YES TRS: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} DP: Strict: { active#(fst(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2), active#(fst(X1, X2)) -> fst#(X1, active(X2)), active#(fst(X1, X2)) -> fst#(active(X1), X2), active#(fst(s(X), cons(Y, Z))) -> fst#(X, Z), active#(fst(s(X), cons(Y, Z))) -> cons#(Y, fst(X, Z)), active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> cons#(active(X1), X2), active#(from(X)) -> active#(X), active#(from(X)) -> cons#(X, from(s(X))), active#(from(X)) -> s#(X), active#(from(X)) -> from#(active(X)), active#(from(X)) -> from#(s(X)), active#(add(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> active#(X2), active#(add(X1, X2)) -> add#(X1, active(X2)), active#(add(X1, X2)) -> add#(active(X1), X2), active#(add(s(X), Y)) -> s#(add(X, Y)), active#(add(s(X), Y)) -> add#(X, Y), active#(len(X)) -> active#(X), active#(len(X)) -> len#(active(X)), active#(len(cons(X, Z))) -> s#(len(Z)), active#(len(cons(X, Z))) -> len#(Z), fst#(X1, mark(X2)) -> fst#(X1, X2), fst#(mark(X1), X2) -> fst#(X1, X2), fst#(ok(X1), ok(X2)) -> fst#(X1, X2), cons#(mark(X1), X2) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2), s#(ok(X)) -> s#(X), from#(mark(X)) -> from#(X), from#(ok(X)) -> from#(X), add#(X1, mark(X2)) -> add#(X1, X2), add#(mark(X1), X2) -> add#(X1, X2), add#(ok(X1), ok(X2)) -> add#(X1, X2), len#(mark(X)) -> len#(X), len#(ok(X)) -> len#(X), proper#(fst(X1, X2)) -> fst#(proper(X1), proper(X2)), proper#(fst(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2)), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> s#(proper(X)), proper#(s(X)) -> proper#(X), proper#(from(X)) -> from#(proper(X)), proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> add#(proper(X1), proper(X2)), proper#(add(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2), proper#(len(X)) -> len#(proper(X)), proper#(len(X)) -> proper#(X), top#(mark(X)) -> proper#(X), top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> active#(X), top#(ok(X)) -> top#(active(X))} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} EDG: { (fst#(X1, mark(X2)) -> fst#(X1, X2), fst#(ok(X1), ok(X2)) -> fst#(X1, X2)) (fst#(X1, mark(X2)) -> fst#(X1, X2), fst#(mark(X1), X2) -> fst#(X1, X2)) (fst#(X1, mark(X2)) -> fst#(X1, X2), fst#(X1, mark(X2)) -> fst#(X1, X2)) (fst#(ok(X1), ok(X2)) -> fst#(X1, X2), fst#(ok(X1), ok(X2)) -> fst#(X1, X2)) (fst#(ok(X1), ok(X2)) -> fst#(X1, X2), fst#(mark(X1), X2) -> fst#(X1, X2)) (fst#(ok(X1), ok(X2)) -> fst#(X1, X2), fst#(X1, mark(X2)) -> fst#(X1, X2)) (cons#(ok(X1), ok(X2)) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)) (cons#(ok(X1), ok(X2)) -> cons#(X1, X2), cons#(mark(X1), X2) -> cons#(X1, X2)) (add#(mark(X1), X2) -> add#(X1, X2), add#(ok(X1), ok(X2)) -> add#(X1, X2)) (add#(mark(X1), X2) -> add#(X1, X2), add#(mark(X1), X2) -> add#(X1, X2)) (add#(mark(X1), X2) -> add#(X1, X2), add#(X1, mark(X2)) -> add#(X1, X2)) (active#(fst(s(X), cons(Y, Z))) -> fst#(X, Z), fst#(ok(X1), ok(X2)) -> fst#(X1, X2)) (active#(fst(s(X), cons(Y, Z))) -> fst#(X, Z), fst#(mark(X1), X2) -> fst#(X1, X2)) (active#(fst(s(X), cons(Y, Z))) -> fst#(X, Z), fst#(X1, mark(X2)) -> fst#(X1, X2)) (active#(add(X1, X2)) -> add#(X1, active(X2)), add#(ok(X1), ok(X2)) -> add#(X1, X2)) (active#(add(X1, X2)) -> add#(X1, active(X2)), add#(mark(X1), X2) -> add#(X1, X2)) (active#(add(X1, X2)) -> add#(X1, active(X2)), add#(X1, mark(X2)) -> add#(X1, X2)) (proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2)), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)) (proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2)), cons#(mark(X1), X2) -> cons#(X1, X2)) (active#(from(X)) -> cons#(X, from(s(X))), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)) (active#(from(X)) -> cons#(X, from(s(X))), cons#(mark(X1), X2) -> cons#(X1, X2)) (active#(fst(s(X), cons(Y, Z))) -> cons#(Y, fst(X, Z)), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)) (active#(fst(s(X), cons(Y, Z))) -> cons#(Y, fst(X, Z)), cons#(mark(X1), X2) -> cons#(X1, X2)) (active#(from