Input TRS: 1: minus(x,o()) -> x 2: minus(s(x),s(y)) -> minus(x,y) 3: div(|0|(),s(y)) -> |0|() 4: div(s(x),s(y)) -> s(div(minus(x,y),s(y))) 5: divL(x,nil()) -> x 6: divL(x,cons(y,xs)) -> divL(div(x,y),xs) 7: cons(x,cons(y,xs)) ->= cons(y,cons(x,xs)) Number of strict rules: 6 Direct Order(PosReal,>,Poly) ... failed. Freezing ... failed. Dependency Pairs: #1: #minus(s(x),s(y)) -> #minus(x,y) #2: #divL(x,cons(y,xs)) -> #divL(div(x,y),xs) #3: #divL(x,cons(y,xs)) -> #div(x,y) #4: #div(s(x),s(y)) -> #div(minus(x,y),s(y)) #5: #div(s(x),s(y)) -> #minus(x,y) Number of SCCs: 3, DPs: 3, edges: 3 SCC { #1 } Removing DPs: Order(PosReal,>,Sum)... succeeded. |0|() weight: 0 #div(x1,x2) weight: 0 s(x1) weight: (/ 1 2) + x1 minus(x1,x2) weight: 0 div(x1,x2) weight: 0 o() weight: 0 nil() weight: 0 divL(x1,x2) weight: 0 #minus(x1,x2) weight: x2 cons(x1,x2) weight: 0 #divL(x1,x2) weight: 0 Usable rules: { } Removed DPs: #1 Number of SCCs: 2, DPs: 2, edges: 2 SCC { #2 } Removing DPs: Order(PosReal,>,Sum)... succeeded. |0|() weight: 0 #div(x1,x2) weight: 0 s(x1) weight: (/ 1 2) minus(x1,x2) weight: (/ 1 4) div(x1,x2) weight: (/ 1 4) o() weight: 0 nil() weight: 0 divL(x1,x2) weight: 0 #minus(x1,x2) weight: 0 cons(x1,x2) weight: (/ 1 4) + x1 + x2 #divL(x1,x2) weight: x2 Usable rules: { 3 } Removed DPs: #2 Number of SCCs: 1, DPs: 1, edges: 1 SCC { #4 } Removing DPs: Order(PosReal,>,Sum)... succeeded. |0|() weight: 0 #div(x1,x2) weight: x1 s(x1) weight: (/ 1 2) + x1 minus(x1,x2) weight: x1 div(x1,x2) weight: x1 o() weight: 0 nil() weight: 0 divL(x1,x2) weight: 0 #minus(x1,x2) weight: 0 cons(x1,x2) weight: (/ 1 2) #divL(x1,x2) weight: 0 Usable rules: { 1 2 } Removed DPs: #4 Number of SCCs: 0, DPs: 0, edges: 0 YES