# count up to ack(10,10) where ack is the Ackermann function
(VAR x y)
(RULES
f(TRUE, x) -> f(ack(10,10) >= x, x+1)

ack(x, y) -> ackNat(x >= 0 && y >= 0, x, y)

ackNat(TRUE, x, y) -> cond1(x = 0, x, y)
ackNat(FALSE, x, y) -> 0

cond1(TRUE, x, y) -> y+1
cond1(FALSE, x, y) -> cond2(y = 0, x, y)

cond2(TRUE, x, y) -> ack(x-1, y+1)
cond2(FALSE, x, y) -> ack(x-1, ack(x, y-1))
)