YES TRS: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} DP: Strict: { +#(x, +(y, z)) -> +#(x, y), +#(x, +(y, z)) -> +#(+(x, y), z), +#(0(x), 0(y)) -> 0#(+(x, y)), +#(0(x), 0(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> 0#(+(+(x, y), 1(#()))), +#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#())), -#(0(x), 0(y)) -> 0#(-(x, y)), -#(0(x), 0(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(1(x), 0(y)) -> -#(x, y), -#(1(x), 1(y)) -> 0#(-(x, y)), -#(1(x), 1(y)) -> -#(x, y), ge#(#(), 0(x)) -> ge#(#(), x), ge#(0(x), 0(y)) -> ge#(x, y), ge#(0(x), 1(y)) -> not#(ge(y, x)), ge#(0(x), 1(y)) -> ge#(y, x), ge#(1(x), 0(y)) -> ge#(x, y), ge#(1(x), 1(y)) -> ge#(x, y), min#(n(x, y, z)) -> min#(y), max#(n(x, y, z)) -> max#(z), bs#(n(x, y, z)) -> and#(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z))), bs#(n(x, y, z)) -> and#(ge(x, max(y)), ge(min(z), x)), bs#(n(x, y, z)) -> and#(bs(y), bs(z)), bs#(n(x, y, z)) -> ge#(x, max(y)), bs#(n(x, y, z)) -> ge#(min(z), x), bs#(n(x, y, z)) -> min#(z), bs#(n(x, y, z)) -> max#(y), bs#(n(x, y, z)) -> bs#(y), bs#(n(x, y, z)) -> bs#(z), size#(n(x, y, z)) -> +#(+(size(x), size(y)), 1(#())), size#(n(x, y, z)) -> +#(size(x), size(y)), size#(n(x, y, z)) -> size#(x), size#(n(x, y, z)) -> size#(y), wb#(n(x, y, z)) -> -#(size(y), size(z)), wb#(n(x, y, z)) -> -#(size(z), size(y)), 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))), wb#(n(x, y, z)) -> and#(wb(y), wb(z)), wb#(n(x, y, z)) -> if#(ge(size(y), size(z)), ge(1(#()), -(size(y), size(z))), ge(1(#()), -(size(z), size(y)))), wb#(n(x, y, z)) -> ge#(1(#()), -(size(y), size(z))), wb#(n(x, y, z)) -> ge#(1(#()), -(size(z), size(y))), wb#(n(x, y, z)) -> ge#(size(y), size(z)), wb#(n(x, y, z)) -> size#(y), wb#(n(x, y, z)) -> size#(z), wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> wb#(z)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} EDG: { (size#(n(x, y, z)) -> size#(x), size#(n(x, y, z)) -> size#(y)) (size#(n(x, y, z)) -> size#(x), size#(n(x, y, z)) -> size#(x)) (size#(n(x, y, z)) -> size#(x), size#(n(x, y, z)) -> +#(size(x), size(y))) (size#(n(x, y, z)) -> size#(x), size#(n(x, y, z)) -> +#(+(size(x), size(y)), 1(#()))) (+#(x, +(y, z)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (+#(x, +(y, z)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y)) (+#(x, +(y, z)) -> +#(x, y), +#(1(x), 1(y)) -> 0#(+(+(x, y), 1(#())))) (+#(x, +(y, z)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y)) (+#(x, +(y, z)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y)) (+#(x, +(y, z)) -> +#(x, y), +#(0(x), 0(y)) -> +#(x, y)) (+#(x, +(y, z)) -> +#(x, y), +#(0(x), 0(y)) -> 0#(+(x, y))) (+#(x, +(y, z)) -> +#(x, y), +#(x, +(y, z)) -> +#(+(x, y), z)) (+#(x, +(y, z)) -> +#(x, y), +#(x, +(y, z)) -> +#(x, y)) (+#(0(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (+#(0(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y)) (+#(0(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> 0#(+(+(x, y), 1(#())))) (+#(0(x), 1(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y)) (+#(0(x), 1(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y)) (+#(0(x), 1(y)) -> +#(x, y), +#(0(x), 0(y)) -> +#(x, y)) (+#(0(x), 1(y)) -> +#(x, y), +#(0(x), 0(y)) -> 0#(+(x, y))) (+#(0(x), 1(y)) -> +#(x, y), +#(x, +(y, z)) -> +#(+(x, y), z)) (+#(0(x), 1(y)) -> +#(x, y), +#(x, +(y, z)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (+#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> 0#(+(+(x, y), 1(#())))) (+#(1(x), 1(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(x, y), +#(0(x), 