(VAR x y z ) (RULES 0(#) -> # +(x, #) -> x +(#, x) -> x +(0(x), 0(y)) -> 0(+(x, y)) +(0(x), 1(y)) -> 1(+(x, y)) +(1(x), 0(y)) -> 1(+(x, y)) +(1(x), 1(y)) -> 0(+(+(x, y), 1(#))) +(x, +(y, z)) -> +(+(x, y), z) -(x, #) -> x -(#, x) -> # -(0(x), 0(y)) -> 0(-(x, y)) -(0(x), 1(y)) -> 1(-(-(x, y), 1(#))) -(1(x), 0(y)) -> 1(-(x, y)) -(1(x), 1(y)) -> 0(-(x, y)) not(false) -> true not(true) -> false and(x, true) -> x and(x, false) -> false if(true, x, y) -> x if(false, x, y) -> y ge(0(x), 0(y)) -> ge(x, y) ge(0(x), 1(y)) -> not(ge(y, x)) ge(1(x), 0(y)) -> ge(x, y) ge(1(x), 1(y)) -> ge(x, y) ge(x, #) -> true ge(#, 1(x)) -> false ge(#, 0(x)) -> ge(#, x) val(l(x)) -> x val(n(x, y, z)) -> x min(l(x)) -> x min(n(x, y, z)) -> min(y) max(l(x)) -> x max(n(x, y, z)) -> max(z) bs(l(x)) -> true bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z))) size(l(x)) -> 1(#) size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#)) wb(l(x)) -> true wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z))) )