YES Input TRS: 1: from(X) -> cons(X,n__from(s(X))) 2: sel(0(),cons(X,XS)) -> X 3: sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) 4: minus(X,0()) -> 0() 5: minus(s(X),s(Y)) -> minus(X,Y) 6: quot(0(),s(Y)) -> 0() 7: quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) 8: zWquot(XS,nil()) -> nil() 9: zWquot(nil(),XS) -> nil() 10: zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS))) 11: from(X) -> n__from(X) 12: zWquot(X1,X2) -> n__zWquot(X1,X2) 13: activate(n__from(X)) -> from(X) 14: activate(n__zWquot(X1,X2)) -> zWquot(X1,X2) 15: activate(X) -> X Number of strict rules: 15 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #activate(n__from(X)) -> #from(X) #2: #activate(n__zWquot(X1,X2)) -> #zWquot(X1,X2) #3: #quot(s(X),s(Y)) -> #quot(minus(X,Y),s(Y)) #4: #quot(s(X),s(Y)) -> #minus(X,Y) #5: #zWquot(cons(X,XS),cons(Y,YS)) -> #quot(X,Y) #6: #zWquot(cons(X,XS),cons(Y,YS)) -> #activate(XS) #7: #zWquot(cons(X,XS),cons(Y,YS)) -> #activate(YS) #8: #minus(s(X),s(Y)) -> #minus(X,Y) #9: #sel(s(N),cons(X,XS)) -> #sel(N,activate(XS)) #10: #sel(s(N),cons(X,XS)) -> #activate(XS) Number of SCCs: 3, DPs: 5 SCC { #8 } POLO(Sum)... succeeded. s w: x1 + 1 #zWquot w: 0 minus w: 0 activate w: 0 n__from w: 0 #activate w: 0 zWquot w: 0 n__zWquot w: 0 0 w: 0 quot w: 0 #sel w: 0 from w: 0 sel w: 0 nil w: 0 #minus w: x1 #from w: 0 cons w: 0 #quot w: 0 USABLE RULES: { } Removed DPs: #8 Number of SCCs: 2, DPs: 4 SCC { #9 } POLO(Sum)... succeeded. s w: x1 + 1 #zWquot w: 0 minus w: 1 activate w: x1 + 1 n__from w: 282 #activate w: 0 zWquot w: x2 + 2 n__zWquot w: x2 + 1 0 w: 20540 quot w: x2 + 20538 #sel w: x1 + x2 from w: 283 sel w: 0 nil w: 1 #minus w: 0 #from w: 0 cons w: x2 + 1 #quot w: 0 USABLE RULES: { 1 8..15 } Removed DPs: #9 Number of SCCs: 1, DPs: 3 SCC { #2 #6 #7 } POLO(Sum)... succeeded. s w: x1 + 1 #zWquot w: x1 + x2 minus w: 1 activate w: x1 + 1 n__from w: 34889 #activate w: x1 + 1 zWquot w: x2 + 35658 n__zWquot w: x1 + x2 + 35657 0 w: 20540 quot w: x2 + 20538 #sel w: 0 from w: 34890 sel w: 0 nil w: 1 #minus w: 0 #from w: 0 cons w: x2 + 1 #quot w: 0 USABLE RULES: { 1 8 9 11 13 15 } Removed DPs: #2 #6 #7 Number of SCCs: 0, DPs: 0