(X)) -> s#(X), s#(ok(X)) -> s#(X)) (s#(ok(X)) -> s#(X), s#(ok(X)) -> s#(X)) (from#(ok(X)) -> from#(X), from#(ok(X)) -> from#(X)) (from#(ok(X)) -> from#(X), from#(mark(X)) -> from#(X)) (len#(ok(X)) -> len#(X), len#(ok(X)) -> len#(X)) (len#(ok(X)) -> len#(X), len#(mark(X)) -> len#(X)) (proper#(from(X)) -> proper#(X), proper#(len(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(len(X)) -> len#(proper(X))) (proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> add#(proper(X1), proper(X2))) (proper#(from(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(from(X)) -> from#(proper(X))) (proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(s(X)) -> s#(proper(X))) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2))) (proper#(from(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(fst(X1, X2)) -> fst#(proper(X1), proper(X2))) (top#(mark(X)) -> proper#(X), proper#(len(X)) -> proper#(X)) (top#(mark(X)) -> proper#(X), proper#(len(X)) -> len#(proper(X))) (top#(mark(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)) (top#(mark(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X1)) (top#(mark(X)) -> proper#(X), proper#(add(X1, X2)) -> add#(proper(X1), proper(X2))) (top#(mark(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (top#(mark(X)) -> proper#(X), proper#(from(X)) -> from#(proper(X))) (top#(mark(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (top#(mark(X)) -> proper#(X), proper#(s(X)) -> s#(proper(X))) (top#(mark(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (top#(mark(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (top#(mark(X)) -> proper#(X), proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2))) (top#(mark(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X2)) (top#(mark(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X1)) (top#(mark(X)) -> proper#(X), proper#(fst(X1, X2)) -> fst#(proper(X1), proper(X2))) (active#(fst(X1, X2)) -> active#(X1), active#(len(cons(X, Z))) -> len#(Z)) (active#(fst(X1, X2)) -> active#(X1), active#(len(cons(X, Z))) -> s#(len(Z))) (active#(fst(X1, X2)) -> active#(X1), active#(len(X)) -> len#(active(X))) (active#(fst(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)) (active#(fst(X1, X2)) -> active#(X1), active#(add(s(X), Y)) -> add#(X, Y)) (active#(fst(X1, X2)) -> active#(X1), active#(add(s(X), Y)) -> s#(add(X, Y))) (active#(fst(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> add#(active(X1), X2)) (active#(fst(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> add#(X1, active(X2))) (active#(fst(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> active#(X2)) (active#(fst(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> active#(X1)) (active#(fst(X1, X2)) -> active#(X1), active#(from(X)) -> from#(s(X))) (active#(fst(X1, X2)) -> active#(X1), active#(from(X)) -> from#(active(X))) (active#(fst(X1, X2)) -> active#(X1), active#(from(X)) -> s#(X)) (active#(fst(X1, X2)) -> active#(X1), active#(from(X)) -> cons#(X, from(s(X)))) (active#(fst(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(fst(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (active#(fst(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(fst(X1, X2)) -> active#(X1), active#(fst(s(X), cons(Y, Z))) -> cons#(Y, fst(X, Z))) (active#(fst(X1, X2)) -> active#(X1), active#(fst(s(X), cons(Y, Z))) -> fst#(X, Z)) (active#(fst(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> fst#(active(X1), X2)) (active#(fst(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> fst#(X1, active(X2))) (active#(fst(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2)) (active#(fst(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X1)) (active#(add(X1, X2)) -> active#(X1), active#(len(cons(X, Z))) -> len#(Z)) (active#(add(X1, X2)) -> active#(X1), active#(len(cons(X, Z))) -> s#(len(Z))) (active#(add(X1, X2)) -> active#(X1), active#(len(X)) -> len#(active(X))) (active#(add(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)) (active#(add(X1, X2)) -> active#(X1), active#(add(s(X), Y)) -> add#(X, Y)) (active#(add(X1, X2)) -> active#(X1), active#(add(s(X), Y)) -> s#(add(X, Y))) (active#(add(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> add#(active(X1), X2)) (active#(add(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> add#(X1, active(X2))) (active#(add(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> active#(X2)) (active#(add(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> active#(X1)) (active#(add(X1, X2)) -> active#(X1), active#(from(X)) -> from#(s(X))) (active#(add(X1, X2)) -> active#(X1), active#(from(X)) -> from#(active(X))) (active#(add(X1, X2)) -> active#(X1), active#(from(X)) -> s#(X)) (active#(add(X1, X2)) -> active#(X1), active#(from(X)) -> cons#(X, from(s(X)))) (active#(add(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(add(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (active#(add(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(add(X1, X2)) -> active#(X1), active#(fst(s(X), cons(Y, Z))) -> cons#(Y, fst(X, Z))) (active#(add(X1, X2)) -> active#(X1), active#(fst(s(X), cons(Y, Z))) -> fst#(X, Z)) (active#(add(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> fst#(active(X1), X2)) (active#(add(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> fst#(X1, active(X2))) (active#(add(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2)) (active#(add(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(len(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(len(X)) -> len#(proper(X))) (proper#(cons(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> add#(proper(X1), proper(X2))) (proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> from#(proper(X))) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> s#(proper(X))) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2))) (proper#(cons(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> fst#(proper(X1), 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(proper#(len(X)) -> proper#(X), proper#(len(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(fst(X1, X2)) -> fst#(proper(X1), proper(X2))) (proper#(s(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2))) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> s#(proper(X))) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(from(X)) -> from#(proper(X))) (proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(add(X1, X2)) -> add#(proper(X1), proper(X2))) (proper#(s(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(len(X)) -> len#(proper(X))) (proper#(s(X)) -> proper#(X), proper#(len(X)) -> proper#(X)) (len#(mark(X)) -> len#(X), len#(mark(X)) -> len#(X)) (len#(mark(X)) -> len#(X), len#(ok(X)) -> len#(X)) (from#(mark(X)) -> from#(X), from#(mark(X)) -> from#(X)) (from#(mark(X)) -> from#(X), from#(ok(X)) -> from#(X)) (active#(len(X)) -> active#(X), active#(fst(X1, X2)) -> active#(X1)) (active#(len(X)) -> active#(X), active#(fst(X1, X2)) -> active#(X2)) (active#(len(X)) -> active#(X), active#(fst(X1, X2)) -> fst#(X1, active(X2))) (active#(len(X)) -> active#(X), active#(fst(X1, X2)) -> fst#(active(X1), X2)) (active#(len(X)) -> active#(X), active#(fst(s(X), cons(Y, Z))) -> fst#(X, Z)) (active#(len(X)) -> active#(X), active#(fst(s(X), cons(Y, Z))) -> cons#(Y, fst(X, Z))) (active#(len(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(len(X)) -> active#(X), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (active#(len(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(len(X)) -> active#(X), active#(from(X)) -> cons#(X, from(s(X)))) (active#(len(X)) -> active#(X), active#(from(X)) -> s#(X)) (active#(len(X)) -> active#(X), active#(from(X)) -> from#(active(X))) (active#(len(X)) -> active#(X), active#(from(X)) -> from#(s(X))) (active#(len(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1)) (active#(len(X)) -> active#(X), active#(add(X1, X2)) -> active#(X2)) (active#(len(X)) -> active#(X), active#(add(X1, X2)) -> add#(X1, active(X2))) (active#(len(X)) -> active#(X), active#(add(X1, X2)) -> add#(active(X1), X2)) (active#(len(X)) -> active#(X), active#(add(s