; @origtpdbfilename ./TRS/TRCSR/OvConsOS_nokinds_noand_GM.trs
; @xtcfilename "./TRS_Standard/Transformed_CSR_04/OvConsOS_nokinds_noand_GM.xml"
(format TRS)
(fun a__zeros 0)
(fun cons 2)
(fun |0| 0)
(fun zeros 0)
(fun a__U11 1)
(fun tt 0)
(fun a__U21 1)
(fun a__U31 1)
(fun a__U41 2)
(fun a__U42 1)
(fun a__isNatIList 1)
(fun a__U51 2)
(fun a__U52 1)
(fun a__isNatList 1)
(fun a__U61 2)
(fun a__U62 1)
(fun a__U71 3)
(fun a__U72 2)
(fun a__isNat 1)
(fun s 1)
(fun a__length 1)
(fun mark 1)
(fun a__U81 1)
(fun nil 0)
(fun a__U91 4)
(fun a__U92 4)
(fun a__U93 4)
(fun take 2)
(fun length 1)
(fun a__take 2)
(fun U11 1)
(fun U21 1)
(fun U31 1)
(fun U41 2)
(fun U42 1)
(fun isNatIList 1)
(fun U51 2)
(fun U52 1)
(fun isNatList 1)
(fun U61 2)
(fun U62 1)
(fun U71 3)
(fun U72 2)
(fun isNat 1)
(fun U81 1)
(fun U91 4)
(fun U92 4)
(fun U93 4)
(rule a__zeros (cons |0| zeros))
(rule (a__U11 tt) tt)
(rule (a__U21 tt) tt)
(rule (a__U31 tt) tt)
(rule (a__U41 tt V2) (a__U42 (a__isNatIList V2)))
(rule (a__U42 tt) tt)
(rule (a__U51 tt V2) (a__U52 (a__isNatList V2)))
(rule (a__U52 tt) tt)
(rule (a__U61 tt V2) (a__U62 (a__isNatIList V2)))
(rule (a__U62 tt) tt)
(rule (a__U71 tt L N) (a__U72 (a__isNat N) L))
(rule (a__U72 tt L) (s (a__length (mark L))))
(rule (a__U81 tt) nil)
(rule (a__U91 tt IL M N) (a__U92 (a__isNat M) IL M N))
(rule (a__U92 tt IL M N) (a__U93 (a__isNat N) IL M N))
(rule (a__U93 tt IL M N) (cons (mark N) (take M IL)))
(rule (a__isNat |0|) tt)
(rule (a__isNat (length V1)) (a__U11 (a__isNatList V1)))
(rule (a__isNat (s V1)) (a__U21 (a__isNat V1)))
(rule (a__isNatIList V) (a__U31 (a__isNatList V)))
(rule (a__isNatIList zeros) tt)
(rule (a__isNatIList (cons V1 V2)) (a__U41 (a__isNat V1) V2))
(rule (a__isNatList nil) tt)
(rule (a__isNatList (cons V1 V2)) (a__U51 (a__isNat V1) V2))
(rule (a__isNatList (take V1 V2)) (a__U61 (a__isNat V1) V2))
(rule (a__length nil) |0|)
(rule (a__length (cons N L)) (a__U71 (a__isNatList L) L N))
(rule (a__take |0| IL) (a__U81 (a__isNatIList IL)))
(rule (a__take (s M) (cons N IL)) (a__U91 (a__isNatIList IL) IL M N))
(rule (mark zeros) a__zeros)
(rule (mark (U11 X)) (a__U11 (mark X)))
(rule (mark (U21 X)) (a__U21 (mark X)))
(rule (mark (U31 X)) (a__U31 (mark X)))
(rule (mark (U41 X1 X2)) (a__U41 (mark X1) X2))
(rule (mark (U42 X)) (a__U42 (mark X)))
(rule (mark (isNatIList X)) (a__isNatIList X))
(rule (mark (U51 X1 X2)) (a__U51 (mark X1) X2))
(rule (mark (U52 X)) (a__U52 (mark X)))
(rule (mark (isNatList X)) (a__isNatList X))
(rule (mark (U61 X1 X2)) (a__U61 (mark X1) X2))
(rule (mark (U62 X)) (a__U62 (mark X)))
(rule (mark (U71 X1 X2 X3)) (a__U71 (mark X1) X2 X3))
(rule (mark (U72 X1 X2)) (a__U72 (mark X1) X2))
(rule (mark (isNat X)) (a__isNat X))
(rule (mark (length X)) (a__length (mark X)))
(rule (mark (U81 X)) (a__U81 (mark X)))
(rule (mark (U91 X1 X2 X3 X4)) (a__U91 (mark X1) X2 X3 X4))
(rule (mark (U92 X1 X2 X3 X4)) (a__U92 (mark X1) X2 X3 X4))
(rule (mark (U93 X1 X2 X3 X4)) (a__U93 (mark X1) X2 X3 X4))
(rule (mark (take X1 X2)) (a__take (mark X1) (mark X2)))
(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 X) (U11 X))
(rule (a__U21 X) (U21 X))
(rule (a__U31 X) (U31 X))
(rule (a__U41 X1 X2) (U41 X1 X2))
(rule (a__U42 X) (U42 X))
(rule (a__isNatIList X) (isNatIList X))
(rule (a__U51 X1 X2) (U51 X1 X2))
(rule (a__U52 X) (U52 X))
(rule (a__isNatList X) (isNatList X))
(rule (a__U61 X1 X2) (U61 X1 X2))
(rule (a__U62 X) (U62 X))
(rule (a__U71 X1 X2 X3) (U71 X1 X2 X3))
(rule (a__U72 X1 X2) (U72 X1 X2))
(rule (a__isNat X) (isNat X))
(rule (a__length X) (length X))
(rule (a__U81 X) (U81 X))
(rule (a__U91 X1 X2 X3 X4) (U91 X1 X2 X3 X4))
(rule (a__U92 X1 X2 X3 X4) (U92 X1 X2 X3 X4))
(rule (a__U93 X1 X2 X3 X4) (U93 X1 X2 X3 X4))
(rule (a__take X1 X2) (take X1 X2))