x,y) -> 0
if2(true,x,y) -> s(div(minus(x,y),y))
if2(false,x,y) -> 0
)