(X), Y)) -> s#(add(X, Y))) (active#(len(X)) -> active#(X), active#(add(s(X), Y)) -> add#(X, Y)) (active#(len(X)) -> active#(X), active#(len(X)) -> active#(X)) (active#(len(X)) -> active#(X), active#(len(X)) -> len#(active(X))) (active#(len(X)) -> active#(X), active#(len(cons(X, Z))) -> s#(len(Z))) (active#(len(X)) -> active#(X), active#(len(cons(X, Z))) -> len#(Z)) (active#(from(X)) -> active#(X), active#(fst(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(fst(X1, X2)) -> active#(X2)) (active#(from(X)) -> active#(X), active#(fst(X1, X2)) -> fst#(X1, active(X2))) (active#(from(X)) -> active#(X), active#(fst(X1, X2)) -> fst#(active(X1), X2)) (active#(from(X)) -> active#(X), active#(fst(s(X), cons(Y, Z))) -> fst#(X, Z)) (active#(from(X)) -> active#(X), active#(fst(s(X), cons(Y, Z))) -> cons#(Y, fst(X, Z))) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(from(X)) -> cons#(X, from(s(X)))) (active#(from(X)) -> active#(X), active#(from(X)) -> s#(X)) (active#(from(X)) -> active#(X), active#(from(X)) -> from#(active(X))) (active#(from(X)) -> active#(X), active#(from(X)) -> from#(s(X))) (active#(from(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(add(X1, X2)) -> active#(X2)) (active#(from(X)) -> active#(X), active#(add(X1, X2)) -> add#(X1, active(X2))) (active#(from(X)) -> active#(X), active#(add(X1, X2)) -> add#(active(X1), X2)) (active#(from(X)) -> active#(X), active#(add(s(X), Y)) -> s#(add(X, Y))) (active#(from(X)) -> active#(X), active#(add(s(X), Y)) -> add#(X, Y)) (active#(from(X)) -> active#(X), active#(len(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(len(X)) -> len#(active(X))) (active#(from(X)) -> active#(X), active#(len(cons(X, Z))) -> s#(len(Z))) (active#(from(X)) -> active#(X), active#(len(cons(X, Z))) -> len#(Z)) (active#(len(cons(X, Z))) -> len#(Z), len#(mark(X)) -> len#(X)) (active#(len(cons(X, Z))) -> len#(Z), len#(ok(X)) -> len#(X)) (proper#(add(X1, X2)) -> add#(proper(X1), proper(X2)), add#(X1, mark(X2)) -> add#(X1, X2)) (proper#(add(X1, X2)) -> add#(proper(X1), proper(X2)), add#(mark(X1), X2) -> add#(X1, X2)) (proper#(add(X1, X2)) -> add#(proper(X1), proper(X2)), add#(ok(X1), ok(X2)) -> add#(X1, X2)) (proper#(fst(X1, X2)) -> fst#(proper(X1), proper(X2)), fst#(X1, mark(X2)) -> fst#(X1, X2)) (proper#(fst(X1, X2)) -> fst#(proper(X1), proper(X2)), fst#(mark(X1), X2) -> fst#(X1, X2)) (proper#(fst(X1, X2)) -> fst#(proper(X1), proper(X2)), fst#(ok(X1), ok(X2)) -> fst#(X1, X2)) (active#(fst(X1, X2)) -> fst#(X1, active(X2)), fst#(X1, mark(X2)) -> fst#(X1, X2)) (active#(fst(X1, X2)) -> fst#(X1, active(X2)), fst#(mark(X1), X2) -> fst#(X1, X2)) (active#(fst(X1, X2)) -> fst#(X1, active(X2)), fst#(ok(X1), ok(X2)) -> fst#(X1, X2)) (add#(ok(X1), ok(X2)) -> add#(X1, X2), add#(X1, mark(X2)) -> add#(X1, X2)) (add#(ok(X1), ok(X2)) -> add#(X1, X2), add#(mark(X1), X2) -> add#(X1, X2)) (add#(ok(X1), ok(X2)) -> add#(X1, X2), add#(ok(X1), ok(X2)) -> add#(X1, X2)) (add#(X1, mark(X2)) -> add#(X1, X2), add#(X1, mark(X2)) -> add#(X1, X2)) (add#(X1, mark(X2)) -> add#(X1, X2), add#(mark(X1), X2) -> add#(X1, X2)) (add#(X1, mark(X2)) -> add#(X1, X2), add#(ok(X1), ok(X2)) -> add#(X1, X2)) (cons#(mark(X1), X2) -> cons#(X1, X2), cons#(mark(X1), X2) -> cons#(X1, X2)) (cons#(mark(X1), X2) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)) (fst#(mark(X1), X2) -> fst#(X1, X2), fst#(X1, mark(X2)) -> fst#(X1, X2)) (fst#(mark(X1), X2) -> fst#(X1, X2), fst#(mark(X1), X2) -> fst#(X1, X2)) (fst#(mark(X1), X2) -> fst#(X1, X2), fst#(ok(X1), ok(X2)) -> fst#(X1, X2)) (active#(add(s(X), Y)) -> s#(add(X, Y)), s#(ok(X)) -> s#(X)) } SCCS: Scc: {top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> top#(active(X))} Scc: { proper#(fst(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2), proper#(len(X)) -> proper#(X)} Scc: {len#(mark(X)) -> len#(X), len#(ok(X)) -> len#(X)} Scc: { add#(X1, mark(X2)) -> add#(X1, X2), add#(mark(X1), X2) -> add#(X1, X2), add#(ok(X1), ok(X2)) -> add#(X1, X2)} Scc: {from#(mark(X)) -> from#(X), from#(ok(X)) -> from#(X)} Scc: {s#(ok(X)) -> s#(X)} Scc: { cons#(mark(X1), X2) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)} Scc: { fst#(X1, mark(X2)) -> fst#(X1, X2), fst#(mark(X1), X2) -> fst#(X1, X2), fst#(ok(X1), ok(X2)) -> fst#(X1, X2)} Scc: { active#(fst(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> active#(X2), active#(len(X)) -> active#(X)} SCC: Strict: {top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> top#(active(X))} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} POLY: Argument Filtering: pi(top#) = 0, pi(top) = [], pi(proper) = 0, pi(ok) = 0, pi(len) = [0], pi(add) = [0,1], pi(from) = [0], pi(s) = [], pi(cons) = 0, pi(0) = [], pi(fst) = [0,1], pi(active) = 0, pi(nil) = [], pi(mark) = [0] Usable Rules: {} Interpretation: [mark](x0) = x0 + 1 Strict: {top#(ok(X)) -> top#(active(X))} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} EDG: {(top#(ok(X)) -> top#(active(X)), top#(ok(X)) -> top#(active(X)))} SCCS: Scc: {top#(ok(X)) -> top#(active(X))} SCC: Strict: {top#(ok(X)) -> top#(active(X))} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} POLY: Argument Filtering: pi(top#) = 0, pi(top) = [], pi(proper) = [], pi(ok) = [0], pi(len) = [0], pi(add) = 1, pi(from) = 0, pi(s) = [], pi(cons) = 0, pi(0) = [], pi(fst) = 1, pi(active) = 0, pi(nil) = [], pi(mark) = [] Usable Rules: {} Interpretation: [ok](x0) = x0 + 1 Strict: {} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} Qed SCC: Strict: { proper#(fst(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2), proper#(len(X)) -> proper#(X)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: { proper#(fst(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)} EDG: {(proper#(cons(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(add(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X1)) (proper#(add(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(add(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(add(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(add(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(add(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(add(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(add(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(add(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X1)) (proper#(add(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2))} SCCS: Scc: { proper#(fst(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)} SCC: Strict: { proper#(fst(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: { proper#(fst(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)} EDG: {(proper#(cons(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(add(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(add(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(add(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(add(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2))} SCCS: Scc: { proper#(fst(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)} SCC: Strict: { proper#(fst(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: { proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)} EDG: {(proper#(cons(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(add(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(add(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(add(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2))} SCCS: Scc: { proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)} SCC: Strict: { proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: { proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)} EDG: {(proper#(cons(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(add(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(add(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2))} SCCS: Scc: { proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)} SCC: Strict: { proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(add(X1, X2)) -> proper#(X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: { proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)} EDG: {(proper#(cons(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(add(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2))} SCCS: Scc: { proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)} SCC: Strict: { proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: { proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)} EDG: {(proper#(add(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(add(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2))} SCCS: Scc: { proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)} SCC: Strict: { proper#(fst(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(add(X1, X2)) -> proper#(X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(fst(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)} EDG: {(proper#(add(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)) (proper#(add(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(fst(X1, X2)) -> proper#(X2)) (proper#(fst(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2))} SCCS: Scc: {proper#(fst(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)} SCC: Strict: {proper#(fst(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(add(X1, X2)) -> proper#(X2)} EDG: {(proper#(add(X1, X2)) -> proper#(X2), proper#(add(X1, X2)) -> proper#(X2))} SCCS: Scc: {proper#(add(X1, X2)) -> proper#(X2)} SCC: Strict: {proper#(add(X1, X2)) -> proper#(X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {} Qed SCC: Strict: {len#(mark(X)) -> len#(X), len#(ok(X)) -> len#(X)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(len#) = 0 Strict: {len#(ok(X)) -> len#(X)} EDG: {(len#(ok(X)) -> len#(X), len#(ok(X)) -> len#(X))} SCCS: Scc: {len#(ok(X)) -> len#(X)} SCC: Strict: {len#(ok(X)) -> len#(X)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(len#) = 0 Strict: {} Qed SCC: Strict: { add#(X1, mark(X2)) -> add#(X1, X2), add#(mark(X1), X2) -> add#(X1, X2), add#(ok(X1), ok(X2)) -> add#(X1, X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(add#) = 0 Strict: { add#(X1, mark(X2)) -> add#(X1, X2), add#(ok(X1), ok(X2)) -> add#(X1, X2)} EDG: {(add#(ok(X1), ok(X2)) -> add#(X1, X2), add#(ok(X1), ok(X2)) -> add#(X1, X2)) (add#(ok(X1), ok(X2)) -> add#(X1, X2), add#(X1, mark(X2)) -> add#(X1, X2)) (add#(X1, mark(X2)) -> add#(X1, X2), add#(X1, mark(X2)) -> add#(X1, X2)) (add#(X1, mark(X2)) -> add#(X1, X2), add#(ok(X1), ok(X2)) -> add#(X1, X2))} SCCS: Scc: { add#(X1, mark(X2)) -> add#(X1, X2), add#(ok(X1), ok(X2)) -> add#(X1, X2)} SCC: Strict: { add#(X1, mark(X2)) -> add#(X1, X2), add#(ok(X1), ok(X2)) -> add#(X1, X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(add#) = 1 Strict: {add#(ok(X1), ok(X2)) -> add#(X1, X2)} EDG: {(add#(ok(X1), ok(X2)) -> add#(X1, X2), add#(ok(X1), ok(X2)) -> add#(X1, X2))} SCCS: Scc: {add#(ok(X1), ok(X2)) -> add#(X1, X2)} SCC: Strict: {add#(ok(X1), ok(X2)) -> add#(X1, X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(add#) = 0 Strict: {} Qed SCC: Strict: {from#(mark(X)) -> from#(X), from#(ok(X)) -> from#(X)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(from#) = 0 Strict: {from#(ok(X)) -> from#(X)} EDG: {(from#(ok(X)) -> from#(X), from#(ok(X)) -> from#(X))} SCCS: Scc: {from#(ok(X)) -> from#(X)} SCC: Strict: {from#(ok(X)) -> from#(X)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(from#) = 0 Strict: {} Qed SCC: Strict: {s#(ok(X)) -> s#(X)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(s#) = 0 Strict: {} Qed SCC: Strict: { cons#(mark(X1), X2) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(cons#) = 0 Strict: {cons#(mark(X1), X2) -> cons#(X1, X2)} EDG: {(cons#(mark(X1), X2) -> cons#(X1, X2), cons#(mark(X1), X2) -> cons#(X1, X2))} SCCS: Scc: {cons#(mark(X1), X2) -> cons#(X1, X2)} SCC: Strict: {cons#(mark(X1), X2) -> cons#(X1, X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(cons#) = 0 Strict: {} Qed SCC: Strict: { fst#(X1, mark(X2)) -> fst#(X1, X2), fst#(mark(X1), X2) -> fst#(X1, X2), fst#(ok(X1), ok(X2)) -> fst#(X1, X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(fst#) = 0 Strict: {fst#(X1, mark(X2)) -> fst#(X1, X2), fst#(mark(X1), X2) -> fst#(X1, X2)} EDG: {(fst#(mark(X1), X2) -> fst#(X1, X2), fst#(mark(X1), X2) -> fst#(X1, X2)) (fst#(mark(X1), X2) -> fst#(X1, X2), fst#(X1, mark(X2)) -> fst#(X1, X2)) (fst#(X1, mark(X2)) -> fst#(X1, X2), fst#(X1, mark(X2)) -> fst#(X1, X2)) (fst#(X1, mark(X2)) -> fst#(X1, X2), fst#(mark(X1), X2) -> fst#(X1, X2))} SCCS: Scc: {fst#(X1, mark(X2)) -> fst#(X1, X2), fst#(mark(X1), X2) -> fst#(X1, X2)} SCC: Strict: {fst#(X1, mark(X2)) -> fst#(X1, X2), fst#(mark(X1), X2) -> fst#(X1, X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(fst#) = 0 Strict: {fst#(X1, mark(X2)) -> fst#(X1, X2)} EDG: {(fst#(X1, mark(X2)) -> fst#(X1, X2), fst#(X1, mark(X2)) -> fst#(X1, X2))} SCCS: Scc: {fst#(X1, mark(X2)) -> fst#(X1, X2)} SCC: Strict: {fst#(X1, mark(X2)) -> fst#(X1, X2)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(fst#) = 1 Strict: {} Qed SCC: Strict: { active#(fst(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> active#(X2), active#(len(X)) -> active#(X)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: { active#(fst(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)} EDG: {(active#(from(X)) -> active#(X), active#(len(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(fst(X1, X2)) -> active#(X2)) (active#(from(X)) -> active#(X), active#(fst(X1, X2)) -> active#(X1)) (active#(fst(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)) (active#(fst(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> active#(X1)) (active#(fst(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(fst(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(fst(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2)) (active#(fst(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X1)) (active#(add(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)) (active#(add(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> active#(X1)) (active#(add(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(add(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(add(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2)) (active#(add(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)) (active#(len(X)) -> active#(X), active#(fst(X1, X2)) -> active#(X1)) (active#(len(X)) -> active#(X), active#(fst(X1, X2)) -> active#(X2)) (active#(len(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(len(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(len(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1)) (active#(len(X)) -> active#(X), active#(len(X)) -> active#(X)) (active#(fst(X1, X2)) -> active#(X2), active#(fst(X1, X2)) -> active#(X1)) (active#(fst(X1, X2)) -> active#(X2), active#(fst(X1, X2)) -> active#(X2)) (active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1)) (active#(fst(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X)) (active#(fst(X1, X2)) -> active#(X2), active#(add(X1, X2)) -> active#(X1)) (active#(fst(X1, X2)) -> active#(X2), active#(len(X)) -> active#(X))} SCCS: Scc: { active#(fst(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)} SCC: Strict: { active#(fst(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: { active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)} EDG: {(active#(len(X)) -> active#(X), active#(len(X)) -> active#(X)) (active#(len(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1)) (active#(len(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(len(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(len(X)) -> active#(X), active#(fst(X1, X2)) -> active#(X2)) (active#(add(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)) (active#(add(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> active#(X1)) (active#(add(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(add(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(add(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2)) (active#(fst(X1, X2)) -> active#(X2), active#(fst(X1, X2)) -> active#(X2)) (active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1)) (active#(fst(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X)) (active#(fst(X1, X2)) -> active#(X2), active#(add(X1, X2)) -> active#(X1)) (active#(fst(X1, X2)) -> active#(X2), active#(len(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(add(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(fst(X1, X2)) -> active#(X2)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(len(X)) -> active#(X))} SCCS: Scc: { active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)} SCC: Strict: { active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(add(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: { active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(len(X)) -> active#(X)} EDG: {(active#(from(X)) -> active#(X), active#(len(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(fst(X1, X2)) -> active#(X2)) (active#(cons(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2)) (active#(len(X)) -> active#(X), active#(fst(X1, X2)) -> active#(X2)) (active#(len(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(len(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(len(X)) -> active#(X), active#(len(X)) -> active#(X)) (active#(fst(X1, X2)) -> active#(X2), active#(fst(X1, X2)) -> active#(X2)) (active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1)) (active#(fst(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X)) (active#(fst(X1, X2)) -> active#(X2), active#(len(X)) -> active#(X))} SCCS: Scc: { active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(len(X)) -> active#(X)} SCC: Strict: { active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(len(X)) -> active#(X)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: { active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)} EDG: {(active#(cons(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(fst(X1, X2)) -> active#(X2)) (active#(len(X)) -> active#(X), active#(fst(X1, X2)) -> active#(X2)) (active#(len(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(len(X)) -> active#(X), active#(len(X)) -> active#(X)) (active#(fst(X1, X2)) -> active#(X2), active#(fst(X1, X2)) -> active#(X2)) (active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1)) (active#(fst(X1, X2)) -> active#(X2), active#(len(X)) -> active#(X))} SCCS: Scc: { active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)} SCC: Strict: { active#(fst(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(cons(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)} EDG: {(active#(cons(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(len(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(len(X)) -> active#(X), active#(len(X)) -> active#(X))} SCCS: Scc: {active#(cons(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)} SCC: Strict: {active#(cons(X1, X2)) -> active#(X1), active#(len(X)) -> active#(X)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(len(X)) -> active#(X)} EDG: {(active#(len(X)) -> active#(X), active#(len(X)) -> active#(X))} SCCS: Scc: {active#(len(X)) -> active#(X)} SCC: Strict: {active#(len(X)) -> active#(X)} Weak: { active(fst(X1, X2)) -> fst(X1, active(X2)), active(fst(X1, X2)) -> fst(active(X1), X2), active(fst(0(), Z)) -> mark(nil()), active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(add(X1, X2)) -> add(X1, active(X2)), active(add(X1, X2)) -> add(active(X1), X2), active(add(0(), X)) -> mark(X), active(add(s(X), Y)) -> mark(s(add(X, Y))), active(len(X)) -> len(active(X)), active(len(nil())) -> mark(0()), active(len(cons(X, Z))) -> mark(s(len(Z))), fst(X1, mark(X2)) -> mark(fst(X1, X2)), fst(mark(X1), X2) -> mark(fst(X1, X2)), fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), add(X1, mark(X2)) -> mark(add(X1, X2)), add(mark(X1), X2) -> mark(add(X1, X2)), add(ok(X1), ok(X2)) -> ok(add(X1, X2)), len(mark(X)) -> mark(len(X)), len(ok(X)) -> ok(len(X)), proper(nil()) -> ok(nil()), proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), proper(add(X1, X2)) -> add(proper(X1), proper(X2)), proper(len(X)) -> len(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {} Qed