0(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(x, y), +#(0(x), 0(y)) -> 0#(+(x, y))) (+#(1(x), 1(y)) -> +#(x, y), +#(x, +(y, z)) -> +#(+(x, y), z)) (+#(1(x), 1(y)) -> +#(x, y), +#(x, +(y, z)) -> +#(x, y)) (-#(0(x), 1(y)) -> -#(x, y), -#(1(x), 1(y)) -> -#(x, y)) (-#(0(x), 1(y)) -> -#(x, y), -#(1(x), 1(y)) -> 0#(-(x, y))) (-#(0(x), 1(y)) -> -#(x, y), -#(1(x), 0(y)) -> -#(x, y)) (-#(0(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(-(x, y), 1(#()))) (-#(0(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(x, y)) (-#(0(x), 1(y)) -> -#(x, y), -#(0(x), 0(y)) -> -#(x, y)) (-#(0(x), 1(y)) -> -#(x, y), -#(0(x), 0(y)) -> 0#(-(x, y))) (-#(1(x), 1(y)) -> -#(x, y), -#(1(x), 1(y)) -> -#(x, y)) (-#(1(x), 1(y)) -> -#(x, y), -#(1(x), 1(y)) -> 0#(-(x, y))) (-#(1(x), 1(y)) -> -#(x, y), -#(1(x), 0(y)) -> -#(x, y)) (-#(1(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(-(x, y), 1(#()))) (-#(1(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(x, y)) (-#(1(x), 1(y)) -> -#(x, y), -#(0(x), 0(y)) -> -#(x, y)) (-#(1(x), 1(y)) -> -#(x, y), -#(0(x), 0(y)) -> 0#(-(x, y))) (ge#(1(x), 0(y)) -> ge#(x, y), ge#(1(x), 1(y)) -> ge#(x, y)) (ge#(1(x), 0(y)) -> ge#(x, y), ge#(1(x), 0(y)) -> ge#(x, y)) (ge#(1(x), 0(y)) -> ge#(x, y), ge#(0(x), 1(y)) -> ge#(y, x)) (ge#(1(x), 0(y)) -> ge#(x, y), ge#(0(x), 1(y)) -> not#(ge(y, x))) (ge#(1(x), 0(y)) -> ge#(x, y), ge#(0(x), 0(y)) -> ge#(x, y)) (ge#(1(x), 0(y)) -> ge#(x, y), ge#(#(), 0(x)) -> ge#(#(), x)) (+#(x, +(y, z)) -> +#(+(x, y), z), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (+#(x, +(y, z)) -> +#(+(x, y), z), +#(1(x), 1(y)) -> +#(x, y)) (+#(x, +(y, z)) -> +#(+(x, y), z), +#(1(x), 1(y)) -> 0#(+(+(x, y), 1(#())))) (+#(x, +(y, z)) -> +#(+(x, y), z), +#(1(x), 0(y)) -> +#(x, y)) (+#(x, +(y, z)) -> +#(+(x, y), z), +#(0(x), 1(y)) -> +#(x, y)) (+#(x, +(y, z)) -> +#(+(x, y), z), +#(0(x), 0(y)) -> +#(x, y)) (+#(x, +(y, z)) -> +#(+(x, y), z), +#(0(x), 0(y)) -> 0#(+(x, y))) (+#(x, +(y, z)) -> +#(+(x, y), z), +#(x, +(y, z)) -> +#(+(x, y), z)) (+#(x, +(y, z)) -> +#(+(x, y), z), +#(x, +(y, z)) -> +#(x, y)) (bs#(n(x, y, z)) -> min#(z), min#(n(x, y, z)) -> min#(y)) (wb#(n(x, y, z)) -> wb#(z), wb#(n(x, y, z)) -> wb#(z)) (wb#(n(x, y, z)) -> wb#(z), wb#(n(x, y, z)) -> wb#(y)) (wb#(n(x, y, z)) -> wb#(z), wb#(n(x, y, z)) -> size#(z)) (wb#(n(x, y, z)) -> wb#(z), wb#(n(x, y, z)) -> size#(y)) (wb#(n(x, y, z)) -> wb#(z), wb#(n(x, y, z)) -> ge#(size(y), size(z))) (wb#(n(x, y, z)) -> wb#(z), wb#(n(x, y, z)) -> ge#(1(#()), -(size(z), size(y)))) (wb#(n(x, y, z)) -> wb#(z), wb#(n(x, y, z)) -> ge#(1(#()), -(size(y), size(z)))) (wb#(n(x, y, z)) -> wb#(z), wb#(n(x, y, z)) -> if#(ge(size(y), size(z)), ge(1(#()), -(size(y), size(z))), ge(1(#()), -(size(z), size(y))))) (wb#(n(x, y, z)) -> wb#(z), wb#(n(x, y, z)) -> and#(wb(y), wb(z))) (wb#(n(x, y, z)) -> wb#(z), 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)))) (wb#(n(x, y, z)) -> wb#(z), wb#(n(x, y, z)) -> -#(size(z), size(y))) (wb#(n(x, y, z)) -> wb#(z), wb#(n(x, y, z)) -> -#(size(y), size(z))) (-#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(1(x), 1(y)) -> -#(x, y)) (-#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(1(x), 1(y)) -> 0#(-(x, y))) (-#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(0(x), 1(y)) -> -#(-(x, y), 1(#()))) (-#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(0(x), 1(y)) -> -#(x, y)) (wb#(n(x, y, z)) -> ge#(1(#()), -(size(y), size(z))), ge#(1(x), 1(y)) -> ge#(x, y)) (wb#(n(x, y, z)) -> ge#(1(#()), -(size(y), size(z))), ge#(1(x), 0(y)) -> ge#(x, y)) (ge#(#(), 0(x)) -> ge#(#(), x), ge#(#(), 