Using an approach first presented in this answerthis answer:
xf = ListInterpolation[x]; yf = ListInterpolation[y]; g1 = Plot3D[{xf[x, y], yf[x, y]}, {x, 1, 11}, {y, 1, 11}, AxesLabel -> {"a", "b", "z"}, Mesh -> None, PlotStyle -> Opacity[0.5]]; g2 = Plot3D[{xf[x, y], yf[x, y]}, {x, 1, 11}, {y, 1, 11}, BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> {Directive[Thick, Red]}}, Mesh -> None, PlotStyle -> None]; Show[g1, g2] 
Using an approach first presented in this answer:
xf = ListInterpolation[x]; yf = ListInterpolation[y]; g1 = Plot3D[{xf[x, y], yf[x, y]}, {x, 1, 11}, {y, 1, 11}, AxesLabel -> {"a", "b", "z"}, Mesh -> None, PlotStyle -> Opacity[0.5]]; g2 = Plot3D[{xf[x, y], yf[x, y]}, {x, 1, 11}, {y, 1, 11}, BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> {Directive[Thick, Red]}}, Mesh -> None, PlotStyle -> None]; Show[g1, g2]
Using an approach first presented in this answer:
xf = ListInterpolation[x]; yf = ListInterpolation[y]; g1 = Plot3D[{xf[x, y], yf[x, y]}, {x, 1, 11}, {y, 1, 11}, AxesLabel -> {"a", "b", "z"}, Mesh -> None, PlotStyle -> Opacity[0.5]]; g2 = Plot3D[{xf[x, y], yf[x, y]}, {x, 1, 11}, {y, 1, 11}, BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> {Directive[Thick, Red]}}, Mesh -> None, PlotStyle -> None]; Show[g1, g2]
Using an approach first presented in this answer:
xf = ListInterpolation[x]; yf = ListInterpolation[y]; g1 = Plot3D[{xf[x, y], yf[x, y]}, {x, 1, 11}, {y, 1, 11}, AxesLabel -> {"a", "b", "z"}, Mesh -> None, PlotStyle -> Opacity[0.5]]; g2 = Plot3D[{xf[x, y], yf[x, y]}, {x, 1, 11}, {y, 1, 11}, BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> {Directive[Thick, Red]}}, Mesh -> None, PlotStyle -> None]; Show[g1, g2]