/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /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) = 6x0, [size](x0) = x0, [bs](x0) = 4x0 + 3, [max](x0) = 2x0, [min](x0) = 4x0, [n](x0, x1, x2) = 2x0 + 5x1 + 5x2 + 4, [val](x0) = 2x0, [l](x0) = 4x0 + 3, [ge](x0, x1) = 4x0 + 4x1, [if](x0, x1, x2) = x0 + 2x1 + x2 + 1, [and](x0, x1) = x0 + x1 + 2, [true] = 0, [not](x0) = 4x0, [false] = 0, [-](x0, x1) = x0 + 2x1, [1](x0) = 4x0, [+](x0, x1) = x0 + x1, [0](x0) = 4x0, [#] = 0 orientation: 0(#()) = 0 >= 0 = #() +(x,#()) = x >= x = x +(#(),x) = x >= x = x +(0(x),0(y)) = 4x + 4y >= 4x + 4y = 0(+(x,y)) +(0(x),1(y)) = 4x + 4y >= 4x + 4y = 1(+(x,y)) +(1(x),0(y)) = 4x + 4y >= 4x + 4y = 1(+(x,y)) +(1(x),1(y)) = 4x + 4y >= 4x + 4y = 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),0(y)) = 4x + 8y >= 4x + 8y = 0(-(x,y)) -(0(x),1(y)) = 4x + 8y >= 4x + 8y = 1(-(-(x,y),1(#()))) -(1(x),0(y)) = 4x + 8y >= 4x + 8y = 1(-(x,y)) -(1(x),1(y)) = 4x + 8y >= 4x + 8y = 0(-(x,y)) not(false()) = 0 >= 0 = true() not(true()) = 0 >= 0 = false() and(x,true()) = x + 2 >= x = x and(x,false()) = x + 2 >= 0 = false() if(true(),x,y) = 2x + y + 1 >= x = x if(false(),x,y) = 2x + y + 1 >= y = y ge(0(x),0(y)) = 16x + 16y >= 4x + 4y = ge(x,y) ge(0(x),1(y)) = 16x + 16y >= 16x + 16y = not(ge(y,x)) ge(1(x),0(y)) = 16x + 16y >= 4x + 4y = ge(x,y) ge(1(x),1(y)) = 16x + 16y >= 4x + 4y = ge(x,y) ge(x,#()) = 4x >= 0 = true() ge(#(),1(x)) = 16x >= 0 = false() ge(#(),0(x)) = 16x >= 4x = ge(#(),x) val(l(x)) = 8x + 6 >= x = x val(n(x,y,z)) = 4x + 10y + 10z + 8 >= x = x min(l(x)) = 16x + 12 >= x = x min(n(x,y,z)) = 8x + 20y + 20z + 16 >= 4y = min(y) max(l(x)) = 8x + 6 >= x = x max(n(x,y,z)) = 4x + 10y + 10z + 8 >= 2z = max(z) bs(l(x)) = 16x + 15 >= 0 = true() bs(n(x,y,z)) = 8x + 20y + 20z + 19 >= 8x + 12y + 20z + 12 = and(and(ge(x,max(y)),ge(min(z),x)),and(bs(y),bs(z))) size(l(x)) = 4x + 3 >= 0 = 1(#()) size(n(x,y,z)) = 2x + 5y + 5z + 4 >= x + y = +(+(size(x),size(y)),1(#())) wb(l(x)) = 24x + 18 >= 0 = true() wb(n(x,y,z)) = 12x + 30y + 30z + 24 >= 26y + 30z + 5 = 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=1 interpretation: [ge](x0, x1) = x0 + x1 + 4, [true] = 0, [not](x0) = x0, [false] = 0, [-](x0, x1) = x0 + x1, [1](x0) = x0, [+](x0, x1) = x0 + 4x1, [0](x0) = x0, [#] = 0 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) = 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() ge(0(x),0(y)) = x + y + 4 >= x + y + 4 = ge(x,y) ge(0(x),1(y)) = x + y + 4 >= x + y + 4 = not(ge(y,x)) ge(1(x),0(y)) = x + y + 4 >= x + y + 4 = ge(x,y) ge(1(x),1(y)) = x + y + 4 >= x + y + 4 = ge(x,y) ge(x,#()) = x + 4 >= 0 = true() ge(#(),1(x)) = x + 4 >= 0 = false() ge(#(),0(x)) = x + 4 >= x + 4 = 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() 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: [ge](x0, x1) = x0 + x1, [true] = 2, [not](x0) = 2x0, [false] = 1, [-](x0, x1) = x0 + x1, [1](x0) = 2x0, [+](x0, x1) = x0 + 2x1, [0](x0) = 2x0, [#] = 0 orientation: 0(#()) = 0 >= 0 = #() +(x,#()) = x >= x = x +(#(),x) = 2x >= x = x +(0(x),0(y)) = 2x + 4y >= 2x + 4y = 0(+(x,y)) +(0(x),1(y)) = 2x + 4y >= 2x + 4y = 