; @origtpdbfilename ./TRS/TRCSR/Ex4_DLMMU04_GM.trs
; @xtcfilename "./TRS_Standard/Transformed_CSR_04/Ex4_DLMMU04_GM.xml"
(format TRS)
(fun a__and 2)
(fun tt 0)
(fun mark 1)
(fun a__isNatIList 1)
(fun a__isNatList 1)
(fun a__isNat 1)
(fun |0| 0)
(fun s 1)
(fun length 1)
(fun zeros 0)
(fun cons 2)
(fun nil 0)
(fun take 2)
(fun a__zeros 0)
(fun a__take 2)
(fun a__uTake1 1)
(fun a__uTake2 4)
(fun a__length 1)
(fun a__uLength 2)
(fun and 2)
(fun isNatIList 1)
(fun isNatList 1)
(fun isNat 1)
(fun uTake1 1)
(fun uTake2 4)
(fun uLength 2)
(rule (a__and tt T) (mark T))
(rule (a__isNatIList IL) (a__isNatList IL))
(rule (a__isNat |0|) tt)
(rule (a__isNat (s N)) (a__isNat N))
(rule (a__isNat (length L)) (a__isNatList L))
(rule (a__isNatIList zeros) tt)
(rule (a__isNatIList (cons N IL)) (a__and (a__isNat N) (a__isNatIList IL)))
(rule (a__isNatList nil) tt)
(rule (a__isNatList (cons N L)) (a__and (a__isNat N) (a__isNatList L)))
(rule (a__isNatList (take N IL)) (a__and (a__isNat N) (a__isNatIList IL)))
(rule a__zeros (cons |0| zeros))
(rule (a__take |0| IL) (a__uTake1 (a__isNatIList IL)))
(rule (a__uTake1 tt) nil)
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(rule (a__uTake2 tt M N IL) (cons (mark N) (take M IL)))
(rule (a__length (cons N L)) (a__uLength (a__and (a__isNat N) (a__isNatList L)) L))
(rule (a__uLength tt L) (s (a__length (mark L))))
(rule (mark (and X1 X2)) (a__and (mark X1) (mark X2)))
(rule (mark (isNatIList X)) (a__isNatIList X))
(rule (mark (isNatList X)) (a__isNatList X))
(rule (mark (isNat X)) (a__isNat X))
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(rule (mark zeros) a__zeros)
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(rule (mark (uTake1 X)) (a__uTake1 (mark X)))
(rule (mark (uTake2 X1 X2 X3 X4)) (a__uTake2 (mark X1) X2 X3 X4))
(rule (mark (uLength X1 X2)) (a__uLength (mark X1) X2))
(rule (mark tt) tt)
(rule (mark |0|) |0|)
(rule (mark (s X)) (s (mark X)))
(rule (mark (cons X1 X2)) (cons (mark X1) X2))
(rule (mark nil) nil)
(rule (a__and X1 X2) (and X1 X2))
(rule (a__isNatIList X) (isNatIList X))
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(rule (a__length X) (length X))
(rule a__zeros zeros)
(rule (a__take X1 X2) (take X1 X2))
(rule (a__uTake1 X) (uTake1 X))
(rule (a__uTake2 X1 X2 X3 X4) (uTake2 X1 X2 X3 X4))
(rule (a__uLength X1 X2) (uLength X1 X2))