YES TRS: { not(not(x)) -> x, not(and(x, y)) -> or(not(not(not(x))), not(not(not(y)))), not(or(x, y)) -> and(not(not(not(x))), not(not(not(y))))} DP: Strict: {not#(and(x, y)) -> not#(x), not#(and(x, y)) -> not#(y), not#(and(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(x), not#(or(x, y)) -> not#(y), not#(or(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(not(not(y)))} Weak: { not(not(x)) -> x, not(and(x, y)) -> or(not(not(not(x))), not(not(not(y)))), not(or(x, y)) -> and(not(not(not(x))), not(not(not(y))))} EDG: {(not#(and(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(not(not(y)))) (not#(and(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(not(not(x)))) (not#(and(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(not(y))) (not#(and(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(not(x))) (not#(and(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(y)) (not#(and(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(x)) (not#(and(x, y)) -> not#(not(not(y))), not#(and(x, y)) -> not#(not(not(y)))) (not#(and(x, y)) -> not#(not(not(y))), not#(and(x, y)) -> not#(not(not(x)))) (not#(and(x, y)) -> not#(not(not(y))), not#(and(x, y)) -> not#(not(y))) (not#(and(x, y)) -> not#(not(not(y))), not#(and(x, y)) -> not#(not(x))) (not#(and(x, y)) -> not#(not(not(y))), not#(and(x, y)) -> not#(y)) (not#(and(x, y)) -> not#(not(not(y))), not#(and(x, y)) -> not#(x)) (not#(or(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(not(not(y)))) (not#(or(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(not(not(x)))) (not#(or(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(not(y))) (not#(or(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(not(x))) (not#(or(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(y)) (not#(or(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(x)) (not#(or(x, y)) -> not#(not(not(y))), not#(and(x, y)) -> not#(not(not(y)))) (not#(or(x, y)) -> not#(not(not(y))), not#(and(x, y)) -> not#(not(not(x)))) (not#(or(x, y)) -> not#(not(not(y))), not#(and(x, y)) -> not#(not(y))) (not#(or(x, y)) -> not#(not(not(y))), not#(and(x, y)) -> not#(not(x))) (not#(or(x, y)) -> not#(not(not(y))), not#(and(x, y)) -> not#(y)) (not#(or(x, y)) -> not#(not(not(y))), not#(and(x, y)) -> not#(x)) (not#(or(x, y)) -> not#(x), not#(or(x, y)) -> not#(not(not(y)))) (not#(or(x, y)) -> not#(x), not#(or(x, y)) -> not#(not(not(x)))) (not#(or(x, y)) -> not#(x), not#(or(x, y)) -> not#(not(y))) (not#(or(x, y)) -> not#(x), not#(or(x, y)) -> not#(not(x))) (not#(or(x, y)) -> not#(x), not#(or(x, y)) -> not#(y)) (not#(or(x, y)) -> not#(x), not#(or(x, y)) -> not#(x)) (not#(or(x, y)) -> not#(x), not#(and(x, y)) -> not#(not(not(y)))) (not#(or(x, y)) -> not#(x), not#(and(x, y)) -> not#(not(not(x)))) (not#(or(x, y)) -> not#(x), not#(and(x, y)) -> not#(not(y))) (not#(or(x, y)) -> not#(x), not#(and(x, y)) -> not#(not(x))) (not#(or(x, y)) -> not#(x), not#(and(x, y)) -> not#(y)) (not#(or(x, y)) -> not#(x), not#(and(x, y)) -> not#(x)) (not#(or(x, y)) -> not#(y), not#(or(x, y)) -> not#(not(not(y)))) (not#(or(x, y)) -> not#(y), not#(or(x, y)) -> not#(not(not(x)))) (not#(or(x, y)) -> not#(y), not#(or(x, y)) -> not#(not(y))) (not#(or(x, y)) -> not#(y), not#(or(x, y)) -> not#(not(x))) (not#(or(x, y)) -> not#(y), not#(or(x, y)) -> not#(y)) (not#(or(x, y)) -> not#(y), not#(or(x, y)) -> not#(x)) (not#(or(x, y)) -> not#(y), not#(and(x, y)) -> not#(not(not(y)))) (not#(or(x, y)) -> not#(y), not#(and(x, y)) -> not#(not(not(x)))) (not#(or(x, y)) -> not#(y), not#(and(x, y)) -> not#(not(y))) (not#(or(x, y)) -> not#(y), not#(and(x, y)) -> not#(not(x))) (not#(or(x, y)) -> not#(y), not#(and(x, y)) -> not#(y)) (not#(or(x, y)) -> not#(y), not#(and(x, y)) -> not#(x)) (not#(or(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(not(not(y)))) (not#(or(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(not(not(x)))) (not#(or(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(not(y))) (not#(or(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(not(x))) (not#(or(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(y)) (not#(or(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(x)) (not#(or(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(not(not(y)))) (not#(or(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(not(not(x)))) (not#(or(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(not(y))) (not#(or(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(not(x))) (not#(or(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(y)) (not#(or(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(x)) (not#(or(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(not(not(y)))) (not#(or(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(not(not(x)))) (not#(or(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(not(y))) (not#(or(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(not(x))) (not#(or(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(y)) (not#(or(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(x)) (not#(or(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(not(not(y)))) (not#(or(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(not(not(x)))) (not#(or(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(not(y))) (not#(or(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(not(x))) (not#(or(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(y)) (not#(or(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(x)) (not#(and(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(x)) (not#(and(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(y)) (not#(and(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(not(x))) (not#(and(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(not(y))) (not#(and(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