0(x)) -> ge#(#(), x)) (bs#(n(x, y, z)) -> ge#(x, max(y)), ge#(1(x), 1(y)) -> ge#(x, y)) (bs#(n(x, y, z)) -> ge#(x, max(y)), ge#(1(x), 0(y)) -> ge#(x, y)) (bs#(n(x, y, z)) -> ge#(x, max(y)), ge#(0(x), 1(y)) -> ge#(y, x)) (bs#(n(x, y, z)) -> ge#(x, max(y)), ge#(0(x), 1(y)) -> not#(ge(y, x))) (bs#(n(x, y, z)) -> ge#(x, max(y)), ge#(0(x), 0(y)) -> ge#(x, y)) (bs#(n(x, y, z)) -> ge#(x, max(y)), ge#(#(), 0(x)) -> ge#(#(), x)) (wb#(n(x, y, z)) -> -#(size(y), size(z)), -#(1(x), 1(y)) -> -#(x, y)) (wb#(n(x, y, z)) -> -#(size(y), size(z)), -#(1(x), 1(y)) -> 0#(-(x, y))) (wb#(n(x, y, z)) -> -#(size(y), size(z)), -#(1(x), 0(y)) -> -#(x, y)) (wb#(n(x, y, z)) -> -#(size(y), size(z)), -#(0(x), 1(y)) -> -#(-(x, y), 1(#()))) (wb#(n(x, y, z)) -> -#(size(y), size(z)), -#(0(x), 1(y)) -> -#(x, y)) (wb#(n(x, y, z)) -> -#(size(y), size(z)), -#(0(x), 0(y)) -> -#(x, y)) (wb#(n(x, y, z)) -> -#(size(y), size(z)), -#(0(x), 0(y)) -> 0#(-(x, y))) (min#(n(x, y, z)) -> min#(y), min#(n(x, y, z)) -> min#(y)) (bs#(n(x, y, z)) -> bs#(y), bs#(n(x, y, z)) -> bs#(z)) (bs#(n(x, y, z)) -> bs#(y), bs#(n(x, y, z)) -> bs#(y)) (bs#(n(x, y, z)) -> bs#(y), bs#(n(x, y, z)) -> max#(y)) (bs#(n(x, y, z)) -> bs#(y), bs#(n(x, y, z)) -> min#(z)) (bs#(n(x, y, z)) -> bs#(y), bs#(n(x, y, z)) -> ge#(min(z), x)) (bs#(n(x, y, z)) -> bs#(y), bs#(n(x, y, z)) -> ge#(x, max(y))) (bs#(n(x, y, z)) -> bs#(y), bs#(n(x, y, z)) -> and#(bs(y), bs(z))) (bs#(n(x, y, z)) -> bs#(y), bs#(n(x, y, z)) -> and#(ge(x, max(y)), ge(min(z), x))) (bs#(n(x, y, z)) -> bs#(y), bs#(n(x, y, z)) -> and#(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))) (wb#(n(x, y, z)) -> size#(y), size#(n(x, y, z)) -> size#(y)) (wb#(n(x, y, z)) -> size#(y), size#(n(x, y, z)) -> size#(x)) (wb#(n(x, y, z)) -> size#(y), size#(n(x, y, z)) -> +#(size(x), size(y))) (wb#(n(x, y, z)) -> size#(y), size#(n(x, y, z)) -> +#(+(size(x), size(y)), 1(#()))) (bs#(n(x, y, z)) -> ge#(min(z), x), ge#(1(x), 1(y)) -> ge#(x, y)) (bs#(n(x, y, z)) -> ge#(min(z), x), ge#(1(x), 0(y)) -> ge#(x, y)) (bs#(n(x, y, z)) -> ge#(min(z), x), ge#(0(x), 1(y)) -> ge#(y, x)) (bs#(n(x, y, z)) -> ge#(min(z), x), ge#(0(x), 1(y)) -> not#(ge(y, x))) (bs#(n(x, y, z)) -> ge#(min(z), x), ge#(0(x), 0(y)) -> ge#(x, y)) (bs#(n(x, y, z)) -> ge#(min(z), x), ge#(#(), 0(x)) -> ge#(#(), x)) (wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> -#(size(y), size(z))) (wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> -#(size(z), size(y))) (wb#(n(x, y, z)) -> wb#(y), 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)))) (wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> and#(wb(y), wb(z))) (wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> if#(ge(size(y), size(z)), ge(1(#()), -(size(y), size(z))), ge(1(#()), -(size(z), size(y))))) (wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> ge#(1(#()), -(size(y), size(z)))) (wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> ge#(1(#()), -(size(z), size(y)))) (wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> ge#(size(y), size(z))) (wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> size#(y)) (wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> size#(z)) (wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> wb#(y)) (wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> wb#(z)) (size#(n(x, y, z)) -> size#(y), size#(n(x, y, z)) -> +#(+(size(x), size(y)), 1(#()))) (size#(n(x, y, z)) -> size#(y), size#(n(x, y, z)) -> +#(size(x), size(y))) (size#(n(x, y, z)) -> size#(y), size#(n(x, y, z)) -> size#(x)) (size#(n(x, y, z)) -> size#(y), size#(n(x, y, z)) -> size#(y)) (bs#(n(x, y, z)) -> max#(y), max#(n(x, y, z)) -> max#(z)) (wb#(n(x, y, z)) -> ge#(size(y), size(z)), ge#(#(), 