/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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(true()) -> false() not(false()) -> true() 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(#(),0(x)) -> ge(#(),x) ge(#(),1(x)) -> false() log(x) -> -(log'(x),1(#())) log'(#()) -> #() log'(1(x)) -> +(log'(x),1(#())) log'(0(x)) -> if(ge(x,1(#())),+(log'(x),1(#())),#()) Proof: Matrix Interpretation Processor: dim=1 interpretation: [log'](x0) = x0 + 7, [log](x0) = x0 + 7, [ge](x0, x1) = x0 + x1, [if](x0, x1, x2) = 3x0 + x1 + x2, [false] = 0, [not](x0) = 4x0, [true] = 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) = 2x >= 0 = #() -(x,#()) = x >= x = x -(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(true()) = 0 >= 0 = false() not(false()) = 0 >= 0 = true() if(true(),x,y) = x + y >= x = x if(false(),x,y) = x + y >= y = y ge(0(x),0(y)) = 4x + 4y >= x + y = ge(x,y) ge(0(x),1(y)) = 4x + 4y >= 4x + 4y = not(ge(y,x)) ge(1(x),0(y)) = 4x + 4y >= x + y = ge(x,y) ge(1(x),1(y)) = 4x + 4y >= x + y = ge(x,y) ge(x,#()) = x >= 0 = true() ge(#(),0(x)) = 4x >= x = ge(#(),x) ge(#(),1(x)) = 4x >= 0 = false() log(x) = x + 7 >= x + 7 = -(log'(x),1(#())) log'(#()) = 7 >= 0 = #() log'(1(x)) = 4x + 7 >= x + 7 = +(log'(x),1(#())) log'(0(x)) = 4x + 7 >= 4x + 7 = if(ge(x,1(#())),+(log'(x),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(true()) -> false() not(false()) -> true() 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(#(),0(x)) -> ge(#(),x) ge(#(),1(x)) -> false() log(x) -> -(log'(x),1(#())) log'(1(x)) -> +(log'(x),1(#())) log'(0(x)) -> if(ge(x,1(#())),+(log'(x),1(#())),#()) Matrix Interpretation Processor: dim=1 interpretation: [log'](x0) = x0, [log](x0) = 4x0 + 4, [ge](x0, x1) = x0 + 2x1, [if](x0, x1, x2) = 2x0 + x1 + 4x2, [false] = 0, [not](x0) = x0, [true] = 0, [-](x0, x1) = x0 + 4x1, [1](x0) = 3x0, [+](x0, x1) = x0 + x1, [0](x0) = 3x0, [#] = 0 orientation: 0(#()) = 0 >= 0 = #() +(#(),x) = x >= x = x +(x,#()) = x >= x = x +(0(x),0(y)) = 3x + 3y >= 3x + 3y = 0(+(x,y)) +(0(x),1(y)) = 3x + 3y >= 3x + 3y = 1(+(x,y)) +(1(x),0(y)) = 3x + 3y >= 3x + 3y = 1(+(x,y)) +(1(x),1(y)) = 3x + 3y >= 3x + 3y = 0(+(+(x,y),1(#()))) +(+(x,y),z) = x + y + z >= x + y + z = +(x,+(y,z)) -(#(),x) = 4x >= 0 = #() -(x,#()) = x >= x = x -(0(x),0(y)) = 3x + 12y >= 3x + 12y = 0(-(x,y)) -(0(x),1(y)) = 3x + 12y >= 3x + 12y = 1(-(-(x,y),1(#()))) -(1(x),0(y)) = 3x + 12y >= 3x + 12y = 1(-(x,y)) -(1(x),1(y)) = 3x + 12y >= 3x + 12y = 0(-(x,y)) not(true()) = 0 >= 0 = false() not(false()) = 0 >= 0 = true() if(true(),x,y) = x + 4y >= x = x if(false(),x,y) = x + 4y >= y = y ge(0(x),0(y)) = 3x + 6y >= x + 2y = ge(x,y) ge(0(x),1(y)) = 3x + 6y >= 2x + y = not(ge(y,x)) ge(1(x),0(y)) = 3x + 6y >= x + 2y = ge(x,y) ge(1(x),1(y)) = 3x + 6y >= x + 2y = ge(x,y) ge(x,#()) = x >= 0 = true() ge(#(),0(x)) = 6x >= 2x = ge(#(),x) ge(#(),1(x)) = 6x >= 0 = false() log(x) = 4x + 4 >= x = -(log'(x),1(#())) log'(1(x)) = 3x >= x = +(log'(x),1(#())) log'(0(x)) = 3x >= 3x = if(ge(x,1(#())),+(log'(x),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(true()) -> false() not(false()) -> true() 