The putative grammar is [[{[[[-2], [3, -2, -2, 3]], {[[-2], [-2, 3, -2, -2, 3]], [[-2], [3, 3, -2, -2, 3]]}], [[[-2, -2], [3, 3]], {[[-2, -2, 3], [3, 3]], [[-2, -2, -2], [3, 3]]}], [[[], [3, 3]], {[[3], [3, 3]], [[-2], [3, 3]]}], [ [[3, -2], [3, -2, -2, 3]], {[[3, -2, 3], [3, -2, -2, 3]], [[3, -2, -2], [3, -2, -2, 3]]}], [ [[3, -2, -2, -2], [3, 3]], {[[3, -2, -2, -2, -2], [3, 3]], [[3, -2, -2, -2, 3], [3, 3]]}], [ [[-2, -2], [-2, 3, -2, 3]], {[[-2, -2], [-2, -2, 3, -2, 3]], [[-2, -2], [3, -2, 3, -2, 3]]}], [ [[3, -2, -2], [3, 3]], {[[3, -2, -2, 3], [3, 3]], [[3, -2, -2, -2], [3, 3]]}], [ [[], [-2, -2, 3, -2, 3, -2, -2]], {[[], [-2, -2, -2, 3, -2, 3, -2, -2]], [[], [3, -2, -2, 3, -2, 3, -2, -2]]} ], [[[3, -2, -2, -2], [3, 3, -2, -2]], { [[3, -2, -2, -2, 3], [3, 3, -2, -2]], [[3, -2, -2, -2, -2], [3, 3, -2, -2]] }], [[[], [3, -2, -2, 3, -2]], {[[], [3, 3, -2, -2, 3, -2]], [[], [-2, 3, -2, -2, 3, -2]]}], [[[-2, 3], [3, 3]], {[[-2, 3, 3], [3, 3]], [[-2, 3, -2], [3, 3]]}], [ [[], [-2, 3, -2, 3, -2, -2]], {[[], [3, -2, 3, -2, 3, -2, -2]], [[], [-2, -2, 3, -2, 3, -2, -2]]}], [[[3], [3, -2, 3]], {[[3, -2], [3, -2, 3]], [[3, 3], [3, -2, 3]]}], [[[], [-2]], {[[], [3, -2]], [[], [-2, -2]]}], [ [[-2, 3, -2], [3, 3, -2, 3]], {[[-2, 3, -2, 3], [3, 3, -2, 3]], [[-2, 3, -2, -2], [3, 3, -2, 3]]}], [ [[3, -2, -2, -2], [3, 3, -2, 3, -2]], { [[3, -2, -2, -2, 3], [3, 3, -2, 3, -2]], [[3, -2, -2, -2, -2], [3, 3, -2, 3, -2]]}], [ [[-2, -2], [-2, -2, 3, -2, 3]], {[[-2, -2], [-2, -2, -2, 3, -2, 3]], [[-2, -2], [3, -2, -2, 3, -2, 3]]}], [ [[], [-2, 3, -2, -2, 3, -2]], {[[], [3, -2, 3, -2, -2, 3, -2]], [[], [-2, -2, 3, -2, -2, 3, -2]]}], [ [[3, -2], [3, -2, 3]], {[[3, -2, -2], [3, -2, 3]], [[3, -2, 3], [3, -2, 3]]}], [ [[3], [3, 3, -2, 3, -2]], {[[3, 3], [3, 3, -2, 3, -2]], [[3, -2], [3, 3, -2, 3, -2]]}], [ [[], [-2, 3, -2, -2]], {[[], [-2, -2, 3, -2, -2]], [[], [3, -2, 3, -2, -2]]}], [[[], [3, 3, -2]], {[[3], [3, 3, -2]], [[-2], [3, 3, -2]]}], [[[], [3, -2, -2, 3]], {[[3], [3, -2, -2, 3]], [[-2], [3, -2, -2, 3]]}], [ [[3, -2, -2], [3, -2, -2, 3]], {[[3, -2, -2, -2], [3, -2, -2, 