0(x)) -> ge#(#(), x)) (wb#(n(x, y, z)) -> ge#(size(y), size(z)), ge#(0(x), 0(y)) -> ge#(x, y)) (wb#(n(x, y, z)) -> ge#(size(y), size(z)), ge#(0(x), 1(y)) -> not#(ge(y, x))) (wb#(n(x, y, z)) -> ge#(size(y), size(z)), ge#(0(x), 1(y)) -> ge#(y, x)) (wb#(n(x, y, z)) -> ge#(size(y), size(z)), ge#(1(x), 0(y)) -> ge#(x, y)) (wb#(n(x, y, z)) -> ge#(size(y), size(z)), ge#(1(x), 1(y)) -> ge#(x, y)) (wb#(n(x, y, z)) -> -#(size(z), size(y)), -#(0(x), 0(y)) -> 0#(-(x, y))) (wb#(n(x, y, z)) -> -#(size(z), size(y)), -#(0(x), 0(y)) -> -#(x, y)) (wb#(n(x, y, z)) -> -#(size(z), size(y)), -#(0(x), 1(y)) -> -#(x, y)) (wb#(n(x, y, z)) -> -#(size(z), size(y)), -#(0(x), 1(y)) -> -#(-(x, y), 1(#()))) (wb#(n(x, y, z)) -> -#(size(z), size(y)), -#(1(x), 0(y)) -> -#(x, y)) (wb#(n(x, y, z)) -> -#(size(z), size(y)), -#(1(x), 1(y)) -> 0#(-(x, y))) (wb#(n(x, y, z)) -> -#(size(z), size(y)), -#(1(x), 1(y)) -> -#(x, y)) (size#(n(x, y, z)) -> +#(size(x), size(y)), +#(x, +(y, z)) -> +#(x, y)) (size#(n(x, y, z)) -> +#(size(x), size(y)), +#(x, +(y, z)) -> +#(+(x, y), z)) (size#(n(x, y, z)) -> +#(size(x), size(y)), +#(0(x), 0(y)) -> 0#(+(x, y))) (size#(n(x, y, z)) -> +#(size(x), size(y)), +#(0(x), 0(y)) -> +#(x, y)) (size#(n(x, y, z)) -> +#(size(x), size(y)), +#(0(x), 1(y)) -> +#(x, y)) (size#(n(x, y, z)) -> +#(size(x), size(y)), +#(1(x), 0(y)) -> +#(x, y)) (size#(n(x, y, z)) -> +#(size(x), size(y)), +#(1(x), 1(y)) -> 0#(+(+(x, y), 1(#())))) (size#(n(x, y, z)) -> +#(size(x), size(y)), +#(1(x), 1(y)) -> +#(x, y)) (size#(n(x, y, z)) -> +#(size(x), size(y)), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (wb#(n(x, y, z)) -> ge#(1(#()), -(size(z), size(y))), ge#(1(x), 0(y)) -> ge#(x, y)) (wb#(n(x, y, z)) -> ge#(1(#()), -(size(z), size(y))), ge#(1(x), 1(y)) -> ge#(x, y)) (size#(n(x, y, z)) -> +#(+(size(x), size(y)), 1(#())), +#(0(x), 1(y)) -> +#(x, y)) (size#(n(x, y, z)) -> +#(+(size(x), size(y)), 1(#())), +#(1(x), 1(y)) -> 0#(+(+(x, y), 1(#())))) (size#(n(x, y, z)) -> +#(+(size(x), size(y)), 1(#())), +#(1(x), 1(y)) -> +#(x, y)) (size#(n(x, y, z)) -> +#(+(size(x), size(y)), 1(#())), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (+#(1(x), 1(y)) -> +#(+(x, y), 1(#())), +#(0(x), 1(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(+(x, y), 1(#())), +#(1(x), 1(y)) -> 0#(+(+(x, y), 1(#())))) (+#(1(x), 1(y)) -> +#(+(x, y), 1(#())), +#(1(x), 1(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(+(x, y), 1(#())), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (wb#(n(x, y, z)) -> size#(z), size#(n(x, y, z)) -> +#(+(size(x), size(y)), 1(#()))) (wb#(n(x, y, z)) -> size#(z), size#(n(x, y, z)) -> +#(size(x), size(y))) (wb#(n(x, y, z)) -> size#(z), size#(n(x, y, z)) -> size#(x)) (wb#(n(x, y, z)) -> size#(z), size#(n(x, y, z)) -> size#(y)) (bs#(n(x, y, z)) -> bs#(z), bs#(n(x, y, z)) -> and#(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))) (bs#(n(x, y, z)) -> bs#(z), bs#(n(x, y, z)) -> and#(ge(x, max(y)), ge(min(z), x))) (bs#(n(x, y, z)) -> bs#(z), bs#(n(x, y, z)) -> and#(bs(y), bs(z))) (bs#(n(x, y, z)) -> bs#(z), bs#(n(x, y, z)) -> ge#(x, max(y))) (bs#(n(x, y, z)) -> bs#(z), bs#(n(x, y, z)) -> ge#(min(z), x)) (bs#(n(x, y, z)) -> bs#(z), bs#(n(x, y, z)) -> min#(z)) (bs#(n(x, y, z)) -> bs#(z), bs#(n(x, y, z)) -> max#(y)) (bs#(n(x, y, z)) -> bs#(z), bs#(n(x, y, z)) -> bs#(y)) (bs#(n(x, y, z)) -> bs#(z), bs#(n(x, y, z)) -> bs#(z)) (max#(n(x, y, z)) -> max#(z), max#(n(x, y, z)) -> max#(z)) (ge#(1(x), 1(y)) -> ge#(x, y), ge#(#(), 