; @origtpdbfilename ./TRS/Thiemann/identity.trs
; @xtcfilename "./TRS_Standard/AProVE_06/identity.xml"
(format TRS)
(fun g 2)
(fun |0| 0)
(fun d 0)
(fun s 1)
(fun h 0)
(fun double 1)
(fun half 1)
(fun f 2)
(fun id 1)
(rule (g x |0|) |0|)
(rule (g d (s x)) (s (s (g d x))))
(rule (g h (s |0|)) |0|)
(rule (g h (s (s x))) (s (g h x)))
(rule (double x) (g d x))
(rule (half x) (g h x))
(rule (f (s x) y) (f (half (s x)) (double y)))
(rule (f (s |0|) y) y)
(rule (id x) (f x (s |0|)))