YES Input TRS: 1: app(nil(),k) -> k 2: app(l,nil()) -> l 3: app(cons(x,l),k) -> cons(x,app(l,k)) 4: sum(cons(x,nil())) -> cons(x,nil()) 5: sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) 6: sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) 7: plus(0(),y) -> y 8: plus(s(x),y) -> s(plus(x,y)) 9: cons(x,cons(y,l)) ->= cons(y,cons(x,l)) Number of strict rules: 8 Direct POLO(bPol) ... removes: 1 3 5 7 2 s w: x1 + 1 sum w: x1 0 w: 30613 nil w: 1 plus w: x1 + x2 + 2 cons w: x1 + x2 + 3 app w: 2 * x1 + x2 + 1 Number of strict rules: 3 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #sum(app(l,cons(x,cons(y,k)))) -> #sum(app(l,sum(cons(x,cons(y,k))))) #2: #sum(app(l,cons(x,cons(y,k)))) -> #sum(cons(x,cons(y,k))) #3: #plus(s(x),y) -> #plus(x,y) Number of SCCs: 1, DPs: 1 SCC { #3 } POLO(Sum)... succeeded. s w: x1 + 1 #plus w: x1 sum w: 0 0 w: 0 nil w: 0 plus w: 0 cons w: 0 #sum w: 0 app w: 0 USABLE RULES: { } Removed DPs: #3 Number of SCCs: 0, DPs: 0