0(x)) -> ge#(#(), x)) (ge#(1(x), 1(y)) -> ge#(x, y), ge#(0(x), 0(y)) -> ge#(x, y)) (ge#(1(x), 1(y)) -> ge#(x, y), ge#(0(x), 1(y)) -> not#(ge(y, x))) (ge#(1(x), 1(y)) -> ge#(x, y), ge#(0(x), 1(y)) -> ge#(y, x)) (ge#(1(x), 1(y)) -> ge#(x, y), ge#(1(x), 0(y)) -> ge#(x, y)) (ge#(1(x), 1(y)) -> ge#(x, y), ge#(1(x), 1(y)) -> ge#(x, y)) (ge#(0(x), 0(y)) -> ge#(x, y), ge#(#(), 0(x)) -> ge#(#(), x)) (ge#(0(x), 0(y)) -> ge#(x, y), ge#(0(x), 0(y)) -> ge#(x, y)) (ge#(0(x), 0(y)) -> ge#(x, y), ge#(0(x), 1(y)) -> not#(ge(y, x))) (ge#(0(x), 0(y)) -> ge#(x, y), ge#(0(x), 1(y)) -> ge#(y, x)) (ge#(0(x), 0(y)) -> ge#(x, y), ge#(1(x), 0(y)) -> ge#(x, y)) (ge#(0(x), 0(y)) -> ge#(x, y), ge#(1(x), 1(y)) -> ge#(x, y)) (-#(1(x), 0(y)) -> -#(x, y), -#(0(x), 0(y)) -> 0#(-(x, y))) (-#(1(x), 0(y)) -> -#(x, y), -#(0(x), 0(y)) -> -#(x, y)) (-#(1(x), 0(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(x, y)) (-#(1(x), 0(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(-(x, y), 1(#()))) (-#(1(x), 0(y)) -> -#(x, y), -#(1(x), 0(y)) -> -#(x, y)) (-#(1(x), 0(y)) -> -#(x, y), -#(1(x), 1(y)) -> 0#(-(x, y))) (-#(1(x), 0(y)) -> -#(x, y), -#(1(x), 1(y)) -> -#(x, y)) (-#(0(x), 0(y)) -> -#(x, y), -#(0(x), 0(y)) -> 0#(-(x, y))) (-#(0(x), 0(y)) -> -#(x, y), -#(0(x), 0(y)) -> -#(x, y)) (-#(0(x), 0(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(x, y)) (-#(0(x), 0(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(-(x, y), 1(#()))) (-#(0(x), 0(y)) -> -#(x, y), -#(1(x), 0(y)) -> -#(x, y)) (-#(0(x), 0(y)) -> -#(x, y), -#(1(x), 1(y)) -> 0#(-(x, y))) (-#(0(x), 0(y)) -> -#(x, y), -#(1(x), 1(y)) -> -#(x, y)) (+#(1(x), 0(y)) -> +#(x, y), +#(x, +(y, z)) -> +#(x, y)) (+#(1(x), 0(y)) -> +#(x, y), +#(x, +(y, z)) -> +#(+(x, y), z)) (+#(1(x), 0(y)) -> +#(x, y), +#(0(x), 0(y)) -> 0#(+(x, y))) (+#(1(x), 0(y)) -> +#(x, y), +#(0(x), 0(y)) -> +#(x, y)) (+#(1(x), 0(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y)) (+#(1(x), 0(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y)) (+#(1(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> 0#(+(+(x, y), 1(#())))) (+#(1(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y)) (+#(1(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (+#(0(x), 0(y)) -> +#(x, y), +#(x, +(y, z)) -> +#(x, y)) (+#(0(x), 0(y)) -> +#(x, y), +#(x, +(y, z)) -> +#(+(x, y), z)) (+#(0(x), 0(y)) -> +#(x, y), +#(0(x), 0(y)) -> 0#(+(x, y))) (+#(0(x), 0(y)) -> +#(x, y), +#(0(x), 0(y)) -> +#(x, y)) (+#(0(x), 0(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y)) (+#(0(x), 0(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y)) (+#(0(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> 0#(+(+(x, y), 1(#())))) (+#(0(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y)) (+#(0(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (ge#(0(x), 1(y)) -> ge#(y, x), ge#(#(), 0(x)) -> ge#(#(), x)) (ge#(0(x), 1(y)) -> ge#(y, x), ge#(0(x), 0(y)) -> ge#(x, y)) (ge#(0(x), 1(y)) -> ge#(y, x), ge#(0(x), 1(y)) -> not#(ge(y, x))) (ge#(0(x), 1(y)) -> ge#(y, x), ge#(0(x), 1(y)) -> ge#(y, x)) (ge#(0(x), 1(y)) -> ge#(y, x), ge#(1(x), 0(y)) -> ge#(x, y)) (ge#(0(x), 1(y)) -> ge#(y, x), ge#(1(x), 1(y)) -> ge#(x, y)) } SCCS: Scc: {wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> wb#(z)} Scc: {size#(n(x, y, z)) -> size#(x), size#(n(x, y, z)) -> size#(y)} Scc: {bs#(n(x, y, z)) -> bs#(y), bs#(n(x, y, z)) -> bs#(z)} Scc: {max#(n(x, y, z)) -> max#(z)} Scc: {min#(n(x, y, z)) -> min#(y)} Scc: {ge#(0(x), 0(y)) -> ge#(x, y), ge#(0(x), 1(y)) -> ge#(y, x), ge#(1(x), 0(y)) -> ge#(x, y), ge#(1(x), 1(y)) -> ge#(x, y)} Scc: {ge#(#(), 0(x)) -> ge#(#(), x)} Scc: {-#(0(x), 0(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(1(x), 0(y)) -> -#(x, y), -#(1(x), 1(y)) -> -#(x, y)} Scc: {+#(x, +(y, z)) -> +#(x, y), +#(x, +(y, z)) -> +#(+(x, y), z), +#(0(x), 0(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))} SCC: Strict: {wb#(n(x, y, z)) -> wb#(y), wb#(n(x, y, z)) -> wb#(z)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} SPSC: Simple Projection: pi(wb#) = 0 Strict: {wb#(n(x, y, z)) -> wb#(z)} EDG: {(wb#(n(x, y, z)) -> wb#(z), wb#(n(x, y, z)) -> wb#(z))} SCCS: Scc: {wb#(n(x, y, z)) -> wb#(z)} SCC: Strict: {wb#(n(x, y, z)) -> wb#(z)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} SPSC: Simple Projection: pi(wb#) = 0 Strict: {} Qed SCC: Strict: {size#(n(x, y, z)) -> size#(x), size#(n(x, y, z)) -> size#(y)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} SPSC: Simple Projection: pi(size#) = 0 Strict: {size#(n(x, y, z)) -> size#(y)} EDG: {(size#(n(x, y, z)) -> size#(y), size#(n(x, y, z)) -> size#(y))} SCCS: Scc: {size#(n(x, y, z)) -> size#(y)} SCC: Strict: {size#(n(x, y, z)) -> size#(y)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} SPSC: Simple Projection: pi(size#) = 0 Strict: {} Qed SCC: Strict: {bs#(n(x, y, z)) -> bs#(y), bs#(n(x, y, z)) -> bs#(z)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} SPSC: Simple Projection: pi(bs#) = 0 Strict: {bs#(n(x, y, z)) -> bs#(z)} EDG: {(bs#(n(x, y, z)) -> bs#(z), bs#(n(x, y, z)) -> bs#(z))} SCCS: Scc: {bs#(n(x, y, z)) -> bs#(z)} SCC: Strict: {bs#(n(x, y, z)) -> bs#(z)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} SPSC: Simple Projection: pi(bs#) = 0 Strict: {} Qed SCC: Strict: {max#(n(x, y, z)) -> max#(z)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} SPSC: Simple Projection: pi(max#) = 0 Strict: {} Qed SCC: Strict: {min#(n(x, y, z)) -> min#(y)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} SPSC: Simple Projection: pi(min#) = 0 Strict: {} Qed SCC: Strict: {ge#(0(x), 0(y)) -> ge#(x, y), ge#(0(x), 1(y)) -> ge#(y, x), ge#(1(x), 0(y)) -> ge#(x, y), ge#(1(x), 1(y)) -> ge#(x, y)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} POLY: Argument Filtering: pi(wb) = [], pi(size) = [], pi(bs) = [], pi(max) = [], pi(min) = [], pi(n) = [], pi(l) = [], pi(val) = [], pi(ge#) = [0,1], pi(ge) = [], pi(if) = [], pi(and) = [], pi(false) = [], pi(not) = [], pi(true) = [], pi(-) = [], pi(1) = [0], pi(+) = [], pi(0) = 0, pi(#) = [] Usable Rules: {} Interpretation: [ge#](x0, x1) = x0 + x1, [1](x0) = x0 + 1 Strict: {ge#(0(x), 0(y)) -> ge#(x, y)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} EDG: {(ge#(0(x), 0(y)) -> ge#(x, y), ge#(0(x), 0(y)) -> ge#(x, y))} SCCS: Scc: {ge#(0(x), 0(y)) -> ge#(x, y)} SCC: Strict: {ge#(0(x), 0(y)) -> ge#(x, y)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} SPSC: Simple Projection: pi(ge#) = 0 Strict: {} Qed SCC: Strict: {ge#(#(), 0(x)) -> ge#(#(), x)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} SPSC: Simple Projection: pi(ge#) = 1 Strict: {} Qed SCC: Strict: {-#(0(x), 0(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(1(x), 0(y)) -> -#(x, y), -#(1(x), 1(y)) -> -#(x, y)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} POLY: Argument Filtering: pi(wb) = [], pi(size) = [], pi(bs) = [], pi(max) = [], pi(min) = [], pi(n) = [], pi(l) = [], pi(val) = [], pi(ge) = [], pi(if) = [], pi(and) = [], pi(false) = [], pi(not) = [], pi(true) = [], pi(-#) = 1, pi(-) = [], pi(1) = 0, pi(+) = [], pi(0) = [0], pi(#) = [] Usable Rules: {} Interpretation: [0](x0) = x0 + 1, [#] = 0 Strict: {-#(0(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(1(x), 