/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: 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))) Proof: Matrix Interpretation Processor: dim=1 interpretation: [wb](x0) = 4x0, [-](x0, x1) = x0 + x1, [max](x0) = x0, [and](x0, x1) = x0 + x1 + 4, [0](x0) = x0, [1](x0) = x0, [bs](x0) = 4x0, [size](x0) = 2x0, [false] = 0, [ge](x0, x1) = 4x0 + 4x1, [#] = 0, [true] = 0, [min](x0) = x0, [val](x0) = x0 + 4, [l](x0) = 4x0 + 7, [if](x0, x1, x2) = x0 + x1 + x2 + 4, [n](x0, x1, x2) = 4x0 + 7x1 + 7x2 + 3, [not](x0) = x0, [+](x0, x1) = x0 + x1 orientation: 0(#()) = 0 >= 0 = #() +(x,#()) = x >= x = x +(#(),x) = x >= x = x +(0(x),0(y)) = x + y >= x + y = 0(+(x,y)) +(0(x),1(y)) = x + y >= x + y = 1(+(x,y)) +(1(x),0(y)) = x + y >= x + y = 1(+(x,y)) +(1(x),1(y)) = x + y >= x + y = 0(+(+(x,y),1(#()))) +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z) -(x,#()) = x >= x = x -(#(),x) = x >= 0 = #() -(0(x),0(y)) = x + y >= x + y = 0(-(x,y)) -(0(x),1(y)) = x + y >= x + y = 1(-(-(x,y),1(#()))) -(1(x),0(y)) = x + y >= x + y = 1(-(x,y)) -(1(x),1(y)) = x + y >= x + y = 0(-(x,y)) not(false()) = 0 >= 0 = true() not(true()) = 0 >= 0 = false() and(x,true()) = x + 4 >= x = x and(x,false()) = x + 4 >= 0 = false() if(true(),x,y) = x + y + 4 >= x = x if(false(),x,y) = x + y + 4 >= y = y ge(0(x),0(y)) = 4x + 4y >= 4x + 4y = ge(x,y) ge(0(x),1(y)) = 4x + 4y >= 4x + 4y = not(ge(y,x)) ge(1(x),0(y)) = 4x + 4y >= 4x + 4y = ge(x,y) ge(1(x),1(y)) = 4x + 4y >= 4x + 4y = ge(x,y) ge(x,#()) = 4x >= 0 = true() ge(#(),1(x)) = 4x >= 0 = false() ge(#(),0(x)) = 4x >= 4x = ge(#(),x) val(l(x)) = 4x + 11 >= x = x val(n(x,y,z)) = 4x + 7y + 7z + 7 >= x = x min(l(x)) = 4x + 7 >= x = x min(n(x,y,z)) = 4x + 7y + 7z + 3 >= y = min(y) max(l(x)) = 4x + 7 >= x = x max(n(x,y,z)) = 4x + 7y + 7z + 3 >= z = max(z) bs(l(x)) = 16x + 28 >= 0 = true() bs(n(x,y,z)) = 16x + 28y + 28z + 12 >= 8x + 8y + 8z + 12 = and(and(ge(x,max(y)),ge(min(z),x)),and(bs(y),bs(z))) size(l(x)) = 8x + 14 >= 0 = 1(#()) size(n(x,y,z)) = 8x + 14y + 14z + 6 >= 2x + 2y = +(+(size(x),size(y)),1(#())) wb(l(x)) = 16x + 28 >= 0 = true() wb(n(x,y,z)) = 16x + 28y + 28z + 12 >= 28y + 28z + 12 = and(if(ge(size(y),size(z)),ge(1(#()),-(size(y),size(z))),ge(1(#()),-( size(z), size (y)))), and(wb(y),wb(z))) problem: 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() 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) 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)) -> and(if(ge(size(y),size(z)),ge(1(#()),-(size(y),size(z))),ge(1(#()),-(size(z),size(y)))), and(wb(y),wb(z))) Matrix Interpretation Processor: dim=1 interpretation: [wb](x0) = 7x0, [-](x0, x1) = x0 + 2x1, [max](x0) = 2x0 + 2, [and](x0, x1) = x0 + x1, [0](x0) = x0, [1](x0) = x0, [bs](x0) = 4x0 + 4, [size](x0) = x0, [false] = 0, [ge](x0, x1) = 4x0 + 4x1, [#] = 0, [true] = 0, [min](x0) = 3x0, [if](x0, x1, x2) = 2x0 + x1 + x2, [n](x0, x1, x2) = 4x0 + 4x1 + 4x2 + 4, [not](x0) = x0, [+](x0, x1) = x0 + 