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(#(),0(x)) -> ge(#(),x) ge(#(),1(x)) -> false() log'(1(x)) -> +(log'(x),1(#())) log'(0(x)) -> if(ge(x,1(#())),+(log'(x),1(#())),#()) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [0] [log'](x0) = [1 1 0]x0 + [0] [0 1 0] [1], [1 0 0] [1 0 0] [ge](x0, x1) = [1 0 0]x0 + [0 0 0]x1 [0 0 0] [1 0 0] , [1 0 0] [if](x0, x1, x2) = [0 0 0]x0 + x1 + x2 [0 0 0] , [0] [false] = [0] [0], [1 0 0] [not](x0) = [0 0 0]x0 [0 0 0] , [0] [true] = [0] [0], [1 0 0] [-](x0, x1) = x0 + [0 1 0]x1 [1 0 0] , [1 0 0] [0] [1](x0) = [1 1 0]x0 + [1] [0 0 0] [0], [+](x0, x1) = x0 + x1 , [1 0 0] [0] [0](x0) = [1 1 0]x0 + [1] [0 0 0] [0], [0] [#] = [0] [0] orientation: [0] [0] 0(#()) = [1] >= [0] = #() [0] [0] +(#(),x) = x >= x = x +(x,#()) = x >= x = x [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] +(0(x),0(y)) = [1 1 0]x + [1 1 0]y + [2] >= [1 1 0]x + [1 1 0]y + [1] = 0(+(x,y)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] +(0(x),1(y)) = [1 1 0]x + [1 1 0]y + [2] >= [1 1 0]x + [1 1 0]y + [1] = 1(+(x,y)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] +(1(x),0(y)) = [1 1 0]x + [1 1 0]y + [2] >= [1 1 0]x + [1 1 0]y + [1] = 1(+(x,y)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] +(1(x),1(y)) = [1 1 0]x + [1 1 0]y + [2] >= [1 1 0]x + [1 1 0]y + [2] = 0(+(+(x,y),1(#()))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] +(+(x,y),z) = x + y + z >= x + y + z = +(x,+(y,z)) [1 0 0] [0] -(#(),x) = [0 1 0]x >= [0] = #() [1 0 0] [0] -(x,#()) = x >= x = x [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] -(0(x),0(y)) = [1 1 0]x + [1 1 0]y + [2] >= [1 1 0]x + [1 1 0]y + [1] = 0(-(x,y)) [0 0 0] [1 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] -(0(x),1(y)) = [1 1 0]x + [1 1 0]y + [2] >= [1 1 0]x + [1 1 0]y + [2] = 1(-(-(x,y),1(#()))) [0 0 0] [1 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] -(1(x),0(y)) = [1 1 0]x + [1 1 0]y + [2] >= [1 1 0]x + [1 1 0]y + [1] = 1(-(x,y)) [0 0 0] [1 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] -(1(x),1(y)) = [1 1 0]x + [1 1 0]y + [2] >= [1 1 0]x + [1 1 0]y + [1] = 0(-(x,y)) [0 0 0] [1 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] not(true()) = [0] >= [0] = false() [0] [0] [0] [0] not(false()) = [0] >= [0] = true() [0] [0] if(true(),x,y) = x + y >= x = x if(false(),x,y) = x + y >= y = y [1 0 0] [1 0 0] [1 0 0] [1 0 0] ge(0(x),0(y)) = [1 0 0]x + [0 0 0]y >= [1 0 0]x + [0 0 0]y = ge(x,y) [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] ge(0(x),1(y)) = [1 0 0]x + [0 0 0]y >= [0 0 0]x + [0 0 0]y = not(ge(y,x)) [0 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] ge(1(x),0(y)) = [1 0 0]x + [0 0 0]y >= [1 0 0]x + [0 0 0]y = ge(x,y) [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] ge(1(x),1(y)) = [1 0 0]x + [0 0 0]y >= [1 0 0]x + [0 0 0]y = ge(x,y) [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [0] ge(x,#()) = [1 0 0]x >= [0] = true() [0 0 0] [0] [1 0 0] [1 0 0] ge(#(),0(x)) = [0 0 0]x >= [0 0 0]x = ge(#(),x) [1 0 0] [1 0 0] [1 0 0] [0] ge(#(),1(x)) = [0 0 0]x >= [0] = false() [1 0 