3]], [[3, -2, -2, 3], [3, -2, -2, 3]]}], [ [[-2, 3, -2, -2, -2], [3, 3]], {[[-2, 3, -2, -2, -2, 3], [3, 3]], [[-2, 3, -2, -2, -2, -2], [3, 3]]}], [ [[3, -2, -2, -2], [3, -2, 3]], {[[3, -2, -2, -2, 3], [3, -2, 3]], [[3, -2, -2, -2, -2], [3, -2, 3]]}], [ [[-2, -2, 3, -2], [3, 3]], {[[-2, -2, 3, -2, 3], [3, 3]], [[-2, -2, 3, -2, -2], [3, 3]]}], [ [[3], [3, -2, -2, 3]], {[[3, 3], [3, -2, -2, 3]], [[3, -2], [3, -2, -2, 3]]}], [ [[-2, 3, -2], [3, 3]], {[[-2, 3, -2, -2], [3, 3]], [[-2, 3, -2, 3], [3, 3]]}], [ [[], [-2, 3, -2, 3, -2]], {[[-2], [-2, 3, -2, 3, -2]], [[3], [-2, 3, -2, 3, -2]]}], [ [[-2, 3, -2, -2], [3, 3, -2]], {[[-2, 3, -2, -2, -2], [3, 3, -2]], [[-2, 3, -2, -2, 3], [3, 3, -2]]}], [[[], [3, -2, -2]], {[[], [-2, 3, -2, -2]], [[], [3, 3, -2, -2]]}], [[[], [3, -2, 3]], {[[3], [3, -2, 3]], [[-2], [3, -2, 3]]}], [[[], [-2, 3, -2]], {[[], [3, -2, 3, -2]], [[], [-2, -2, 3, -2]]}], [ [[3, -2, -2], [3, -2, 3]], {[[3, -2, -2, 3], [3, -2, 3]], [[3, -2, -2, -2], [3, -2, 3]]}], [ [[3], [3, 3, -2, -2]], {[[3, 3], [3, 3, -2, -2]], [[3, -2], [3, 3, -2, -2]]}], [[[], [-2, -2]], {[[], [-2, -2, -2]], [[], [3, -2, -2]]}], [[[], [-2, -2, -2]], {%1, [[], [-2, -2, -2, -2]]}], [[[-2], [3, -2, 3]], {[[-2], [3, 3, -2, 3]], [[-2], [-2, 3, -2, 3]]}], [ [[-2, -2, 3, -2, -2], [3, 3]], {[[-2, -2, 3, -2, -2, 3], [3, 3]], [[-2, -2, 3, -2, -2, -2], [3, 3]]}], [ [[3, -2, -2, -2], [3, 3, -2]], {[[3, -2, -2, -2, 3], [3, 3, -2]], [[3, -2, -2, -2, -2], [3, 3, -2]]}], [[[], [3]], {[[], [-2, 3]], [[], [3, 3]]}], [[[], [3, -2]], {[[], [3, 3, -2]], [[], [-2, 3, -2]]}], [ [[-2, -2, 3, -2, -2, -2], [3, 3]], { [[-2, -2, 3, -2, -2, -2, 3], [3, 3]], [[-2, -2, 3, -2, -2, -2, -2], [3, 3]] }], [[[3], [3, 3, -2]], {[[3, 3], [3, 3, -2]], [[3, -2], [3, 3, -2]]}], [ [[-2, 3, -2, -2], [3, 3, -2, 3]], {[[-2, 3, -2, -2, 3], [3, 3, -2, 3]], [[-2, 3, -2, -2, -2], [3, 3, -2, 3]]} ], [[[3], [3, 3]], {[[3, 3], [3, 3]], [[3, -2], [3, 3]]}], [ [[], [3, -2, -2, -2, 3]], {[[], [3, 3, -2, -2, -2, 3]], [[], [-2, 3, -2, -2, -2, 3]]}], [ [[-2, 3, -2, -2], [3, 3]], {[[-2, 3, -2, -2, 3], [3, 3]], [[-2, 3, -2, -2, -2], [3, 