; @origtpdbfilename ./TRS/TRCSR/LengthOfFiniteLists_nokinds_GM.trs
; @xtcfilename "./TRS_Standard/Transformed_CSR_04/LengthOfFiniteLists_nokinds_GM.xml"
(format TRS)
(fun a__zeros 0)
(fun cons 2)
(fun |0| 0)
(fun zeros 0)
(fun a__U11 2)
(fun tt 0)
(fun s 1)
(fun a__length 1)
(fun mark 1)
(fun a__and 2)
(fun a__isNat 1)
(fun length 1)
(fun a__isNatList 1)
(fun a__isNatIList 1)
(fun isNatIList 1)
(fun nil 0)
(fun isNatList 1)
(fun isNat 1)
(fun U11 2)
(fun and 2)
(rule a__zeros (cons |0| zeros))
(rule (a__U11 tt L) (s (a__length (mark L))))
(rule (a__and tt X) (mark X))
(rule (a__isNat |0|) tt)
(rule (a__isNat (length V1)) (a__isNatList V1))
(rule (a__isNat (s V1)) (a__isNat V1))
(rule (a__isNatIList V) (a__isNatList V))
(rule (a__isNatIList zeros) tt)
(rule (a__isNatIList (cons V1 V2)) (a__and (a__isNat V1) (isNatIList V2)))
(rule (a__isNatList nil) tt)
(rule (a__isNatList (cons V1 V2)) (a__and (a__isNat V1) (isNatList V2)))
(rule (a__length nil) |0|)
(rule (a__length (cons N L)) (a__U11 (a__and (a__isNatList L) (isNat N)) L))
(rule (mark zeros) a__zeros)
(rule (mark (U11 X1 X2)) (a__U11 (mark X1) X2))
(rule (mark (length X)) (a__length (mark X)))
(rule (mark (and X1 X2)) (a__and (mark X1) X2))
(rule (mark (isNat X)) (a__isNat X))
(rule (mark (isNatList X)) (a__isNatList X))
(rule (mark (isNatIList X)) (a__isNatIList X))
(rule (mark (cons X1 X2)) (cons (mark X1) X2))
(rule (mark |0|) |0|)
(rule (mark tt) tt)
(rule (mark (s X)) (s (mark X)))
(rule (mark nil) nil)
(rule a__zeros zeros)
(rule (a__U11 X1 X2) (U11 X1 X2))
(rule (a__length X) (length X))
(rule (a__and X1 X2) (and X1 X2))
(rule (a__isNat X) (isNat X))
(rule (a__isNatList X) (isNatList X))
(rule (a__isNatIList X) (isNatIList X))