Input TRS: 1: intlist(nil()) -> nil() 2: int(s(x),0()) -> nil() 3: int(x,x) -> cons(x,nil()) 4: intlist(cons(x,y)) -> cons(s(x),intlist(y)) 5: int(s(x),s(y)) -> intlist(int(x,y)) 6: int(0(),s(y)) -> cons(0(),int(s(0()),s(y))) 7: intlist(cons(x,nil())) -> cons(s(x),nil()) Number of strict rules: 7 Direct Order(PosReal,>,Poly) ... removes: 3 2 s(x1) weight: x1 0() weight: 0 nil() weight: 0 intlist(x1) weight: x1 int(x1,x2) weight: (/ 1 4) + x1 + x2 cons(x1,x2) weight: x1 + x2 Number of strict rules: 5 Direct Order(PosReal,>,Poly) ... failed. Freezing int 1: intlist(nil()) -> nil() 4: intlist(cons(x,y)) -> cons(s(x),intlist(y)) 5: int❆1_s(x,s(y)) -> intlist(int(x,y)) 6: int❆1_0(s(y)) -> cons(0(),int❆1_s(0(),s(y))) 7: intlist(cons(x,nil())) -> cons(s(x),nil()) 8: int(0(),_1) ->= int❆1_0(_1) 9: int(s(_1),_2) ->= int❆1_s(_1,_2) Number of strict rules: 5 Direct Order(PosReal,>,Poly) ... removes: 9 s(x1) weight: (/ 1 8) + 2 * x1 int❆1_0(x1) weight: (/ 1 8) + 2 * x1 int❆1_s(x1,x2) weight: 2 * x1 + 2 * x2 0() weight: 0 nil() weight: 0 intlist(x1) weight: 2 * x1 int(x1,x2) weight: (/ 1 8) + x1 + 2 * x2 cons(x1,x2) weight: (/ 1 8) + x1 + x2 Number of strict rules: 5 Direct Order(PosReal,>,Poly) ... failed. Dependency Pairs: #1: #int❆1_0(s(y)) -> #int❆1_s(0(),s(y)) #2: #int❆1_s(x,s(y)) -> #intlist(int(x,y)) #3: #int❆1_s(x,s(y)) -> #int(x,y) #4: #int(0(),_1) ->? #int❆1_0(_1) #5: #intlist(cons(x,y)) -> #intlist(y) Number of SCCs: 2, DPs: 4, edges: 4 SCC { #5 } Removing DPs: Order(PosReal,>,Sum)... succeeded. #intlist(x1) weight: x1 s(x1) weight: 0 int❆1_0(x1) weight: 0 int❆1_s(x1,x2) weight: 0 #int❆1_0(x1) weight: 0 #int❆1_s(x1,x2) weight: 0 0() weight: 0 nil() weight: 0 intlist(x1) weight: 0 int(x1,x2) weight: 0 cons(x1,x2) weight: (/ 1 2) + x2 #int(x1,x2) weight: 0 Usable rules: { } Removed DPs: #5 Number of SCCs: 1, DPs: 3, edges: 3 SCC { #1 #3 #4 } Removing DPs: Order(PosReal,>,Sum)... succeeded. #intlist(x1) weight: 0 s(x1) weight: (/ 3 4) + x1 int❆1_0(x1) weight: 0 int❆1_s(x1,x2) weight: 0 #int❆1_0(x1) weight: (/ 1 4) + x1 #int❆1_s(x1,x2) weight: x2 0() weight: 0 nil() weight: 0 intlist(x1) weight: 0 int(x1,x2) weight: 0 cons(x1,x2) weight: (/ 1 4) #int(x1,x2) weight: (/ 1 2) + x2 Usable rules: { } Removed DPs: #1 #3 #4 Number of SCCs: 0, DPs: 0, edges: 0 YES