MAYBE Problem: app(app(max(),0()),x) -> x app(app(max(),x),0()) -> x app(app(max(),app(s(),x)),app(s(),y)) -> app(app(max(),x),y) app(app(min(),0()),x) -> 0() app(app(min(),x),0()) -> 0() app(app(min(),app(s(),x)),app(s(),y)) -> app(app(min(),x),y) app(app(app(app(insert(),f),g),nil()),x) -> app(app(cons(),x),nil()) app(app(app(app(insert(),f),g),app(app(cons(),h),t)),x) -> app(app(cons(),app(app(f,x),h)),app(app(app(app(insert(),f),g),t),app(app(g,x),h))) app(app(app(sort(),f),g),nil()) -> nil() app(app(app(sort(),f),g),app(app(cons(),h),t)) -> app(app(app(app(insert(),f),g),app(app(app(sort(),f),g),t)),h) app(ascending_sort(),l) -> app(app(app(sort(),min()),max()),l) app(descending_sort(),l) -> app(app(app(sort(),max()),min()),l) Proof: DP Processor: DPs: app#(app(max(),app(s(),x)),app(s(),y)) -> app#(max(),x) app#(app(max(),app(s(),x)),app(s(),y)) -> app#(app(max(),x),y) app#(app(min(),app(s(),x)),app(s(),y)) -> app#(min(),x) app#(app(min(),app(s(),x)),app(s(),y)) -> app#(app(min(),x),y) app#(app(app(app(insert(),f),g),nil()),x) -> app#(cons(),x) app#(app(app(app(insert(),f),g),nil()),x) -> app#(app(cons(),x),nil()) app#(app(app(app(insert(),f),g),app(app(cons(),h),t)),x) -> app#(g,x) app#(app(app(app(insert(),f),g),app(app(cons(),h),t)),x) -> app#(app(g,x),h) app#(app(app(app(insert(),f),g),app(app(cons(),h),t)),x) -> app#(app(app(insert(),f),g),t) app#(app(app(app(insert(),f),g),app(app(cons(),h),t)),x) -> app#(app(app(app(insert(),f),g),t),app(app(g,x),h)) app#(app(app(app(insert(),f),g),app(app(cons(),h),t)),x) -> app#(f,x) app#(app(app(app(insert(),f),g),app(app(cons(),h),t)),x) -> app#(app(f,x),h) app#(app(app(app(insert(),f),g),app(app(cons(),h),t)),x) -> app#(cons(),app(app(f,x),h)) app#(app(app(app(insert(),f),g),app(app(cons(),h),t)),x) -> app#(app(cons(),app(app(f,x),h)),app(app(app(app(insert(),f),g),t),app(app(g,x),h))) app#(app(app(sort(),f),g),app(app(cons(),h),t)) -> app#(app(app(sort(),f),g),t) app#(app(app(sort(),f),g),app(app(cons(),h),t)) -> app#(insert(),f) app#(app(app(sort(),f),g),app(app(cons(),h),t)) -> app#(app(insert(),f),g) app#(app(app(sort(),f),g),app(app(cons(),h),t)) -> app#(app(app(insert(),f),g),app(app(app(sort(),f),g),t)) app#(app(app(sort(),f),g),app(app(cons(),h),t)) -> app#(app(app(app(insert(),f),g),app(app(app(sort(),f),g),t)),h) app#(ascending_sort(),l) -> app#(sort(),min()) app#(ascending_sort(),l) -> app#(app(sort(),min()),max()) app#(ascending_sort(),l) -> app#(app(app(sort(),min()),max()),l) app#(descending_sort(),l) -> app#(sort(),max()) app#(descending_sort(),l) -> app#(app(sort(),max()),min()) app#(descending_sort(),l) -> app#(app(app(sort(),max()),min()),l) TRS: app(app(max(),0()),x) -> x app(app(max(),x),0()) -> x app(app(max(),app(s(),x)),app(s(),y)) -> app(app(max(),x),y) app(app(min(),0()),x) -> 0() app(app(min(),x),0()) -> 0() app(app(min(),app(s(),x)),app(s(),y)) -> app(app(min(),x),y) app(app(app(app(insert(),f),g),nil()),x) -> app(app(cons(),x),nil()) app(app(app(app(insert(),f),g),app(app(cons(),h),t)),x) -> app(app(cons(),app(app(f,x),h)),app(app(app(app(insert(),f),g),t),app(app(g,x),h))) app(app(app(sort(),f),g),nil()) -> nil() app(app(app(sort(),f),g),app(app(cons(),h),t)) -> app(app(app(app(insert(),f),g),app(app(app(sort(),f),g),t)),h) app(ascending_sort(),l) -> app(app(app(sort(),min()),max()),l) app(descending_sort(),l) -> app(app(app(sort(),max()),min()),l) Open