(* "The two-loop helicity amplitudes for qqb' -> V1V2 -> 4 leptons"
 * T. Gehrmann, A. von Manteuffel, L. Tancredi
 *
 * This file contains the relations between crossed variants of the
 * master integrals M[] defined in the file "vvpmasters_def.m".
 * The crossings are given in eq. (4.8):
 *   x12 = \pi_{12} = p1 <-> p2  => { t<->u }
 *   x34 = \pi_{34} = p3 <-> p4  => { t<->u, ma2<->mb2 }.
 *)


{
M[f:Except[_String], r__] :> M[ToString[f], r],
M["addonx12", 1] -> M["addon", 1],
M["addonx12", 2] -> M["addon", 2],
M["addonx12", 3] -> M["addon", 3],
M["addonx12", 4] -> M["addon", 4],
M["addonx12", 7] -> M["addon", 7],
M["addonx12", 8] -> M["addon", 8],
M["addonx34", 1] -> M["addonx34x12", 1],
M["addonx34", 2] -> M["addonx34x12", 2],
M["addonx34", 3] -> M["addonx34x12", 3],
M["addonx34", 4] -> M["addonx34x12", 4],
M["addonx34", 5] -> M["addonx12", 6],
M["addonx34", 6] -> M["addonx12", 5],
M["addonx34", 7] -> M["addonx34x12", 7],
M["addonx34", 8] -> M["addonx34x12", 8],
M["addonx34x12", 1] -> M["addon", 2],
M["addonx34x12", 2] -> M["addon", 1],
M["addonx34x12", 3] -> M["addon", 4],
M["addonx34x12", 4] -> M["addon", 3],
M["addonx34x12", 5] -> M["addon", 6],
M["addonx34x12", 6] -> M["addon", 5],
M["addonx34x12", 7] -> M["addon", 8],
M["addonx34x12", 8] -> M["addon", 7],
M["P12x12", 2] -> M["P12", 2],
M["P12x12", 3] -> M["P12", 3],
M["P12x12", 4] -> M["P12", 4],
M["P12x12", 5] -> M["P12", 5],
M["P12x12", 6] -> M["P12", 6],
M["P12x12", 8] -> M["P12", 8],
M["P12x12", 9] -> M["P12", 9],
M["P12x12", 10] -> M["P12", 10],
M["P12x12", 12] -> M["P12", 12],
M["P12x12", 13] -> M["P12", 13],
M["P12x12", 14] -> M["P12", 14],
M["P12x12", 15] -> M["P12", 15],
M["P12x12", 16] -> M["P12", 16],
M["P12x12", 20] -> M["P12", 20],
M["P12x12", 23] -> M["P12", 23],
M["P12x12", 26] -> M["P12", 26],
M["P12x34", 1] -> M["P12x12", 1],
M["P12x34", 2] -> M["P12x34x12", 2],
M["P12x34", 3] -> M["P12x34x12", 3],
M["P12x34", 4] -> M["P12x34x12", 4],
M["P12x34", 5] -> M["P12x34x12", 5],
M["P12x34", 6] -> M["P12x34x12", 6],
M["P12x34", 7] -> M["P12x12", 11],
M["P12x34", 8] -> M["P12x34x12", 8],
M["P12x34", 9] -> M["P12x34x12", 9],
M["P12x34", 10] -> M["P12x34x12", 10],
M["P12x34", 11] -> M["P12x12", 7],
M["P12x34", 12] -> M["P12x34x12", 12],
M["P12x34", 13] -> M["P12x34x12", 13],
M["P12x34", 14] -> M["P12x34x12", 14],
M["P12x34", 15] -> M["P12x34x12", 15],
M["P12x34", 16] -> M["P12x34x12", 16],
M["P12x34", 17] -> M["P12x12", 17],
