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