/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/Ex5_7_Luc97_GM.trs

The program

(VAR X Y Z X1 X2)
(RULES 
a__dbl(0) -> 0
a__dbl(s(X)) -> s(s(dbl(X)))
a__dbls(nil) -> nil
a__dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
a__sel(0,cons(X,Y)) -> mark(X)
a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
a__indx(nil,X) -> nil
a__indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
a__from(X) -> cons(X,from(s(X)))
a__dbl1(0) -> 01
a__dbl1(s(X)) -> s1(s1(a__dbl1(mark(X))))
a__sel1(0,cons(X,Y)) -> mark(X)
a__sel1(s(X),cons(Y,Z)) -> a__sel1(mark(X),mark(Z))
a__quote(0) -> 01
a__quote(s(X)) -> s1(a__quote(mark(X)))
a__quote(dbl(X)) -> a__dbl1(mark(X))
a__quote(sel(X,Y)) -> a__sel1(mark(X),mark(Y))
mark(dbl(X)) -> a__dbl(mark(X))
mark(dbls(X)) -> a__dbls(mark(X))
mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
mark(indx(X1,X2)) -> a__indx(mark(X1),X2)
mark(from(X)) -> a__from(X)
mark(dbl1(X)) -> a__dbl1(mark(X))
mark(sel1(X1,X2)) -> a__sel1(mark(X1),mark(X2))
mark(quote(X)) -> a__quote(mark(X))
mark(0) -> 0
mark(s(X)) -> s(X)
mark(nil) -> nil
mark(cons(X1,X2)) -> cons(X1,X2)
mark(01) -> 01
mark(s1(X)) -> s1(mark(X))
a__dbl(X) -> dbl(X)
a__dbls(X) -> dbls(X)
a__sel(X1,X2) -> sel(X1,X2)
a__indx(X1,X2) -> indx(X1,X2)
a__from(X) -> from(X)
a__dbl1(X) -> dbl1(X)
a__sel1(X1,X2) -> sel1(X1,X2)
a__quote(X) -> quote(X)
)

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