(from AG01 4.29)
(VAR x y)
(RULES
even(0) -> true
even(s(0)) -> false
even(s(s(x))) -> even(x)
half(0) -> 0
half(s(s(x))) -> s(half(x))

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)
times(0,y) -> 0
times(s(x),y) -> if_times(even(s(x)),s(x),y)
if_times(true,s(x),y) -> plus(times(half(s(x)),y),times(half(s(x)),y))
if_times(false,s(x),y) -> plus(y,times(x,y))
)
(STRATEGY INNERMOST)