MAYBE Problem: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) Proof: DP Processor: DPs: +#(O(x),O(y)) -> +#(x,y) +#(O(x),O(y)) -> O#(+(x,y)) +#(O(x),I(y)) -> +#(x,y) +#(I(x),O(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(x,y) +#(I(x),I(y)) -> +#(+(x,y),I(0())) +#(I(x),I(y)) -> O#(+(+(x,y),I(0()))) *#(O(x),y) -> *#(x,y) *#(O(x),y) -> O#(*(x,y)) *#(I(x),y) -> *#(x,y) *#(I(x),y) -> O#(*(x,y)) *#(I(x),y) -> +#(O(*(x,y)),y) -#(O(x),O(y)) -> -#(x,y) -#(O(x),O(y)) -> O#(-(x,y)) -#(O(x),I(y)) -> -#(x,y) -#(O(x),I(y)) -> -#(-(x,y),I(1())) -#(I(x),O(y)) -> -#(x,y) -#(I(x),I(y)) -> -#(x,y) -#(I(x),I(y)) -> O#(-(x,y)) TRS: O(0()) -> 0() +(0(),x) -> x +(x,0()) -> x +(O(x),O(y)) -> O(+(x,y)) +(O(x),I(y)) -> I(+(x,y)) +(I(x),O(y)) -> I(+(x,y)) +(I(x),I(y)) -> O(+(+(x,y),I(0()))) *(0(),x) -> 0() *(x,0()) -> 0() *(O(x),y) -> O(*(x,y)) *(I(x),y) -> +(O(*(x,y)),y) -(x,0()) -> x -(0(),x) -> 0() -(O(x),O(y)) -> O(-(x,y)) -(O(x),I(y)) -> I(-(-(x,y),I(1()))) -(I(x),O(y)) -> I(-(x,y)) -(I(x),I(y)) -> O(-(x,y)) Open