MAYBE

Problem:
 active(incr(nil())) -> mark(nil())
 active(incr(cons(X,L))) -> mark(cons(s(X),incr(L)))
 active(adx(nil())) -> mark(nil())
 active(adx(cons(X,L))) -> mark(incr(cons(X,adx(L))))
 active(nats()) -> mark(adx(zeros()))
 active(zeros()) -> mark(cons(0(),zeros()))
 active(head(cons(X,L))) -> mark(X)
 active(tail(cons(X,L))) -> mark(L)
 mark(incr(X)) -> active(incr(mark(X)))
 mark(nil()) -> active(nil())
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(s(X)) -> active(s(mark(X)))
 mark(adx(X)) -> active(adx(mark(X)))
 mark(nats()) -> active(nats())
 mark(zeros()) -> active(zeros())
 mark(0()) -> active(0())
 mark(head(X)) -> active(head(mark(X)))
 mark(tail(X)) -> active(tail(mark(X)))
 incr(mark(X)) -> incr(X)
 incr(active(X)) -> incr(X)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons(active(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 s(mark(X)) -> s(X)
 s(active(X)) -> s(X)
 adx(mark(X)) -> adx(X)
 adx(active(X)) -> adx(X)
 head(mark(X)) -> head(X)
 head(active(X)) -> head(X)
 tail(mark(X)) -> tail(X)
 tail(active(X)) -> tail(X)

Proof:
 Open