4x1 orientation: 0(#()) = 0 >= 0 = #() +(x,#()) = x >= x = x +(#(),x) = 4x >= x = x +(0(x),0(y)) = x + 4y >= x + 4y = 0(+(x,y)) +(0(x),1(y)) = x + 4y >= x + 4y = 1(+(x,y)) +(1(x),0(y)) = x + 4y >= x + 4y = 1(+(x,y)) +(1(x),1(y)) = x + 4y >= x + 4y = 0(+(+(x,y),1(#()))) +(x,+(y,z)) = x + 4y + 16z >= x + 4y + 4z = +(+(x,y),z) -(x,#()) = x >= x = x -(#(),x) = 2x >= 0 = #() -(0(x),0(y)) = x + 2y >= x + 2y = 0(-(x,y)) -(0(x),1(y)) = x + 2y >= x + 2y = 1(-(-(x,y),1(#()))) -(1(x),0(y)) = x + 2y >= x + 2y = 1(-(x,y)) -(1(x),1(y)) = x + 2y >= x + 2y = 0(-(x,y)) not(false()) = 0 >= 0 = true() not(true()) = 0 >= 0 = false() ge(0(x),0(y)) = 4x + 4y >= 4x + 4y = ge(x,y) ge(0(x),1(y)) = 4x + 4y >= 4x + 4y = not(ge(y,x)) ge(1(x),0(y)) = 4x + 4y >= 4x + 4y = ge(x,y) ge(1(x),1(y)) = 4x + 4y >= 4x + 4y = ge(x,y) ge(x,#()) = 4x >= 0 = true() ge(#(),1(x)) = 4x >= 0 = false() ge(#(),0(x)) = 4x >= 4x = ge(#(),x) bs(n(x,y,z)) = 16x + 16y + 16z + 20 >= 8x + 12y + 16z + 16 = and(and(ge(x,max(y)),ge(min(z),x)),and(bs(y),bs(z))) wb(n(x,y,z)) = 28x + 28y + 28z + 28 >= 27y + 27z = and(if(ge(size(y),size(z)),ge(1(#()),-(size(y),size(z))),ge(1(#()),-( size(z), size (y)))), and(wb(y),wb(z))) problem: 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() 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) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [-](x0, x1) = x0 + [0 0 0]x1 [0 0 0] , [1 0 1] [0](x0) = [0 1 0]x0 [0 1 0] , [1 0 1] [1](x0) = [0 1 0]x0 [0 1 0] , [0] [false] = [0] [0], [1 1 0] [1 1 0] [1] [ge](x0, x1) = [1 1 0]x0 + [0 0 0]x1 + [0] [1 0 1] [0 0 0] [1], [0] [#] = [0] [0], [0] [true] = [0] [0], [1 0 0] [not](x0) = [0 0 0]x0 [0 0 0] , [+](x0, x1) = x0 + x1 orientation: [0] [0] 0(#()) = [0] >= [0] = #() [0] [0] +(x,#()) = x >= x = x +(#(),x) = x >= x = x [1 0 1] [1 0 1] [1 0 1] [1 0 1] +(0(x),0(y)) = [0 1 0]x + [0 1 0]y >= [0 1 0]x + [0 1 0]y = 0(+(x,y)) [0 1 0] [0 1 0] [0 1 0] [0 1 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] +(0(x),1(y)) = [0 1 0]x + [0 1 0]y >= [0 1 0]x + [0 1 0]y = 1(+(x,y)) [0 1 0] [0 1 0] [0 1 0] [0 1 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] +(1(x),0(y)) = [0 1 0]x + [0 1 0]y >= [0 1 0]x + [0 1 0]y = 1(+(x,y)) [0 1 0] [0 1 0] [0 1 0] [0 1 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] +(1(x),1(y)) = [0 1 0]x + [0 1 0]y >= [0 1 0]x + [0 1 0]y = 0(+(+(x,y),1(#()))) [0 1 0] [0 1 0] [0 1 0] [0 1 0] +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z) -(x,#()) = x >= x = x [1 0 0] [0] -(#(),x) = [0 0 0]x >= [0] = #() [0 0 0] [0] [1 0 1] [1 0 1] [1 0 1] [1 0 0] -(0(x),0(y)) = [0 1 0]x + [0 0 0]y >= [0 1 0]x + [0 0 0]y = 0(-(x,y)) [0 1 0] [0 0 0] [0 1 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 0] -(0(x),1(y)) = [0 1 0]x + [0 0 0]y >= [0 1 0]x + [0 0 0]y = 1(-(-(x,y),1(#()))) [0 1 0] [0 0 0] [0 1 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 0] -(1(x),0(y)) = [0 1 0]x + [0 0 0]y >= [0 1 0]x + [0 0 0]y = 1(-(x,y)) [0 1 