(format LCTRS :logic QF_LIA)

(fun sum1 2 :sort (Int Int Int))
(fun u 3 :sort (Int Int Int Int))

(rule (sum1 n m) (u n m 0))
(rule (u x i z) (u x (+ i 1) (+ z i)) :guard (<= i x))
(rule (u x i z) z :guard (not (<= i x)))