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: divL(z,cons(x,xs)) ->= divL(z,consSwap(x,xs)) 8: consSwap(x,xs) ->= cons(x,xs) 9: consSwap(x,cons(y,xs)) ->= cons(y,consSwap(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: #divL(z,cons(x,xs)) ->? #divL(z,consSwap(x,xs)) #5: #div(s(x),s(y)) -> #div(minus(x,y),s(y)) #6: #div(s(x),s(y)) -> #minus(x,y) Number of SCCs: 3, DPs: 4, edges: 6 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 consSwap(x1,x2) 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: 3, edges: 5 SCC { #5 } Removing DPs: Order(PosReal,>,Sum)... succeeded. |0|() weight: 0 #div(x1,x2) weight: x1 s(x1) weight: (/ 1 2) + x1 minus(x1,x2) weight: (/ 1 4) + x1 div(x1,x2) weight: 0 o() weight: 0 consSwap(x1,x2) weight: 0 nil() weight: 0 divL(x1,x2) weight: 0 #minus(x1,x2) weight: 0 cons(x1,x2) weight: 0 #divL(x1,x2) weight: 0 Usable rules: { 1 2 } Removed DPs: #5 Number of SCCs: 1, DPs: 2, edges: 4 SCC { #2 #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: (/ 1 2) + x1 div(x1,x2) weight: (/ 1 2) o() weight: 0 consSwap(x1,x2) weight: (/ 1 2) + x1 + x2 nil() weight: 0 divL(x1,x2) weight: 0 #minus(x1,x2) weight: 0 cons(x1,x2) weight: (/ 1 2) + x1 + x2 #divL(x1,x2) weight: x2 Usable rules: { 1..3 8 9 } Removed DPs: #2 Number of SCCs: 1, DPs: 1, edges: 1 SCC { #4 } Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed. Removing edges: failed. Finding a loop... failed. MAYBE