M["P12x34", 18] -> -M["P12x12", 21],
M["P12x34", 19] -> M["P12x12", 22],
M["P12x34", 20] -> M["P12x34x12", 20],
M["P12x34", 21] -> -M["P12x12", 18],
M["P12x34", 22] -> M["P12x12", 19],
M["P12x34", 23] -> M["P12x34x12", 23],
M["P12x34", 24] -> M["P12x12", 24],
M["P12x34", 25] -> M["P12x12", 25],
M["P12x34", 26] -> M["P12x34x12", 26],
M["P12x34", 27] -> M["P12x12", 28],
M["P12x34", 28] -> M["P12x12", 27],
M["P12x34", 29] -> M["P12x12", 29],
M["P12x34", 30] -> M["P12x12", 30],
M["P12x34", 31] -> M["P12x12", 31],
M["P12x34x12", 1] -> M["P12", 1],
M["P12x34x12", 2] -> M["P12", 3],
M["P12x34x12", 3] -> M["P12", 2],
M["P12x34x12", 4] -> M["P12", 4],
M["P12x34x12", 5] -> M["P12", 5],
M["P12x34x12", 6] -> M["P12", 2]/2 - M["P12", 3]/2 + M["P12", 6],
M["P12x34x12", 7] -> M["P12", 11],
M["P12x34x12", 8] -> M["P12", 12],
M["P12x34x12", 9] -> M["P12", 13],
M["P12x34x12", 10] -> M["P12", 14],
M["P12x34x12", 11] -> M["P12", 7],
M["P12x34x12", 12] -> M["P12", 8],
M["P12x34x12", 13] -> M["P12", 9],
M["P12x34x12", 14] -> M["P12", 10],
M["P12x34x12", 15] -> M["P12", 15],
M["P12x34x12", 16] -> M["P12", 16],
M["P12x34x12", 17] -> M["P12", 17],
M["P12x34x12", 18] -> -M["P12", 21],
M["P12x34x12", 19] -> M["P12", 22],
M["P12x34x12", 20] -> M["P12", 23],
M["P12x34x12", 21] -> -M["P12", 18],
M["P12x34x12", 22] -> M["P12", 19],
M["P12x34x12", 23] -> M["P12", 20],
M["P12x34x12", 24] -> M["P12", 24],
M["P12x34x12", 25] -> M["P12", 25],
M["P12x34x12", 26] -> M["P12", 26],
M["P12x34x12", 27] -> M["P12", 28],
M["P12x34x12", 28] -> M["P12", 27],
M["P12x34x12", 29] -> M["P12", 29],
M["P12x34x12", 30] -> M["P12", 30],
M["P12x34x12", 31] -> M["P12", 31],
M["P13x12", 12] -> M["P13", 12],
M["P13x12", 22] -> M["P13", 22],
M["P13x34", 7] -> M["P13x12", 14],
M["P13x34", 12] -> M["P13x34x12", 12],
M["P13x34", 13] -> M["P13x12", 15],
M["P13x34", 14] -> M["P13x12", 7],
M["P13x34", 15] -> M["P13x12", 13],
M["P13x34", 16] -> M["P13x12", 16],
M["P13x34", 17] -> M["P13x12", 24],
M["P13x34", 22] -> M["P13x34x12", 22],
M["P13x34", 23] -> M["P13x12", 25],
M["P13x34", 24] -> M["P13x12", 17],
M["P13x34", 25] -> M["P13x12", 23],
M["P13x34", 26] -> M["P13x12", 27],
M["P13x34", 27] -> M["P13x12", 26],
M["P13x34", 28] -> M["P13x12", 28],
M["P13x34", 29] -> (3*M["P12", 2])/4 - (3*M["P12", 3])/4 - M["P12x12", 7] + M["P12x12", 11] - M["P12x12", 19]/2 + M["P12x12", 22]/2 - 2*M["P13x12", 7] - M["P13x12", 13] + 2*M["P13x12", 14] + M["P13x12", 15] - M["P13x12", 17] + M["P13x12", 23] + M["P13x12", 24] - M["P13x12", 25] + M["P13x12", 29],
