MAYBE MAYBE TRS: { f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)), active(f(X, g(X), Y)) -> mark(f(Y, Y, Y)), active(g(X)) -> g(active(X)), active(g(b())) -> mark(c()), active(b()) -> mark(c()), g(mark(X)) -> mark(g(X)), g(ok(X)) -> ok(g(X)), proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)), proper(g(X)) -> g(proper(X)), proper(c()) -> ok(c()), proper(b()) -> ok(b()), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X)) } DUP: We consider a duplicating system. Trs: { f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)), active(f(X, g(X), Y)) -> mark(f(Y, Y, Y)), active(g(X)) -> g(active(X)), active(g(b())) -> mark(c()), active(b()) -> mark(c()), g(mark(X)) -> mark(g(X)), g(ok(X)) -> ok(g(X)), proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)), proper(g(X)) -> g(proper(X)), proper(c()) -> ok(c()), proper(b()) -> ok(b()), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X)) } Fail