; @origtpdbfilename ./TRS/TRCSR/LengthOfFiniteLists_nokinds_C.trs
; @xtcfilename "./TRS_Standard/Transformed_CSR_04/LengthOfFiniteLists_nokinds_C.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)
(fun proper 1)
(fun ok 1)
(fun top 1)
(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 (active (cons X1 X2)) (cons (active X1) X2))
(rule (active (U11 X1 X2)) (U11 (active X1) X2))
(rule (active (s X)) (s (active X)))
(rule (active (length X)) (length (active X)))
(rule (active (and X1 X2)) (and (active X1) X2))
(rule (cons (mark X1) X2) (mark (cons X1 X2)))
(rule (U11 (mark X1) X2) (mark (U11 X1 X2)))
(rule (s (mark X)) (mark (s X)))
(rule (length (mark X)) (mark (length X)))
(rule (and (mark X1) X2) (mark (and X1 X2)))
(rule (proper zeros) (ok zeros))
(rule (proper (cons X1 X2)) (cons (proper X1) (proper X2)))
(rule (proper |0|) (ok |0|))
(rule (proper (U11 X1 X2)) (U11 (proper X1) (proper X2)))
(rule (proper tt) (ok tt))
(rule (proper (s X)) (s (proper X)))
(rule (proper (length X)) (length (proper X)))
(rule (proper (and X1 X2)) (and (proper X1) (proper X2)))
(rule (proper (isNat X)) (isNat (proper X)))
(rule (proper (isNatList X)) (isNatList (proper X)))
(rule (proper (isNatIList X)) (isNatIList (proper X)))
(rule (proper nil) (ok nil))
(rule (cons (ok X1) (ok X2)) (ok (cons X1 X2)))
(rule (U11 (ok X1) (ok X2)) (ok (U11 X1 X2)))
(rule (s (ok X)) (ok (s X)))
(rule (length (ok X)) (ok (length X)))
(rule (and (ok X1) (ok X2)) (ok (and X1 X2)))
(rule (isNat (ok X)) (ok (isNat X)))
(rule (isNatList (ok X)) (ok (isNatList X)))
(rule (isNatIList (ok X)) (ok (isNatIList X)))
(rule (top (mark X)) (top (proper X)))
(rule (top (ok X)) (top (active X)))