M["P13x34x12", 7] -> M["P13", 14],
M["P13x34x12", 12] -> M["P13", 12],
M["P13x34x12", 13] -> M["P13", 15],
M["P13x34x12", 14] -> M["P13", 7],
M["P13x34x12", 15] -> M["P13", 13],
M["P13x34x12", 16] -> M["P13", 16],
M["P13x34x12", 17] -> M["P13", 24],
M["P13x34x12", 22] -> M["P13", 22],
M["P13x34x12", 23] -> M["P13", 25],
M["P13x34x12", 24] -> M["P13", 17],
M["P13x34x12", 25] -> M["P13", 23],
M["P13x34x12", 26] -> M["P13", 27],
M["P13x34x12", 27] -> M["P13", 26],
M["P13x34x12", 28] -> M["P13", 28],
M["P13x34x12", 29] -> (3*M["P12", 2])/4 - (3*M["P12", 3])/4 - M["P12", 7] + M["P12", 11] - M["P12", 19]/2 + M["P12", 22]/2 - 2*M["P13", 7] - M["P13", 13] + 2*M["P13", 14] + M["P13", 15] - M["P13", 17] + M["P13", 23] + M["P13", 24] - M["P13", 25] + M["P13", 29],
M["P23x12", 16] -> M["P23", 16],
M["P23x12", 17] -> M["P23", 17],
M["P23x12", 18] -> 6*M["P12", 7] - 6*M["P12", 11] - 6*M["P12x12", 7] + 6*M["P12x12", 11] + M["P23", 18] - M["P23", 19] + M["P23", 20],
M["P23x12", 19] -> M["P23", 20],
M["P23x12", 20] -> M["P23", 19],
M["P23x12", 22] -> M["P23", 22],
M["P23x34", 15] -> M["P23x12", 23],
M["P23x34", 16] -> M["P23x34x12", 16],
M["P23x34", 17] -> M["P23x34x12", 17],
M["P23x34", 18] -> -6*M["P12x34", 7] + 6*M["P12x34", 11] + 6*M["P12x34x12", 7] - 6*M["P12x34x12", 11] + M["P23x34x12", 18] - M["P23x34x12", 19] + M["P23x34x12", 20],
M["P23x34", 19] -> M["P23x34x12", 20],
M["P23x34", 20] -> M["P23x34x12", 19],
M["P23x34", 22] -> M["P23x34x12", 22],
M["P23x34", 23] -> M["P23x12", 15],
M["P23x34", 25] -> M["P23x12", 26],
M["P23x34", 26] -> M["P23x12", 25],
M["P23x34", 27] -> M["P23x12", 27],
M["P23x34", 28] -> 3*M["P12", 2] - 3*M["P12", 3] - 4*M["P12x12", 7] + 4*M["P12x12", 11] - 8*M["P13x12", 7] - 4*M["P13x12", 13] + 8*M["P13x12", 14] + 4*M["P13x12", 15] + 4*M["P13x12", 23] - 4*M["P13x12", 25] + 2*M["P23x12", 15] - 2*M["P23x12", 23] - M["P23x12", 25] + M["P23x12", 26] + M["P23x12", 28],
M["P23x34x12", 15] -> M["P23", 23],
M["P23x34x12", 16] -> M["P23", 16],
M["P23x34x12", 17] -> M["P23", 17],
M["P23x34x12", 18] -> M["P23", 19],
M["P23x34x12", 19] -> M["P23", 18],
M["P23x34x12", 20] -> 6*M["P12", 7] - 6*M["P12", 11] - 6*M["P12x12", 7] + 6*M["P12x12", 11] + M["P23", 18] - M["P23", 19] + M["P23", 20],
M["P23x34x12", 22] -> M["P23", 22],
M["P23x34x12", 23] -> M["P23", 15],
M["P23x34x12", 25] -> M["P23", 26],
M["P23x34x12", 26] -> M["P23", 25],
M["P23x34x12", 27] -> M["P23", 27],
