(COMMENT harder tail-recursive variant of AG01 3.1)
(VAR x y z)
(RULES
minus(0,y) -> 0
minus(x,0) -> x
minus(s(x),s(y)) -> minus(x,y)
plus(0,y) -> y
plus(s(x),y) -> plus(x,s(y))
zero(s(x)) -> false
zero(0) -> true
p(s(x)) -> x
div(x,y) -> quot(x,y,0)
quot(x,y,z) -> if(zero(x),x,y,plus(z,s(0)))
if(true,x,y,z) -> p(z)
if(false,x,s(y),z) -> quot(minus(x,s(y)),s(y),z)
)