; @origtpdbfilename ./TRS/Cime/list-sum-prod-assoc-append.trs
; @xtcfilename "./TRS_Standard/CiME_04/list-sum-prod-assoc-append.xml"
(format TRS)
(fun + 2)
(fun |0| 0)
(fun s 1)
(fun * 2)
(fun app 2)
(fun nil 0)
(fun cons 2)
(fun sum 1)
(fun prod 1)
(rule (+ x |0|) x)
(rule (+ |0| x) x)
(rule (+ (s x) (s y)) (s (s (+ x y))))
(rule (+ (+ x y) z) (+ x (+ y z)))
(rule (* x |0|) |0|)
(rule (* |0| x) |0|)
(rule (* (s x) (s y)) (s (+ (* x y) (+ x y))))
(rule (* (* x y) z) (* x (* y z)))
(rule (app nil l) l)
(rule (app (cons x l1) l2) (cons x (app l1 l2)))
(rule (sum nil) |0|)
(rule (sum (cons x l)) (+ x (sum l)))
(rule (sum (app l1 l2)) (+ (sum l1) (sum l2)))
(rule (prod nil) (s |0|))
(rule (prod (cons x l)) (* x (prod l)))
(rule (prod (app l1 l2)) (* (prod l1) (prod l2)))