M["P23x34x12", 28] -> 3*M["P12", 2] - 3*M["P12", 3] - 4*M["P12", 7] + 4*M["P12", 11] - 8*M["P13", 7] - 4*M["P13", 13] + 8*M["P13", 14] + 4*M["P13", 15] + 4*M["P13", 23] - 4*M["P13", 25] + 2*M["P23", 15] - 2*M["P23", 23] - M["P23", 25] + M["P23", 26] + M["P23", 28],
M["N12x12", 28] -> M["N12", 28],
M["N12x12", 29] -> M["N12", 29],
M["N12x12", 30] -> M["N12", 30] - M["P12", 1]/8 + M["P12", 7]/2 + M["P12", 18]/2 - M["P12", 19]/4 + M["P12x12", 1]/8 - M["P12x12", 7]/2 - M["P12x12", 18]/2 + M["P12x12", 19]/4,
M["N12x12", 31] -> M["N12", 31],
M["N12x12", 32] -> M["N12", 32] - M["P12", 1]/8 + M["P12", 11]/2 - M["P12", 21]/2 - M["P12", 22]/4 + M["P12x12", 1]/8 - M["P12x12", 11]/2 + M["P12x12", 21]/2 + M["P12x12", 22]/4,
M["N12x12", 33] -> -M["N12", 34],
M["N12x12", 34] -> -M["N12", 33],
M["N12x12", 35] -> M["N12", 35],
M["N12x34", 28] -> M["N12x34x12", 28],
M["N12x34", 29] -> M["N12x34x12", 29],
M["N12x34", 30] -> M["N12x34x12", 30] + M["P12x34", 1]/8 - M["P12x34", 7]/2 - M["P12x34", 18]/2 + M["P12x34", 19]/4 - M["P12x34x12", 1]/8 + M["P12x34x12", 7]/2 + M["P12x34x12", 18]/2 - M["P12x34x12", 19]/4,
M["N12x34", 31] -> M["N12x34x12", 31],
M["N12x34", 32] -> M["N12x34x12", 32] + M["P12x34", 1]/8 - M["P12x34", 11]/2 + M["P12x34", 21]/2 + M["P12x34", 22]/4 - M["P12x34x12", 1]/8 + M["P12x34x12", 11]/2 - M["P12x34x12", 21]/2 - M["P12x34x12", 22]/4,
M["N12x34", 33] -> -M["N12x34x12", 34],
M["N12x34", 34] -> -M["N12x34x12", 33],
M["N12x34", 35] -> M["N12x34x12", 35],
M["N12x34x12", 28] -> M["N12", 28],
M["N12x34x12", 29] -> M["N12", 31],
M["N12x34x12", 30] -> M["N12", 32],
M["N12x34x12", 31] -> M["N12", 29],
M["N12x34x12", 32] -> M["N12", 30],
M["N12x34x12", 33] -> M["N12", 33],
M["N12x34x12", 34] -> M["N12", 34],
M["N12x34x12", 35] -> M["N12", 35],
M["N13x34", 35] -> M["N13", 35],
M["N13x34", 36] -> -M["N13", 36] + M["P13", 22] - M["P23", 16]/4,
M["N13x34", 37] -> -M["N13", 38],
M["N13x34", 38] -> -M["N13", 37],
M["N13x34x12", 35] -> M["N13x12", 35],
M["N13x34x12", 36] -> -M["N13x12", 36] + M["P13", 22] - M["P23", 16]/4,
M["N13x34x12", 37] -> -M["N13x12", 38],
M["N13x34x12", 38] -> -M["N13x12", 37],
M["N34x12", 47] -> M["N34", 47],
M["N34x12", 50] -> M["N34", 50],
M["N34x12", 51] -> -M["N34", 51],
M["N34x34", 47] -> M["N34x34x12", 47],
M["N34x34", 50] -> M["N34x34x12", 50],
M["N34x34", 51] -> -M["N34x34x12", 51],
M["N34x34x12", 47] -> M["N34", 47],
M["N34x34x12", 50] -> M["N34", 50],
M["N34x34x12", 51] -> M["N34", 51]
}