(not(not(x)))) (not#(and(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(not(not(y)))) (not#(and(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(x)) (not#(and(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(y)) (not#(and(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(not(x))) (not#(and(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(not(y))) (not#(and(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(not(not(x)))) (not#(and(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(not(not(y)))) (not#(and(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(x)) (not#(and(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(y)) (not#(and(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(not(x))) (not#(and(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(not(y))) (not#(and(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(not(not(x)))) (not#(and(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(not(not(y)))) (not#(and(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(x)) (not#(and(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(y)) (not#(and(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(not(x))) (not#(and(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(not(y))) (not#(and(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(not(not(x)))) (not#(and(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(not(not(y)))) (not#(and(x, y)) -> not#(y), not#(and(x, y)) -> not#(x)) (not#(and(x, y)) -> not#(y), not#(and(x, y)) -> not#(y)) (not#(and(x, y)) -> not#(y), not#(and(x, y)) -> not#(not(x))) (not#(and(x, y)) -> not#(y), not#(and(x, y)) -> not#(not(y))) (not#(and(x, y)) -> not#(y), not#(and(x, y)) -> not#(not(not(x)))) (not#(and(x, y)) -> not#(y), not#(and(x, y)) -> not#(not(not(y)))) (not#(and(x, y)) -> not#(y), not#(or(x, y)) -> not#(x)) (not#(and(x, y)) -> not#(y), not#(or(x, y)) -> not#(y)) (not#(and(x, y)) -> not#(y), not#(or(x, y)) -> not#(not(x))) (not#(and(x, y)) -> not#(y), not#(or(x, y)) -> not#(not(y))) (not#(and(x, y)) -> not#(y), not#(or(x, y)) -> not#(not(not(x)))) (not#(and(x, y)) -> not#(y), not#(or(x, y)) -> not#(not(not(y)))) (not#(and(x, y)) -> not#(x), not#(and(x, y)) -> not#(x)) (not#(and(x, y)) -> not#(x), not#(and(x, y)) -> not#(y)) (not#(and(x, y)) -> not#(x), not#(and(x, y)) -> not#(not(x))) (not#(and(x, y)) -> not#(x), not#(and(x, y)) -> not#(not(y))) (not#(and(x, y)) -> not#(x), not#(and(x, y)) -> not#(not(not(x)))) (not#(and(x, y)) -> not#(x), not#(and(x, y)) -> not#(not(not(y)))) (not#(and(x, y)) -> not#(x), not#(or(x, y)) -> not#(x)) (not#(and(x, y)) -> not#(x), not#(or(x, y)) -> not#(y)) (not#(and(x, y)) -> not#(x), not#(or(x, y)) -> not#(not(x))) (not#(and(x, y)) -> not#(x), not#(or(x, y)) -> not#(not(y))) (not#(and(x, y)) -> not#(x), not#(or(x, y)) -> not#(not(not(x)))) (not#(and(x, y)) -> not#(x), not#(or(x, y)) -> not#(not(not(y)))) (not#(or(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(x)) (not#(or(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(y)) (not#(or(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(not(x))) (not#(or(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(not(y))) (not#(or(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(not(not(x)))) (not#(or(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(not(not(y)))) (not#(or(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(x)) (not#(or(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(y)) (not#(or(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(not(x))) (not#(or(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(not(y))) (not#(or(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(not(not(x)))) (not#(or(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(not(not(y)))) (not#(and(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(x)) (not#(and(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(y)) (not#(and(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(not(x))) (not#(and(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(not(y))) (not#(and(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(not(not(x)))) (not#(and(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(not(not(y)))) (not#(and(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(x)) (not#(and(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(y)) (not#(and(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(not(x))) (not#(and(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(not(y))) (not#(and(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(not(not(x)))) (not#(and(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(not(not(y))))} SCCS: Scc: {not#(and(x, y)) -> not#(x), not#(and(x, y)) -> not#(y), not#(and(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(x), not#(or(x, y)) -> not#(y), not#(or(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(not(not(y)))} SCC: Strict: {not#(and(x, y)) -> not#(x), not#(and(x, y)) -> not#(y), not#(and(x, y)) -> not#(not(x)), not#(and(x, y)) -> not#(not(y)), not#(and(x, y)) -> not#(not(not(x))), not#(and(x, y)) -> not#(not(not(y))), not#(or(x, y)) -> not#(x), not#(or(x, y)) -> not#(y), not#(or(x, y)) -> not#(not(x)), not#(or(x, y)) -> not#(not(y)), not#(or(x, y)) -> not#(not(not(x))), not#(or(x, y)) -> not#(not(not(y)))} Weak: { not(not(x)) -> x, not(and(x, y)) -> or(not(not(not(x))), not(not(not(y)))), not(or(x, y)) -> and(not(not(not(x))), not(not(not(y))))} POLY: Argument Filtering: pi(or) = [0,1], pi(and) = [0,1], pi(not#) = [0], pi(not) = 0 Usable Rules: {} Interpretation: [not#](x0) = x0 + 1, [or](x0, x1) = x0 + x1 + 1, [and](x0, x1) = x0 + x1 + 1 Strict: {} Weak: { not(not(x)) -> x, not(and(x, y)) -> or(not(not(not(x))), not(not(not(y)))), not(or(x, y)) -> and(not(not(not(x))), not(not(not(y))))} Qed