MAYBE

Problem:
 active(eq(0(),0())) -> mark(true())
 active(eq(s(X),s(Y))) -> mark(eq(X,Y))
 active(eq(X,Y)) -> mark(false())
 active(inf(X)) -> mark(cons(X,inf(s(X))))
 active(take(0(),X)) -> mark(nil())
 active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L)))
 active(length(nil())) -> mark(0())
 active(length(cons(X,L))) -> mark(s(length(L)))
 mark(eq(X1,X2)) -> active(eq(X1,X2))
 mark(0()) -> active(0())
 mark(true()) -> active(true())
 mark(s(X)) -> active(s(X))
 mark(false()) -> active(false())
 mark(inf(X)) -> active(inf(mark(X)))
 mark(cons(X1,X2)) -> active(cons(X1,X2))
 mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
 mark(nil()) -> active(nil())
 mark(length(X)) -> active(length(mark(X)))
 eq(mark(X1),X2) -> eq(X1,X2)
 eq(X1,mark(X2)) -> eq(X1,X2)
 eq(active(X1),X2) -> eq(X1,X2)
 eq(X1,active(X2)) -> eq(X1,X2)
 s(mark(X)) -> s(X)
 s(active(X)) -> s(X)
 inf(mark(X)) -> inf(X)
 inf(active(X)) -> inf(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)
 take(mark(X1),X2) -> take(X1,X2)
 take(X1,mark(X2)) -> take(X1,X2)
 take(active(X1),X2) -> take(X1,X2)
 take(X1,active(X2)) -> take(X1,X2)
 length(mark(X)) -> length(X)
 length(active(X)) -> length(X)

Proof:
 Open