3]]}], [ [[-2, 3, -2], [3, 3, -2]], {[[-2, 3, -2, 3], [3, 3, -2]], [[-2, 3, -2, -2], [3, 3, -2]]}], [ [[-2], [-2, -2, 3, -2, 3, -2]], {[[-2], [3, -2, -2, 3, -2, 3, -2]], [[-2], [-2, -2, -2, 3, -2, 3, -2]]}], [ [[-2], [-2, 3, -2, -2, 3]], {[[-2], [3, -2, 3, -2, -2, 3]], [[-2], [-2, -2, 3, -2, -2, 3]]}], [ [[-2, 3], [3, 3, -2, 3]], {[[-2, 3, -2], [3, 3, -2, 3]], [[-2, 3, 3], [3, 3, -2, 3]]}], [ [[3, -2], [3, 3, -2]], {[[3, -2, 3], [3, 3, -2]], [[3, -2, -2], [3, 3, -2]]}], [ [[3, -2, -2], [3, 3, -2, -2]], {[[3, -2, -2, 3], [3, 3, -2, -2]], [[3, -2, -2, -2], [3, 3, -2, -2]]}], [[[-2], [3, 3, -2]], {[[-2, 3], [3, 3, -2]], [[-2, -2], [3, 3, -2]]}], [ [[3, -2], [3, 3, -2, -2]], {[[3, -2, 3], [3, 3, -2, -2]], [[3, -2, -2], [3, 3, -2, -2]]}], [[[3, -2], [3, 3]], {[[3, -2, 3], [3, 3]], [[3, -2, -2], [3, 3]]}], [[[], []], {[[], [-2]], [[], [3]]}], [%1, {[[], [3, 3, -2, -2, -2]], [[], [-2, 3, -2, -2, -2]]}], [ [[3, -2, -2], [3, 3, -2, 3, -2]], {[[3, -2, -2, 3], [3, 3, -2, 3, -2]], [[3, -2, -2, -2], [3, 3, -2, 3, -2]]} ], [[[], [-2, 3]], {[[], [-2, -2, 3]], [[], [3, -2, 3]]}], [[[], [3, -2, 3, -2]], {[[], [3, 3, -2, 3, -2]], [[], [-2, 3, -2, 3, -2]]}] , [[[], [-2, -2, -2, 3]], {[[], [3, -2, -2, -2, 3]], [[], [-2, -2, -2, -2, 3]]}], [ [[-2], [-2, 3, -2, 3, -2]], {[[-2], [3, -2, 3, -2, 3, -2]], [[-2], [-2, -2, 3, -2, 3, -2]]}], [ [[], [3, 3, -2, 3, -2]], {[[3], [3, 3, -2, 3, -2]], [[-2], [3, 3, -2, 3, -2]]}], [ [[-2], [-2, 3, -2, 3]], {[[-2, 3], [-2, 3, -2, 3]], [[-2, -2], [-2, 3, -2, 3]]}], [ [[3, -2, -2], [3, 3, -2]], {[[3, -2, -2, 3], [3, 3, -2]], [[3, -2, -2, -2], [3, 3, -2]]}], [ [[3, -2], [3, 3, -2, 3, -2]], {[[3, -2, 3], [3, 3, -2, 3, -2]], [[3, -2, -2], [3, 3, -2, 3, -2]]}], [ [[-2, 3], [3, 3, -2]], {[[-2, 3, -2], [3, 3, -2]], [[-2, 3, 3], [3, 3, -2]]}], [ [[], [-2, -2, 3, -2]], {[[], [3, -2, -2, 3, -2]], [[], [-2, -2, -2, 3, -2]]}], [[[], [-2, -2, 3]], {[[], [3, -2, -2, 3]], [[], [-2, -2, -2, 3]]}], [ [[-2, -2, 3], [3, 3]], {[[-2, -2, 3, 3], [3, 3]], [[-2, -2, 3, -2], [3, 3]]}], [ [[-2, 3, -2, -2, -2], [3, 3, -2, 3]], { [[-2, 3, -2, -2, -2, 3], [3, 