YES Problem: minus(X,0()) -> X minus(s(X),s(Y)) -> p(minus(X,Y)) p(s(X)) -> X div(0(),s(Y)) -> 0() div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y))) Proof: DP Processor: DPs: minus#(s(X),s(Y)) -> minus#(X,Y) minus#(s(X),s(Y)) -> p#(minus(X,Y)) div#(s(X),s(Y)) -> minus#(X,Y) div#(s(X),s(Y)) -> div#(minus(X,Y),s(Y)) TRS: minus(X,0()) -> X minus(s(X),s(Y)) -> p(minus(X,Y)) p(s(X)) -> X div(0(),s(Y)) -> 0() div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y))) KBO Processor: argument filtering: pi(0) = [] pi(minus) = 0 pi(s) = [0] pi(p) = 0 pi(div) = 0 pi(minus#) = 0 pi(p#) = 0 pi(div#) = 0 weight function: w0 = 1 w(div#) = w(minus#) = w(p) = w(0) = 1 w(p#) = w(div) = w(s) = w(minus) = 0 precedence: div# ~ p# ~ minus# ~ div ~ p ~ s ~ minus ~ 0 problem: DPs: TRS: minus(X,0()) -> X minus(s(X),s(Y)) -> p(minus(X,Y)) p(s(X)) -> X div(0(),s(Y)) -> 0() div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y))) Qed