YES Input TRS: 1: from(X) -> cons(X,n__from(n__s(X))) 2: sel(0(),cons(X,Y)) -> X 3: sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) 4: from(X) -> n__from(X) 5: s(X) -> n__s(X) 6: activate(n__from(X)) -> from(activate(X)) 7: activate(n__s(X)) -> s(activate(X)) 8: activate(X) -> X Number of strict rules: 8 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #activate(n__from(X)) -> #from(activate(X)) #2: #activate(n__from(X)) -> #activate(X) #3: #activate(n__s(X)) -> #s(activate(X)) #4: #activate(n__s(X)) -> #activate(X) #5: #sel(s(X),cons(Y,Z)) -> #sel(X,activate(Z)) #6: #sel(s(X),cons(Y,Z)) -> #activate(Z) Number of SCCs: 2, DPs: 3 SCC { #5 } POLO(Sum)... succeeded. s w: x1 + 1 activate w: 8856 n__from w: 8858 #activate w: 0 n__s w: 2 0 w: 0 #sel w: x1 from w: 8857 sel w: 0 #s w: 0 #from w: 0 cons w: x1 + 8858 USABLE RULES: { } Removed DPs: #5 Number of SCCs: 1, DPs: 2 SCC { #2 #4 } POLO(Sum)... succeeded. s w: x1 + 1 activate w: 8856 n__from w: x1 + 8858 #activate w: x1 n__s w: x1 0 w: 0 #sel w: 0 from w: 8857 sel w: 0 #s w: 0 #from w: 0 cons w: x1 + 8858 USABLE RULES: { } Removed DPs: #2 Number of SCCs: 1, DPs: 1 SCC { #4 } POLO(Sum)... succeeded. s w: x1 + 1 activate w: 8856 n__from w: x1 + 8858 #activate w: x1 n__s w: x1 + 1 0 w: 0 #sel w: 0 from w: 8857 sel w: 0 #s w: 0 #from w: 0 cons w: x1 + 8858 USABLE RULES: { } Removed DPs: #4 Number of SCCs: 0, DPs: 0