MAYBE MAYBE TRS: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2)), active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2), active(2ndspos(s(N), cons(X, cons(Y, Z)))) -> mark(rcons(posrecip(Y), 2ndsneg(N, Z))), active(2ndspos(0(), Z)) -> mark(rnil()), active(rcons(X1, X2)) -> rcons(X1, active(X2)), active(rcons(X1, X2)) -> rcons(active(X1), X2), active(posrecip(X)) -> posrecip(active(X)), active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2)), active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2), active(2ndsneg(s(N), cons(X, cons(Y, Z)))) -> mark(rcons(negrecip(Y), 2ndspos(N, Z))), active(2ndsneg(0(), Z)) -> mark(rnil()), active(negrecip(X)) -> negrecip(active(X)), active(pi(X)) -> mark(2ndspos(X, from(0()))), active(pi(X)) -> pi(active(X)), active(plus(X1, X2)) -> plus(X1, active(X2)), active(plus(X1, X2)) -> plus(active(X1), X2), active(plus(s(X), Y)) -> mark(s(plus(X, Y))), active(plus(0(), Y)) -> mark(Y), active(times(X1, X2)) -> times(X1, active(X2)), active(times(X1, X2)) -> times(active(X1), X2), active(times(s(X), Y)) -> mark(plus(Y, times(X, Y))), active(times(0(), Y)) -> mark(0()), active(square(X)) -> mark(times(X, X)), active(square(X)) -> square(active(X)), 2ndspos(X1, mark(X2)) -> mark(2ndspos(X1, X2)), 2ndspos(mark(X1), X2) -> mark(2ndspos(X1, X2)), 2ndspos(ok(X1), ok(X2)) -> ok(2ndspos(X1, X2)), rcons(X1, mark(X2)) -> mark(rcons(X1, X2)), rcons(mark(X1), X2) -> mark(rcons(X1, X2)), rcons(ok(X1), ok(X2)) -> ok(rcons(X1, X2)), posrecip(mark(X)) -> mark(posrecip(X)), posrecip(ok(X)) -> ok(posrecip(X)), 2ndsneg(X1, mark(X2)) -> mark(2ndsneg(X1, X2)), 2ndsneg(mark(X1), X2) -> mark(2ndsneg(X1, X2)), 2ndsneg(ok(X1), ok(X2)) -> ok(2ndsneg(X1, X2)), negrecip(mark(X)) -> mark(negrecip(X)), negrecip(ok(X)) -> ok(negrecip(X)), pi(mark(X)) -> mark(pi(X)), pi(ok(X)) -> ok(pi(X)), plus(X1, mark(X2)) -> mark(plus(X1, X2)), plus(mark(X1), X2) -> mark(plus(X1, X2)), plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)), times(X1, mark(X2)) -> mark(times(X1, X2)), times(mark(X1), X2) -> mark(times(X1, X2)), times(ok(X1), ok(X2)) -> ok(times(X1, X2)), square(mark(X)) -> mark(square(X)), square(ok(X)) -> ok(square(X)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(rnil()) -> ok(rnil()), proper(2ndspos(X1, X2)) -> 2ndspos(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(rcons(X1, X2)) -> rcons(proper(X1), proper(X2)), proper(posrecip(X)) -> posrecip(proper(X)), proper(2ndsneg(X1, X2)) -> 2ndsneg(proper(X1), proper(X2)), proper(negrecip(X)) -> negrecip(proper(X)), proper(pi(X)) -> pi(proper(X)), proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)), proper(times(X1, X2)) -> times(proper(X1), proper(X2)), proper(square(X)) -> square(proper(X)), proper(nil()) -> ok(nil()), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X)) } DUP: We consider a duplicating system. Trs: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2)), active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2), active(2ndspos(s(N), cons(X, cons(Y, Z)))) -> mark(rcons(posrecip(Y), 2ndsneg(N, Z))), active(2ndspos(0(), Z)) -> mark(rnil()), active(rcons(X1, X2)) -> rcons(X1, active(X2)), active(rcons(X1, X2)) -> rcons(active(X1), X2), active(posrecip(X)) -> posrecip(active(X)), active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2)), active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2), active(2ndsneg(s(N), cons(X, cons(Y, Z)))) -> mark(rcons(negrecip(Y), 2ndspos(N, Z))), active(2ndsneg(0(), Z)) -> mark(rnil()), active(negrecip(X)) -> negrecip(active(X)), active(pi(X)) -> mark(2ndspos(X, from(0()))), active(pi(X)) -> pi(active(X)), active(plus(X1, X2)) -> plus(X1, active(X2)), active(plus(X1, X2)) -> plus(active(X1), X2), active(plus(s(X), Y)) -> mark(s(plus(X, Y))), active(plus(0(), Y)) -> mark(Y), active(times(X1, X2)) -> times(X1, active(X2)), active(times(X1, X2)) -> times(active(X1), X2), active(times(s(X), Y)) -> mark(plus(Y, times(X, Y))), active(times(0(), Y)) -> mark(0()), active(square(X)) -> mark(times(X, X)), active(square(X)) -> square(active(X)), 2ndspos(X1, mark(X2)) -> mark(2ndspos(X1, X2)), 2ndspos(mark(X1), X2) -> mark(2ndspos(X1, X2)), 2ndspos(ok(X1), ok(X2)) -> ok(2ndspos(X1, X2)), rcons(X1, mark(X2)) -> mark(rcons(X1, X2)), rcons(mark(X1), X2) -> mark(rcons(X1, X2)), rcons(ok(X1), ok(X2)) -> ok(rcons(X1, X2)), posrecip(mark(X)) -> mark(posrecip(X)), posrecip(ok(X)) -> ok(posrecip(X)), 2ndsneg(X1, mark(X2)) -> mark(2ndsneg(X1, X2)), 2ndsneg(mark(X1), X2) -> mark(2ndsneg(X1, X2)), 2ndsneg(ok(X1), ok(X2)) -> ok(2ndsneg(X1, X2)), negrecip(mark(X)) -> mark(negrecip(X)), negrecip(ok(X)) -> ok(negrecip(X)), pi(mark(X)) -> mark(pi(X)), pi(ok(X)) -> ok(pi(X)), plus(X1, mark(X2)) -> mark(plus(X1, X2)), plus(mark(X1), X2) -> mark(plus(X1, X2)), plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)), times(X1, mark(X2)) -> mark(times(X1, X2)), times(mark(X1), X2) -> mark(times(X1, X2)), times(ok(X1), ok(X2)) -> ok(times(X1, X2)), square(mark(X)) -> mark(square(X)), square(ok(X)) -> ok(square(X)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(rnil()) -> ok(rnil()), proper(2ndspos(X1, X2)) -> 2ndspos(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(rcons(X1, X2)) -> rcons(proper(X1), proper(X2)), proper(posrecip(X)) -> posrecip(proper(X)), proper(2ndsneg(X1, X2)) -> 2ndsneg(proper(X1), proper(X2)), proper(negrecip(X)) -> negrecip(proper(X)), proper(pi(X)) -> pi(proper(X)), proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)), proper(times(X1, X2)) -> times(proper(X1), proper(X2)), proper(square(X)) -> square(proper(X)), proper(nil()) -> ok(nil()), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X)) } Fail