; @origtpdbfilename ./TRS/TRCSR/ExSec11_1_Luc02a_GM.trs
; @xtcfilename "./TRS_Standard/Transformed_CSR_04/ExSec11_1_Luc02a_GM.xml"
(format TRS)
(fun a__terms 1)
(fun cons 2)
(fun recip 1)
(fun a__sqr 1)
(fun mark 1)
(fun terms 1)
(fun s 1)
(fun |0| 0)
(fun a__add 2)
(fun a__dbl 1)
(fun a__first 2)
(fun nil 0)
(fun first 2)
(fun a__half 1)
(fun dbl 1)
(fun sqr 1)
(fun add 2)
(fun half 1)
(rule (a__terms N) (cons (recip (a__sqr (mark N))) (terms (s N))))
(rule (a__sqr |0|) |0|)
(rule (a__sqr (s X)) (s (a__add (a__sqr (mark X)) (a__dbl (mark X)))))
(rule (a__dbl |0|) |0|)
(rule (a__dbl (s X)) (s (s (a__dbl (mark X)))))
(rule (a__add |0| X) (mark X))
(rule (a__add (s X) Y) (s (a__add (mark X) (mark Y))))
(rule (a__first |0| X) nil)
(rule (a__first (s X) (cons Y Z)) (cons (mark Y) (first X Z)))
(rule (a__half |0|) |0|)
(rule (a__half (s |0|)) |0|)
(rule (a__half (s (s X))) (s (a__half (mark X))))
(rule (a__half (dbl X)) (mark X))
(rule (mark (terms X)) (a__terms (mark X)))
(rule (mark (sqr X)) (a__sqr (mark X)))
(rule (mark (add X1 X2)) (a__add (mark X1) (mark X2)))
(rule (mark (dbl X)) (a__dbl (mark X)))
(rule (mark (first X1 X2)) (a__first (mark X1) (mark X2)))
(rule (mark (half X)) (a__half (mark X)))
(rule (mark (cons X1 X2)) (cons (mark X1) X2))
(rule (mark (recip X)) (recip (mark X)))
(rule (mark (s X)) (s (mark X)))
(rule (mark |0|) |0|)
(rule (mark nil) nil)
(rule (a__terms X) (terms X))
(rule (a__sqr X) (sqr X))
(rule (a__add X1 X2) (add X1 X2))
(rule (a__dbl X) (dbl X))
(rule (a__first X1 X2) (first X1 X2))
(rule (a__half X) (half X))