/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/ExIntrod_GM04_C.trs

The program

(VAR X Y X1 X2)
(RULES 
active(nats) -> mark(adx(zeros))
active(zeros) -> mark(cons(0,zeros))
active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
active(hd(cons(X,Y))) -> mark(X)
active(tl(cons(X,Y))) -> mark(Y)
active(adx(X)) -> adx(active(X))
active(incr(X)) -> incr(active(X))
active(hd(X)) -> hd(active(X))
active(tl(X)) -> tl(active(X))
adx(mark(X)) -> mark(adx(X))
incr(mark(X)) -> mark(incr(X))
hd(mark(X)) -> mark(hd(X))
tl(mark(X)) -> mark(tl(X))
proper(nats) -> ok(nats)
proper(adx(X)) -> adx(proper(X))
proper(zeros) -> ok(zeros)
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(0) -> ok(0)
proper(incr(X)) -> incr(proper(X))
proper(s(X)) -> s(proper(X))
proper(hd(X)) -> hd(proper(X))
proper(tl(X)) -> tl(proper(X))
adx(ok(X)) -> ok(adx(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
incr(ok(X)) -> ok(incr(X))
s(ok(X)) -> ok(s(X))
hd(ok(X)) -> ok(hd(X))
tl(ok(X)) -> ok(tl(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)

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