; @origtpdbfilename ./TRS/TRCSR/ExIntrod_GM99_GM.trs
; @xtcfilename "./TRS_Standard/Transformed_CSR_04/ExIntrod_GM99_GM.xml"
(format TRS)
(fun a__primes 0)
(fun a__sieve 1)
(fun a__from 1)
(fun s 1)
(fun |0| 0)
(fun cons 2)
(fun mark 1)
(fun from 1)
(fun a__head 1)
(fun a__tail 1)
(fun a__if 3)
(fun true 0)
(fun false 0)
(fun a__filter 2)
(fun divides 2)
(fun filter 2)
(fun sieve 1)
(fun primes 0)
(fun head 1)
(fun tail 1)
(fun if 3)
(rule a__primes (a__sieve (a__from (s (s |0|)))))
(rule (a__from X) (cons (mark X) (from (s X))))
(rule (a__head (cons X Y)) (mark X))
(rule (a__tail (cons X Y)) (mark Y))
(rule (a__if true X Y) (mark X))
(rule (a__if false X Y) (mark Y))
(rule (a__filter (s (s X)) (cons Y Z)) (a__if (divides (s (s (mark X))) (mark Y)) (filter (s (s X)) Z) (cons Y (filter X (sieve Y)))))
(rule (a__sieve (cons X Y)) (cons (mark X) (filter X (sieve Y))))
(rule (mark primes) a__primes)
(rule (mark (sieve X)) (a__sieve (mark X)))
(rule (mark (from X)) (a__from (mark X)))
(rule (mark (head X)) (a__head (mark X)))
(rule (mark (tail X)) (a__tail (mark X)))
(rule (mark (if X1 X2 X3)) (a__if (mark X1) X2 X3))
(rule (mark (filter X1 X2)) (a__filter (mark X1) (mark X2)))
(rule (mark (s X)) (s (mark X)))
(rule (mark |0|) |0|)
(rule (mark (cons X1 X2)) (cons (mark X1) X2))
(rule (mark true) true)
(rule (mark false) false)
(rule (mark (divides X1 X2)) (divides (mark X1) (mark X2)))
(rule a__primes primes)
(rule (a__sieve X) (sieve X))
(rule (a__from X) (from X))
(rule (a__head X) (head X))
(rule (a__tail X) (tail X))
(rule (a__if X1 X2 X3) (if X1 X2 X3))
(rule (a__filter X1 X2) (filter X1 X2))