0] [0] [2 1 0] [1] [1 1 0] [0] log'(1(x)) = [2 1 0]x + [1] >= [1 1 0]x + [1] = +(log'(x),1(#())) [1 1 0] [2] [0 1 0] [1] [2 1 0] [1] [2 1 0] [0] log'(0(x)) = [2 1 0]x + [1] >= [1 1 0]x + [1] = if(ge(x,1(#())),+(log'(x),1(#())),#()) [1 1 0] [2] [0 1 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(true()) -> false() not(false()) -> true() 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(#(),0(x)) -> ge(#(),x) ge(#(),1(x)) -> false() Matrix Interpretation Processor: dim=1 interpretation: [ge](x0, x1) = x0 + x1, [if](x0, x1, x2) = x0 + x1 + x2, [false] = 0, [not](x0) = x0 + 2, [true] = 0, [-](x0, x1) = x0 + x1, [1](x0) = x0 + 1, [+](x0, x1) = x0 + x1, [0](x0) = x0 + 1, [#] = 0 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 >= 0 = #() -(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 + 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)) not(true()) = 2 >= 0 = false() not(false()) = 2 >= 0 = true() if(true(),x,y) = x + y >= x = x if(false(),x,y) = x + y >= y = 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(x,#()) = x >= 0 = true() ge(#(),0(x)) = x + 1 >= x = ge(#(),x) ge(#(),1(x)) = x + 1 >= 0 = false() 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(#()))) if(true(),x,y) -> x if(false(),x,y) -> y ge(0(x),1(y)) -> not(ge(y,x)) ge(x,#()) -> true() Matrix Interpretation Processor: dim=1 interpretation: [ge](x0, x1) = x0 + x1, [if](x0, x1, x2) = 5x0 + x1 + 4x2 + 3, [false] = 3, [not](x0) = x0, [true] = 0, [-](x0, x1) = x0 + x1, [1](x0) = 2x0, [+](x0, x1) = x0 + x1, [0](x0) = 2x0, [#] = 0 orientation: +(#(),x) = x >= x = x +(x,#()) = x >= x = x +(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 >= 0 = #() -(x,#()) = x >= x = x -(0(x),1(y)) = 2x + 2y >= 2x + 2y = 1(-(-(x,y),1(#()))) if(true(),x,y) = x + 4y + 3 >= x = x if(false(),x,y) = x + 4y + 18 >= y = y ge(0(x),1(y)) = 2x + 2y >= x + y = not(ge(y,x)) ge(x,#()) = x >= 0 = true() 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)) ge(x,#()) -> true() Matrix Interpretation Processor: dim=1 interpretation: [ge](x0, x1) = 2x0 + 2x1 + 1, [not](x0) = x0, [true] = 0, [-](x0, x1) = x0 + x1, [1](x0) = 2x0, [+](x0, x1) = x0 + x1, [0](x0) = 2x0, [#] = 0 orientation: +(#(),x) = x >= x = x +(x,#()) = x >= x = x +(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 >= 0 = #() -(x,#()) = x >= x = x -(0(x),1(y)) = 2x + 2y >= 2x + 2y = 1(-(-(x,y),1(#()))) ge(0(x),1(y)) = 4x + 4y + 1 >= 2x + 2y + 1 = not(ge(y,x)) ge(x,#()) = 2x + 1 >= 0 = true() 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) = 2x0 + 2x1 + 1, [not](x0) = x0 + 7, [-](x0, x1) = x0 + 4x1, [1](x0) = x0 + 4, [+](x0, x1) = x0 + x1, [0](x0) = x0 + 4, [#] = 0 orientation: +(#(),x) = x >= x = x +(x,#()) = x >= x = x +(1(x),1(y)) = x + y + 8 >= x + y + 8 = 0(+(+(x,y),1(#()))) +(+(x,y),z) = x + y + z >= x + y + z = +(x,+(y,z)) -(#(),x) = 4x >= 0 = #() -(x,#()) = x >= x = x -(0(x),1(y)) = x + 4y + 20 >= x + 4y + 20 = 1(-(-(x,y),1(#()))) ge(0(x),1(y)) = 2x + 2y + 17 >= 2x + 2y + 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(#()))) DP Processor: DPs: +#(1(x),1(y)) -> +#(x,y) +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(+(x,y),z) -> +#(y,z) +#(+(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) -> +#(y,z) +#(+(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) -> +#(y,z) +#(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) -> +#(y,z) +#(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) -> +#(y,z) -> +#(+(x,y),z) -> +#(x,+(y,z)) +#(+(x,y),z) -> +#(y,z) -> +#(+(x,y),z) -> +#(y,z) +#(+(x,y),z) -> +#(y,z) -> +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(+(x,y),z) -> +#(y,z) -> +#(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) -> +#(y,z) +#(+(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) 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) -> +#(y,z) +#(+(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(#()))) Bounds Processor: bound: 1 enrichment: match-dp automaton: final states: {6} transitions: 00(7) -> 7* +{#,0}(13,7) -> 6* +{#,0}(7,7) -> 6* +{#,1}(13,13) -> 6* +0(13,7) -> 7* +0(13,13) -> 7* +0(7,7) -> 7* 10(13) -> 7* #0() -> 13* f140() -> 7* 13 -> 7* problem: DPs: +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(+(x,y),z) -> +#(y,z) +#(+(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(#()))) Usable Rule Processor: DPs: +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(+(x,y),z) -> +#(y,z) +#(+(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)) Semantic Labeling Processor: dimension: 1 usable rules: interpretation: [1](x0) = x0 + 1, [+](x0, x1) = x0 + x1 + 1, [0](x0) = 0, [#] = 0 labeled: +# usable (for model): +# 1 + # 0 argument filtering: pi(#) = [] pi(0) = [] pi(+) = 0 pi(1) = 0 pi(+#) = [] precedence: +# ~ 1 ~ + ~ 0 ~ # problem: DPs: +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(+(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)) Restore Modifier: DPs: +#(1(x),1(y)) -> +#(+(x,y),1(#())) +#(+(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(#()))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {1} transitions: 00(14) -> 9* 00(16) -> 5* f440() -> 4* +{#,0}(13,3) -> 1* +{#,0}(4,14) -> 1* +{#,0}(4,16) -> 1* +{#,0}(5,3) -> 1* +{#,0}(4,9) -> 1* +0(13,3) -> 14* +0(4,2) -> 13* +0(4,4) -> 5* +0(4,14) -> 14* +0(4,16) -> 16* +0(5,3) -> 16* +0(2,3) -> 3* +0(4,3) -> 9* +0(4,5) -> 5* +0(4,9) -> 16,9 +0(4,13) -> 13* 10(2) -> 3* #0() -> 2* 2 -> 13* 3 -> 14,9 4 -> 13,5 5 -> 13* 9 -> 14,16 problem: DPs: +#(+(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(#()))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {1} transitions: +{#,0}(2,3) -> 1* +0(2,10) -> 10* +0(2,3) -> 3* +0(2,7) -> 10* +0(2,9) -> 9* +0(2,11) -> 11* +0(3,8) -> 9* +0(10,8) -> 11* +0(2,2) -> 3* +0(7,8) -> 8* 10(7) -> 8* #0() -> 7* 00(9) -> 3* 00(11) -> 9* f460() -> 2* 2 -> 10,3 3 -> 10* 7 -> 10* 8 -> 11,9 9 -> 11* 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: -#(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: f480() -> 7* 10(7) -> 7* 10(8) -> 7* -{#,0}(7,8) -> 6* -{#,0}(7,7) -> 6* -0(7,8) -> 7* -0(7,7) -> 7* #0() -> 8* 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* f520() -> 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