Input TRS: 1: pred(s(x)) -> x 2: minus(x,|0|()) -> x 3: minus(x,s(y)) -> pred(minus(x,y)) 4: div(|0|(),s(y)) -> |0|() 5: div(s(x),s(y)) -> s(div(minus(x,y),s(y))) 6: divL(x,nil()) -> x 7: divL(x,cons(y,xs)) -> divL(div(x,y),xs) 8: divL(z,cons(x,cons(y,xs))) ->= divL(z,cons(y,cons(x,xs))) Number of strict rules: 7 Direct Order(PosReal,>,Poly) ... failed. Freezing ... failed. Dependency Pairs: #1: #divL(x,cons(y,xs)) -> #divL(div(x,y),xs) #2: #divL(x,cons(y,xs)) -> #div(x,y) #3: #div(s(x),s(y)) -> #div(minus(x,y),s(y)) #4: #div(s(x),s(y)) -> #minus(x,y) #5: #minus(x,s(y)) -> #pred(minus(x,y)) #6: #minus(x,s(y)) -> #minus(x,y) #7: #divL(z,cons(x,cons(y,xs))) ->? #divL(z,cons(y,cons(x,xs))) Number of SCCs: 3, DPs: 4, edges: 6 SCC { #6 } 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 pred(x1) weight: 0 nil() weight: 0 divL(x1,x2) weight: 0 #minus(x1,x2) weight: x2 #pred(x1) weight: 0 cons(x1,x2) weight: 0 #divL(x1,x2) weight: 0 Usable rules: { } Removed DPs: #6 Number of SCCs: 2, DPs: 3, edges: 5 SCC { #3 } 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 pred(x1) weight: x1 nil() weight: 0 divL(x1,x2) weight: 0 #minus(x1,x2) weight: 0 #pred(x1) weight: 0 cons(x1,x2) weight: 0 #divL(x1,x2) weight: 0 Usable rules: { 1..3 } Removed DPs: #3 Number of SCCs: 1, DPs: 2, edges: 4 SCC { #1 #7 } 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: (/ 1 4) pred(x1) weight: x1 nil() weight: 0 divL(x1,x2) weight: 0 #minus(x1,x2) weight: 0 #pred(x1) weight: 0 cons(x1,x2) weight: (/ 1 4) + x1 + x2 #divL(x1,x2) weight: x2 Usable rules: { 1..4 } Removed DPs: #1 Number of SCCs: 1, DPs: 1, edges: 1 SCC { #7 } 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