3, -2, 3]], [[-2, 3, -2, -2, -2, -2], [3, 3, -2, 3]]}], [[[-2], [3, 3, -2, 3]], {[[-2, 3], [3, 3, -2, 3]], [[-2, -2], [3, 3, -2, 3]]}], [ [[], [3, -2, 3, -2, -2]], {[[], [-2, 3, -2, 3, -2, -2]], [[], [3, 3, -2, 3, -2, -2]]}], [[[], [3, 3, -2, -2]], {[[3], [3, 3, -2, -2]], [[-2], [3, 3, -2, -2]]}], [ [[-2, 3, -2, -2, -2], [3, 3, -2]], { [[-2, 3, -2, -2, -2, 3], [3, 3, -2]], [[-2, 3, -2, -2, -2, -2], [3, 3, -2]] }], [[[-2], [3, 3]], {[[-2, 3], [3, 3]], [[-2, -2], [3, 3]]}], [ [[3, -2, -2, -2], [3, -2, -2, 3]], { [[3, -2, -2, -2, 3], [3, -2, -2, 3]], [[3, -2, -2, -2, -2], [3, -2, -2, 3]] }]}, {[[[-2], [3, -2, 3, -2, 3, -2]], [[], [3, -2]]], [[[-2, -2], [3, 3, -2]], [[], []]], [[[-2, -2, 3, 3], [3, 3]], {}], [[[-2, 3, -2, -2, -2, -2], [3, 3, -2]], %1], [[[], [3, -2, 3, -2, -2, 3, -2]], [[], [3, -2]]], [[[-2], [3, 3, -2, 3, -2]], [[], [3]]], [[[-2, -2, 3, -2, -2, -2, -2], [3, 3]], %1], [[[-2, -2], [3, -2, -2, 3, -2, 3]], [[], [3, -2, -2]]], [[[3, -2, -2, 3], [3, -2, 3]], {}], [[[-2, 3, -2, -2, 3], [3, 3, -2]], {}], [[[-2, 3, -2, -2, 3], [3, 3]], {}], [[[-2, 3, -2, 3], [3, 3]], {}], [[[], [-2, -2, 3, -2, -2, 3, -2]], {}], [[[3, 3], [3, 3, -2, -2]], {}], [[[-2], [3, 3, -2, -2, 3]], [[], [3]]], [[[-2, 3, -2, -2, -2, 3], [3, 3, -2]], {}], [[[], [3, 3, -2, -2, -2, 3]], [[], [3]]], [[[3, -2, -2, -2, -2], [3, -2, -2, 3]], %1], [[[], [-2, 3, -2, -2, -2, 3]], {}], [[[3, -2, -2, -2, 3], [3, 3, -2, -2]], {}], [[[], [-2, -2, -2, 3, -2, 3, -2, -2]], {}], [[[-2, 3, 3], [3, 3]], {}], [[[3, -2, -2, 3], [3, -2, -2, 3]], {}], [[[-2, -2], [3, -2, 3, -2, 3]], [[], [3, -2]]], [[[3], [-2, 3, -2, 3, -2]], {}], [[[], [3, -2, -2, 3, -2, 3, -2, -2]], [[], [3, -2, -2]]], [[[3, 3], [3, 3, -2, 3, -2]], {}], [[[-2, 3, 3], [3, 3, -2, 3]], {}], [[[-2, 3, -2, 3], [3, 3, -2]], {}], [[[3, -2, 3], [3, -2, -2, 3]], {}], [[[3, -2, 3], [3, 3]], {}], [[[-2, -2], [3, 3, -2, 3]], [[], [3]]], [[[-2, 3, -2, -2, -2, 3], [3, 3, -2, 3]], {}], [[[-2, -2, 3, -2, -2, -2, 3], [3, 3]], {}], [[[-2, 3, -2, -2, -2, -2], [3, 3]], [[], [3, -2, -2]]], [[[-2], [3, -2, -2, 3, -2, 3, -2]], [[], [3, -2, -2]]], [[[-2], [-2, -2, -2, 