1(+(x,y)) +(1(x),0(y)) = 2x + 4y >= 2x + 4y = 1(+(x,y)) +(1(x),1(y)) = 2x + 4y >= 2x + 4y = 0(+(+(x,y),1(#()))) +(x,+(y,z)) = x + 2y + 4z >= x + 2y + 2z = +(+(x,y),z) -(x,#()) = x >= x = x -(#(),x) = x >= 0 = #() -(0(x),0(y)) = 2x + 2y >= 2x + 2y = 0(-(x,y)) -(0(x),1(y)) = 2x + 2y >= 2x + 2y = 1(-(-(x,y),1(#()))) -(1(x),0(y)) = 2x + 2y >= 2x + 2y = 1(-(x,y)) -(1(x),1(y)) = 2x + 2y >= 2x + 2y = 0(-(x,y)) not(false()) = 2 >= 2 = true() not(true()) = 4 >= 1 = false() ge(0(x),0(y)) = 2x + 2y >= x + y = ge(x,y) ge(0(x),1(y)) = 2x + 2y >= 2x + 2y = not(ge(y,x)) ge(1(x),0(y)) = 2x + 2y >= x + y = ge(x,y) ge(1(x),1(y)) = 2x + 2y >= x + y = ge(x,y) ge(#(),0(x)) = 2x >= x = 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=3 interpretation: [1 0 1] [1 1 0] [ge](x0, x1) = [1 1 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [true] = [0] [0], [1 0 0] [not](x0) = [0 0 0]x0 [0 0 1] , [1] [false] = [0] [1], [1 0 0] [-](x0, x1) = x0 + [0 0 0]x1 [0 0 0] , [1 1 0] [1](x0) = [0 0 1]x0 [0 0 1] , [+](x0, x1) = x0 + x1 , [1 1 0] [0](x0) = [0 0 1]x0 [0 0 1] , [0] [#] = [0] [0] orientation: [0] [0] 0(#()) = [0] >= [0] = #() [0] [0] +(x,#()) = x >= x = x +(#(),x) = x >= x = x [1 1 0] [1 1 0] [1 1 0] [1 1 0] +(0(x),0(y)) = [0 0 1]x + [0 0 1]y >= [0 0 1]x + [0 0 1]y = 0(+(x,y)) [0 0 1] [0 0 1] [0 0 1] [0 0 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] +(0(x),1(y)) = [0 0 1]x + [0 0 1]y >= [0 0 1]x + [0 0 1]y = 1(+(x,y)) [0 0 1] [0 0 1] [0 0 1] [0 0 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] +(1(x),0(y)) = [0 0 1]x + [0 0 1]y >= [0 0 1]x + [0 0 1]y = 1(+(x,y)) [0 0 1] [0 0 1] [0 0 1] [0 0 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] +(1(x),1(y)) = [0 0 1]x + [0 0 1]y >= [0 0 1]x + [0 0 1]y = 0(+(+(x,y),1(#()))) [0 0 1] [0 0 1] [0 0 1] [0 0 1] +(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 1 0] [1 1 0] [1 1 0] [1 0 0] -(0(x),0(y)) = [0 0 1]x + [0 0 0]y >= [0 0 1]x + [0 0 0]y = 0(-(x,y)) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 0 0] -(0(x),1(y)) = [0 0 1]x + [0 0 0]y >= [0 0 1]x + [0 0 0]y = 1(-(-(x,y),1(#()))) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 0 0] -(1(x),0(y)) = [0 0 1]x + [0 0 0]y >= [0 0 1]x + [0 0 0]y = 1(-(x,y)) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 0 0] -(1(x),1(y)) = [0 0 1]x + [0 0 0]y >= [0 0 1]x + [0 0 0]y = 0(-(x,y)) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [1] [0] not(false()) = [0] >= [0] = true() [1] [0] [1 1 1] [1 1 1] [1 0 1] [1 1 0] ge(0(x),0(y)) = [1 1 1]x + [0 0 0]y >= [1 1 0]x + [0 0 0]y = ge(x,y) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 1 1] [1 1 0] [1 0 1] ge(0(x),1(y)) = [1 1 1]x + [0 0 0]y >= [0 0 0]x + [0 0 0]y = not(ge(y,x)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 1 1] [1 0 1] [1 1 0] ge(1(x),0(y)) = [1 1 1]x + [0 0 0]y >= [1 1 0]x + [0 0 0]y = ge(x,y) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 1 1] [1 0 1] [1 1 0] ge(1(x),1(y)) = [1 1 1]x + [0 0 0]y >= [1 1 0]x + [0 0 0]y = ge(x,y) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 1 0] ge(#(),0(x)) = [0 0 0]x >= [0 0 0]x = ge(#(),x) [0 0 0] [0 0 0] 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: [ge](x0, x1) = x0 + x1, [not](x0) = x0 + 2, [-](x0, x1) = x0 + x1, [1](x0) = x0 + 1, [+](x0, x1) = x0 + 2x1, [0](x0) = x0 + 1, [#] = 0 orientation: 0(#()) = 1 >= 0 = #() +(x,#()) = x >= x = x +(#(),x) = 2x >= x = x +(0(x),0(y)) = x + 2y + 3 >= x + 2y + 1 = 0(+(x,y)) +(0(x),1(y)) = x + 2y + 3 >= x + 2y + 1 = 1(+(x,y)) +(1(x),0(y)) = x + 2y + 3 >= x + 2y + 1 = 1(+(x,y)) +(1(x),1(y)) = x + 2y + 3 >= x + 2y + 3 = 0(+(+(x,y),1(#()))) +(x,+(y,z)) = x + 2y + 4z >= x + 2y + 2z = +(+(x,y),z) -(x,#()) = x >= x = x -(#(),x) = x >= 0 = #() -(0(x),0(y)) = x + y + 2 >= x + y + 1 = 0(-(x,y)) -(0(x),1(y)) = x + y + 2 >= x + y + 2 = 1(-(-(x,y),1(#()))) -(1(x),0(y)) = x + y + 2 >= x + y + 1 = 1(-(x,y)) -(1(x),1(y)) = x + y + 2 >= x + y + 1 = 0(-(x,y)) ge(0(x),0(y)) = x + y + 2 >= x + y = ge(x,y) ge(0(x),1(y)) = x + y + 2 >= x + y + 2 = not(ge(y,x)) ge(1(x),0(y)) = x + y + 2 >= x + y = ge(x,y) ge(1(x),1(y)) = x + y + 2 >= x + y = ge(x,y) ge(#(),0(x)) = x + 1 >= x = 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: [ge](x0, x1) = x0 + x1, [not](x0) = x0 + 1, [-](x0, x1) = x0 + x1, [1](x0) = x0 + 1, [+](x0, x1) = x0 + x1, [0](x0) = x0 + 1, [#] = 0 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) = x >= 0 = #() -(0(x),1(y)) = x + y + 2 >= x + y + 2 = 1(-(-(x,y),1(#()))) ge(0(x),1(y)) = x + y + 2 >= x + y + 1 = 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(#()))) DP Processor: DPs: +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(x,+(y,z)) -> +#(x,y) +#(x,+(y,z)) -> +#(+(x,y),z) -#(0(x),1(y)) -> -#(x,y) -#(0(x),1(y)) -> -#(-(x,y),1(#())) TRS: +(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(#()))) TDG Processor: DPs: +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(x,+(y,z)) -> +#(x,y) +#(x,+(y,z)) -> +#(+(x,y),z) -#(0(x),1(y)) -> -#(x,y) -#(0(x),1(y)) -> -#(-(x,y),1(#())) TRS: +(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(#()))) graph: -#(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) -#(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(x),1(y)) -> +#(+(x,y),1(#())) -> +#(x,+(y,z)) -> +#(+(x,y),z) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(x,+(y,z)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(1(x),1(y)) -> +#(+(x,y),1(#())) -> +#(1(x),1(y)) -> +#(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) +#(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) +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z) +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(x,y) +#(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) -> +#(x,+(y,z)) -> +#(+(x,y),z) +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y) +#(x,+(y,z)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(x,+(y,z)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) SCC Processor: #sccs: 2 #rules: 6 #arcs: 20/36 DPs: +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(1(x),1(y)) -> +#(x,y) +#(x,+(y,z)) -> +#(x,y) +#(x,+(y,z)) -> +#(+(x,y),z) TRS: +(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(#()))) EDG Processor: DPs: +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(1(x),1(y)) -> +#(x,y) +#(x,+(y,z)) -> +#(x,y) +#(x,+(y,z)) -> +#(+(x,y),z) TRS: +(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(#()))) graph: +#(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),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(1(x),1(y)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y) +#(1(x),1(y)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z) +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(1(x),1(y)) -> +#(x,y) +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(x,y) +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z) +#(x,+(y,z)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(x,y) +#(x,+(y,z)) -> +#(x,y) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y) +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z) Bounds Processor: bound: 1 enrichment: match-dp automaton: final states: {6} transitions: +{#,1}(13,13) -> 6* +0(13,13) -> 7* +0(7,7) -> 7* +0(7,13) -> 7* 10(13) -> 7* #0() -> 13* f210() -> 7* 00(7) -> 7* +{#,0}(7,7) -> 6* +{#,0}(7,13) -> 6* 13 -> 7* problem: DPs: +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(x,+(y,z)) -> +#(x,y) +#(x,+(y,z)) -> +#(+(x,y),z) TRS: +(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(#()))) SCC Processor: #sccs: 2 #rules: 3 #arcs: 14/9 DPs: +#(x,+(y,z)) -> +#(+(x,y),z) +#(x,+(y,z)) -> +#(x,y) TRS: +(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(#()))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {4,1} transitions: +0(11,6) -> 12* +0(2,5) -> 11* +0(3,2) -> 3* +0(3,6) -> 7* +0(2,2) -> 3* 10(5) -> 6* #0() -> 5* 00(12) -> 7* 00(7) -> 3* f330() -> 2* +{#,0}(3,2) -> 1* +{#,0}(2,2) -> 4* 1 -> 4* 2 -> 11,3 5 -> 11* 6 -> 12,7 7 -> 12* problem: DPs: TRS: +(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(#()))) Qed DPs: +#(1(x),1(y)) -> +#(+(x,y),1(#())) TRS: +(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(#()))) Usable Rule Processor: DPs: +#(1(x),1(y)) -> +#(+(x,y),1(#())) TRS: +(x,#()) -> x +(#(),x) -> x +(1(x),1(y)) -> 0(+(+(x,y),1(#()))) +(x,+(y,z)) -> +(+(x,y),z) Semantic Labeling Processor: dimension: 1 usable rules: interpretation: [1](x0) = x0 + 1, [+](x0, x1) = x0 + x1, [0](x0) = 0, [#] = 0 labeled: +# usable (for model): +# 1 + # 0 argument filtering: pi(#) = [] pi(0) = 0 pi(+) = [] pi(1) = [] pi(+#) = [] precedence: +# ~ 1 ~ + ~ 0 ~ # problem: DPs: TRS: +(x,#()) -> x +(#(),x) -> x +(1(x),1(y)) -> 0(+(+(x,y),1(#()))) +(x,+(y,z)) -> +(+(x,y),z) Qed DPs: -#(0(x),1(y)) -> -#(-(x,y),1(#())) -#(0(x),1(y)) -> -#(x,y) TRS: +(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(#()))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {6} transitions: -{#,0}(7,8) -> 6* -{#,0}(7,7) -> 6* -0(7,8) -> 7* -0(7,7) -> 7* 10(7) -> 7* 10(8) -> 7* #0() -> 8* f500() -> 7* 8 -> 7* problem: DPs: -#(0(x),1(y)) -> -#(-(x,y),1(#())) TRS: +(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(#()))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {1} transitions: 10(7) -> 5* 10(2) -> 3* #0() -> 7,2 -{#,0}(5,3) -> 1* -0(4,2) -> 5* -0(4,4) -> 5* -0(5,3) -> 7* f540() -> 4* 2 -> 5* 4 -> 5* 5 -> 7* problem: DPs: TRS: +(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(#()))) Qed