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

mod(x,0) -> 0
mod(x,s(y)) -> if1(lt(x,s(y)), x, s(y))
if1(true,x,y) -> x
if1(false,x,y) -> mod(minus(x,y),y)

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

lt(x, 0) -> false
lt(0, s(x)) -> true
lt(s(x), s(y)) -> lt(x, y)
)
(from [Walther 94])