3, -2, 3, -2]], {}], [[[-2], [3, 3, -2, -2]], [[], []]], [[[], [3, 3, -2, -2, 3, -2]], [[], [3]]], [[[3, -2, 3], [3, 3, -2, 3, -2]], {}], [[[3, -2, -2, -2, 3], [3, -2, -2, 3]], {}], [[[3, -2, 3], [3, 3, -2]], {}], [[[3, -2, -2, -2, -2], [3, 3, -2, -2]], %1], [[[3, -2, 3], [3, -2, 3]], {}], [[[], [3, -2, 3, -2, 3, -2, -2]], [[], [3, -2]]], [[[3, -2, -2, -2, -2], [3, 3, -2]], [[], [3, -2, -2]]], [[[3, -2, -2, 3], [3, 3, -2]], {}], [[[-2, 3, -2, -2, 3], [3, 3, -2, 3]], {}], [[[], [-2, -2, -2, -2, 3]], {}], [[[], [3, 3, -2, -2, -2]], [[], []]], [[[], [-2, -2, 3, -2, -2]], {}], [[[-2, 3, 3], [3, 3, -2]], {}], [[[-2, -2, 3, -2, 3], [3, 3]], {}], [[[3, -2, -2, 3], [3, 3, -2, -2]], {}], [[[], [3, 3, -2, 3, -2, -2]], [[], [3]]], [[[3, -2, -2, 3], [3, 3]], {}], [[[3, 3], [3, -2, 3]], {}], [[[3, -2, -2, -2, -2], [3, 3]], [[], [3, -2]]], [[[3, -2, -2, -2, -2], [3, -2, 3]], [[], [3, -2, -2]]], [[[3, -2, -2, -2, 3], [3, 3]], {}], [[[3, 3], [3, 3, -2]], {}], [[[-2, 3, -2, 3], [3, 3, -2, 3]], {}], [[[], [-2, -2, -2, 3, -2]], {}], [[[-2, 3], [-2, 3, -2, 3]], {}], [[[3, -2, -2, -2, 3], [3, 3, -2, 3, -2]], {}], [[[3, -2, -2, -2, -2], [3, 3, -2, 3, -2]], [[], []]], [[[-2, -2], [-2, -2, -2, 3, -2, 3]], {}], [[[-2], [3, -2, 3, -2, -2, 3]], [[], [3, -2]]], [[[-2], [-2, -2, 3, -2, -2, 3]], {}], [[[-2, 3, -2, -2, -2, -2], [3, 3, -2, 3]], [[], []]], [[[3, -2, -2, 3], [3, 3, -2, 3, -2]], {}], [[[3, 3], [3, -2, -2, 3]], {}], [[[], [-2, 3, -2, -2, -2]], {}], [[[3, -2, -2, -2, 3], [3, -2, 3]], {}], [[[3, -2, -2, -2, 3], [3, 3, -2]], {}], [[[3, -2, 3], [3, 3, -2, -2]], {}], [[[-2, -2, 3, -2, -2, 3], [3, 3]], {}], [[[3, 3], [3, 3]], {}], [[[-2, -2, -2], [3, 3]], [[], []]], [[[], [-2, -2, -2, -2]], {}], [[[-2, 3, -2, -2, -2, 3], [3, 3]], {}]}], {[[], []], [[], [3, -2, 3, -2, -2]], [[-2], [-2, 3, -2, 3]], [[], [3, -2, -2, -2, 3]], [[-2], [3, -2, -2, 3]], [[], [3, -2, -2, 3, -2]], [[], [-2, 3, -2, 3, -2]]} ] %1 := [[], [3, -2, -2, -2]] This grammar is , true 1 The weight-enumerator for Loehr-Warrington words is, - ---------- 5 -1 + 10 x The whole thing took, 30.322, second.