0] [0 0 0] [0 1 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 0] -(1(x),1(y)) = [0 1 0]x + [0 0 0]y >= [0 1 0]x + [0 0 0]y = 0(-(x,y)) [0 1 0] [0 0 0] [0 1 0] [0 0 0] [0] [0] not(false()) = [0] >= [0] = true() [0] [0] [0] [0] not(true()) = [0] >= [0] = false() [0] [0] [1 1 1] [1 1 1] [1] [1 1 0] [1 1 0] [1] ge(0(x),0(y)) = [1 1 1]x + [0 0 0]y + [0] >= [1 1 0]x + [0 0 0]y + [0] = ge(x,y) [1 1 1] [0 0 0] [1] [1 0 1] [0 0 0] [1] [1 1 1] [1 1 1] [1] [1 1 0] [1 1 0] [1] ge(0(x),1(y)) = [1 1 1]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = not(ge(y,x)) [1 1 1] [0 0 0] [1] [0 0 0] [0 0 0] [0] [1 1 1] [1 1 1] [1] [1 1 0] [1 1 0] [1] ge(1(x),0(y)) = [1 1 1]x + [0 0 0]y + [0] >= [1 1 0]x + [0 0 0]y + [0] = ge(x,y) [1 1 1] [0 0 0] [1] [1 0 1] [0 0 0] [1] [1 1 1] [1 1 1] [1] [1 1 0] [1 1 0] [1] ge(1(x),1(y)) = [1 1 1]x + [0 0 0]y + [0] >= [1 1 0]x + [0 0 0]y + [0] = ge(x,y) [1 1 1] [0 0 0] [1] [1 0 1] [0 0 0] [1] [1 1 0] [1] [0] ge(x,#()) = [1 1 0]x + [0] >= [0] = true() [1 0 1] [1] [0] [1 1 1] [1] [0] ge(#(),1(x)) = [0 0 0]x + [0] >= [0] = false() [0 0 0] [1] [0] [1 1 1] [1] [1 1 0] [1] ge(#(),0(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = ge(#(),x) [0 0 0] [1] [0 0 0] [1] problem: 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() 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(#(),0(x)) -> ge(#(),x) Matrix Interpretation Processor: dim=1 interpretation: [-](x0, x1) = x0 + 4x1, [0](x0) = 2x0, [1](x0) = 2x0, [false] = 2, [ge](x0, x1) = 4x0 + 4x1, [#] = 0, [true] = 4, [not](x0) = 2x0, [+](x0, x1) = x0 + x1 orientation: 0(#()) = 0 >= 0 = #() +(x,#()) = x >= x = x +(#(),x) = x >= x = x +(0(x),0(y)) = 2x + 2y >= 2x + 2y = 0(+(x,y)) +(0(x),1(y)) = 2x + 2y >= 2x + 2y = 1(+(x,y)) +(1(x),0(y)) = 2x + 2y >= 2x + 2y = 1(+(x,y)) +(1(x),1(y)) = 2x + 2y >= 2x + 2y = 0(+(+(x,y),1(#()))) +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z) -(x,#()) = x >= x = x -(#(),x) = 4x >= 0 = #() -(0(x),0(y)) = 2x + 8y >= 2x + 8y = 0(-(x,y)) -(0(x),1(y)) = 2x + 8y >= 2x + 8y = 1(-(-(x,y),1(#()))) -(1(x),0(y)) = 2x + 8y >= 2x + 8y = 1(-(x,y)) -(1(x),1(y)) = 2x + 8y >= 2x + 8y = 0(-(x,y)) not(false()) = 4 >= 4 = true() not(true()) = 8 >= 2 = false() ge(0(x),0(y)) = 8x + 8y >= 4x + 4y = ge(x,y) ge(0(x),1(y)) = 8x + 8y >= 8x + 8y = not(ge(y,x)) ge(1(x),0(y)) = 8x + 8y >= 4x + 4y = ge(x,y) ge(1(x),1(y)) = 8x + 8y >= 4x + 4y = ge(x,y) ge(#(),0(x)) = 8x >= 4x = ge(#(),x) problem: 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() 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(#(),0(x)) -> ge(#(),x) Matrix Interpretation Processor: dim=1 interpretation: [-](x0, x1) = x0 + 2x1, [0](x0) = x0, [1](x0) = x0, [false] = 2, [ge](x0, x1) = 4x0 + 4x1, [#] = 0, [true] = 0, [not](x0) = x0, [+](x0, x1) = x0 + 4x1 orientation: 0(#()) = 0 >= 0 = #() +(x,#()) = x >= x = x +(#(),x) = 4x >= x = x +(0(x),0(y)) = x + 4y >= x + 4y = 0(+(x,y)) +(0(x),1(y)) = x + 4y >= x + 4y = 1(+(x,y)) +(1(x),0(y)) = x + 4y >= x + 4y = 1(+(x,y)) +(1(x),1(y)) = x + 4y >= x + 4y = 0(+(+(x,y),1(#()))) +(x,+(y,z)) = x + 4y + 16z >= x + 4y + 4z = +(+(x,y),z) -(x,#()) = x >= x = x -(#(),x) = 2x >= 0 = #() -(0(x),0(y)) = x + 2y >= x + 2y = 0(-(x,y)) -(0(x),1(y)) = x + 2y >= x + 2y = 1(-(-(x,y),1(#()))) -(1(x),0(y)) = x + 2y >= x + 2y = 1(-(x,y)) -(1(x),1(y)) = x + 2y >= x + 2y = 0(-(x,y)) not(false()) = 2 >= 0 = true() ge(0(x),0(y)) = 4x + 4y >= 4x + 4y = ge(x,y) ge(0(x),1(y)) = 4x + 4y >= 4x + 4y = not(ge(y,x)) ge(1(x),0(y)) = 4x + 4y >= 4x + 4y = ge(x,y) ge(1(x),1(y)) = 4x + 4y >= 4x + 4y = ge(x,y) ge(#(),0(x)) = 4x >= 4x = ge(#(),x) problem: 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)) 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(#(),0(x)) -> ge(#(),x) Matrix Interpretation Processor: dim=1 interpretation: [-](x0, x1) = x0 + 4x1, [0](x0) = x0 + 1, [1](x0) = x0 + 1, [ge](x0, x1) = x0 + x1 + 6, [#] = 0, [not](x0) = x0 + 2, [+](x0, x1) = x0 + x1 orientation: 0(#()) = 1 >= 0 = #() +(x,#()) = x >= x = x +(#(),x) = x >= x = x +(0(x),0(y)) = x + y + 2 >= x + y + 1 = 0(+(x,y)) +(0(x),1(y)) = x + y + 2 >= x + y + 1 = 1(+(x,y)) +(1(x),0(y)) = x + y + 2 >= x + y + 1 = 1(+(x,y)) +(1(x),1(y)) = x + y + 2 >= x + y + 2 = 0(+(+(x,y),1(#()))) +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z) -(x,#()) = x >= x = x -(#(),x) = 4x >= 0 = #() -(0(x),0(y)) = x + 4y + 5 >= x + 4y + 1 = 0(-(x,y)) -(0(x),1(y)) = x + 4y + 5 >= x + 4y + 5 = 1(-(-(x,y),1(#()))) -(1(x),0(y)) = x + 4y + 5 >= x + 4y + 1 = 1(-(x,y)) -(1(x),1(y)) = x + 4y + 5 >= x + 4y + 1 = 0(-(x,y)) ge(0(x),0(y)) = x + y + 8 >= x + y + 6 = ge(x,y) ge(0(x),1(y)) = x + y + 8 >= x + y + 8 = not(ge(y,x)) ge(1(x),0(y)) = x + y + 8 >= x + y + 6 = ge(x,y) ge(1(x),1(y)) = x + y + 8 >= x + y + 6 = ge(x,y) ge(#(),0(x)) = x + 7 >= x + 6 = ge(#(),x) problem: +(x,#()) -> x +(#(),x) -> x +(1(x),1(y)) -> 0(+(+(x,y),1(#()))) +(x,+(y,z)) -> +(+(x,y),z) -(x,#()) -> x -(#(),x) -> #() -(0(x),1(y)) -> 1(-(-(x,y),1(#()))) ge(0(x),1(y)) -> not(ge(y,x)) Matrix Interpretation Processor: dim=1 interpretation: [-](x0, x1) = x0 + 2x1, [0](x0) = x0 + 1, [1](x0) = x0 + 1, [ge](x0, x1) = 6x0 + 6x1 + 1, [#] = 0, [not](x0) = x0 + 7, [+](x0, x1) = x0 + x1 orientation: +(x,#()) = x >= x = x +(#(),x) = x >= x = x +(1(x),1(y)) = x + y + 2 >= x + y + 2 = 0(+(+(x,y),1(#()))) +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z) -(x,#()) = x >= x = x -(#(),x) = 2x >= 0 = #() -(0(x),1(y)) = x + 2y + 3 >= x + 2y + 3 = 1(-(-(x,y),1(#()))) ge(0(x),1(y)) = 6x + 6y + 13 >= 6x + 6y + 8 = not(ge(y,x)) problem: +(x,#()) -> x +(#(),x) -> x +(1(x),1(y)) -> 0(+(+(x,y),1(#()))) +(x,+(y,z)) -> +(+(x,y),z) -(x,#()) -> x -(#(),x) -> #() -(0(x),1(y)) -> 1(-(-(x,y),1(#()))) WPO Processor: algebra: Sum weight function: w0 = 0 w(1) = w(0) = 1 w(-) = w(+) = w(#) = 0 status function: st(+) = [1, 0] st(-) = [0, 1] st(1) = st(0) = [0] st(#) = [] precedence: - ~ + > 1 ~ 0 ~ # problem: Qed