(from AG01 4.23)
(VAR x y z)
(RULES
quot(0,s(y),s(z)) -> 0
quot(s(x),s(y),z) -> quot(x,y,z)

plus(s(x), s(y)) -> s(s(plus(if(gt(x,y),x,y), if(not(gt(x,y)),id(x),id(y)))))
plus(s(x), x) -> plus(if(gt(x,x), id(x), id(x)), s(x))
plus(zero, y) -> y
plus(id(x), s(y)) -> s(plus(x,if(gt(s(y),y), y, s(y))))

id(x) -> x

if(true, x, y) -> x
if(false, x, y) -> y

not(x) -> if(x, false, true)

gt(s(x), zero) -> true
gt(zero, y) -> false
gt(s(x), s(y)) -> gt(x, y)
quot(x,0,s(z)) -> s(quot(x,plus(z,s(0)),s(z)))
)
(STRATEGY INNERMOST)