1(y)) -> -#(x, y)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} EDG: {(-#(1(x), 1(y)) -> -#(x, y), -#(1(x), 1(y)) -> -#(x, y)) (-#(1(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(-(x, y), 1(#()))) (-#(1(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(x, y)) (-#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(0(x), 1(y)) -> -#(x, y)) (-#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(0(x), 1(y)) -> -#(-(x, y), 1(#()))) (-#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(1(x), 1(y)) -> -#(x, y)) (-#(0(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(x, y)) (-#(0(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(-(x, y), 1(#()))) (-#(0(x), 1(y)) -> -#(x, y), -#(1(x), 1(y)) -> -#(x, y))} SCCS: Scc: {-#(0(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(1(x), 1(y)) -> -#(x, y)} SCC: Strict: {-#(0(x), 1(y)) -> -#(x, y), -#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(1(x), 1(y)) -> -#(x, y)} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} POLY: Argument Filtering: pi(wb) = [], pi(size) = [], pi(bs) = [], pi(max) = [], pi(min) = [], pi(n) = [], pi(l) = [], pi(val) = [], pi(ge) = [], pi(if) = [], pi(and) = [], pi(false) = [], pi(not) = [], pi(true) = [], pi(-#) = 1, pi(-) = [], pi(1) = [0], pi(+) = [], pi(0) = [], pi(#) = [] Usable Rules: {} Interpretation: [1](x0) = x0 + 1, [#] = 0 Strict: {-#(0(x), 1(y)) -> -#(-(x, y), 1(#()))} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} EDG: {(-#(0(x), 1(y)) -> -#(-(x, y), 1(#())), -#(0(x), 1(y)) -> -#(-(x, y), 1(#())))} SCCS: Scc: {-#(0(x), 1(y)) -> -#(-(x, y), 1(#()))} SCC: Strict: {-#(0(x), 1(y)) -> -#(-(x, y), 1(#()))} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} POLY: Argument Filtering: pi(wb) = [], pi(size) = [], pi(bs) = [], pi(max) = [], pi(min) = [], pi(n) = [], pi(l) = [], pi(val) = [], pi(ge) = [], pi(if) = [], pi(and) = [], pi(false) = [], pi(not) = [], pi(true) = [], pi(-#) = 0, pi(-) = 0, pi(1) = [0], pi(+) = [], pi(0) = [0], pi(#) = [] Usable Rules: {} Interpretation: [0](x0) = x0 + 1 Strict: {} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} Qed SCC: Strict: {+#(x, +(y, z)) -> +#(x, y), +#(x, +(y, z)) -> +#(+(x, y), z), +#(0(x), 0(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} POLY: Argument Filtering: pi(wb) = [], pi(size) = [], pi(bs) = [], pi(max) = [], pi(min) = [], pi(n) = [], pi(l) = [], pi(val) = [], pi(ge) = [], pi(if) = [], pi(and) = [], pi(false) = [], pi(not) = [], pi(true) = [], pi(-) = [], pi(1) = 0, pi(+#) = 1, pi(+) = [0,1], pi(0) = 0, pi(#) = [] Usable Rules: {} Interpretation: [+](x0, x1) = x0 + x1 + 1, [#] = 0 Strict: {+#(0(x), 0(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} EDG: {(+#(0(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (+#(0(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y)) (+#(0(x), 1(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y)) (+#(0(x), 1(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y)) (+#(0(x), 1(y)) -> +#(x, y), +#(0(x), 0(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (+#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(x, y), +#(0(x), 0(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(+(x, y), 1(#())), +#(0(x), 1(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(+(x, y), 1(#())), +#(1(x), 1(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(+(x, y), 1(#())), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (+#(1(x), 0(y)) -> +#(x, y), +#(0(x), 0(y)) -> +#(x, y)) (+#(1(x), 0(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y)) (+#(1(x), 0(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y)) (+#(1(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y)) (+#(1(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (+#(0(x), 0(y)) -> +#(x, y), +#(0(x), 0(y)) -> +#(x, y)) (+#(0(x), 0(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y)) (+#(0(x), 0(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y)) (+#(0(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y)) (+#(0(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#())))} SCCS: Scc: {+#(0(x), 0(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))} SCC: Strict: {+#(0(x), 0(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y), +#(1(x), 0(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} POLY: Argument Filtering: pi(wb) = [], pi(size) = [], pi(bs) = [], pi(max) = [], pi(min) = [], pi(n) = [], pi(l) = [], pi(val) = [], pi(ge) = [], pi(if) = [], pi(and) = [], pi(false) = [], pi(not) = [], pi(true) = [], pi(-) = [], pi(1) = 0, pi(+#) = 1, pi(+) = [], pi(0) = [0], pi(#) = [] Usable Rules: {} Interpretation: [0](x0) = x0 + 1, [#] = 0 Strict: {+#(0(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} EDG: {(+#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (+#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(+(x, y), 1(#())), +#(0(x), 1(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(+(x, y), 1(#())), +#(1(x), 1(y)) -> +#(x, y)) (+#(1(x), 1(y)) -> +#(+(x, y), 1(#())), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))) (+#(0(x), 1(y)) -> +#(x, y), +#(0(x), 1(y)) -> +#(x, y)) (+#(0(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y)) (+#(0(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#())))} SCCS: Scc: {+#(0(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))} SCC: Strict: {+#(0(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(x, y), +#(1(x), 1(y)) -> +#(+(x, y), 1(#()))} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} POLY: Argument Filtering: pi(wb) = [], pi(size) = [], pi(bs) = [], pi(max) = [], pi(min) = [], pi(n) = [], pi(l) = [], pi(val) = [], pi(ge) = [], pi(if) = [], pi(and) = [], pi(false) = [], pi(not) = [], pi(true) = [], pi(-) = [], pi(1) = [0], pi(+#) = 1, pi(+) = [], pi(0) = [], pi(#) = [] Usable Rules: {} Interpretation: [1](x0) = x0 + 1, [#] = 0 Strict: {+#(1(x), 1(y)) -> +#(+(x, y), 1(#()))} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} EDG: {(+#(1(x), 1(y)) -> +#(+(x, y), 1(#())), +#(1(x), 1(y)) -> +#(+(x, y), 1(#())))} SCCS: Scc: {+#(1(x), 1(y)) -> +#(+(x, y), 1(#()))} SCC: Strict: {+#(1(x), 1(y)) -> +#(+(x, y), 1(#()))} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} POLY: Argument Filtering: pi(wb) = [], pi(size) = [], pi(bs) = [], pi(max) = [], pi(min) = [], pi(n) = [], pi(l) = [], pi(val) = [], pi(ge) = [], pi(if) = [], pi(and) = [], pi(false) = [], pi(not) = [], pi(true) = [], pi(-) = [], pi(1) = [0], pi(+#) = [0,1], pi(+) = [0,1], pi(0) = 0, pi(#) = [] Usable Rules: {} Interpretation: [+#](x0, x1) = x0 + x1, [+](x0, x1) = x0 + x1, [1](x0) = x0 + 1, [#] = 0 Strict: {} Weak: { 0(#()) -> #(), +(x, #()) -> x, +(x, +(y, z)) -> +(+(x, y), z), +(#(), 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, #()) -> 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(true()) -> false(), not(false()) -> true(), and(x, true()) -> x, and(x, false()) -> false(), if(true(), x, y) -> x, if(false(), x, y) -> y, ge(x, #()) -> true(), ge(#(), 0(x)) -> ge(#(), x), ge(#(), 1(x)) -> false(), 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), 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)))} Qed