Input TRS: 1: pairNs() -> cons(0(),n__incr(oddNs())) 2: oddNs() -> incr(pairNs()) 3: incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS))) 4: take(0(),XS) -> nil() 5: take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS))) 6: zip(nil(),XS) -> nil() 7: zip(X,nil()) -> nil() 8: zip(cons(X,XS),cons(Y,YS)) -> cons(pair(X,Y),n__zip(activate(XS),activate(YS))) 9: tail(cons(X,XS)) -> activate(XS) 10: repItems(nil()) -> nil() 11: repItems(cons(X,XS)) -> cons(X,n__cons(X,n__repItems(activate(XS)))) 12: incr(X) -> n__incr(X) 13: take(X1,X2) -> n__take(X1,X2) 14: zip(X1,X2) -> n__zip(X1,X2) 15: cons(X1,X2) -> n__cons(X1,X2) 16: repItems(X) -> n__repItems(X) 17: activate(n__incr(X)) -> incr(X) 18: activate(n__take(X1,X2)) -> take(X1,X2) 19: activate(n__zip(X1,X2)) -> zip(X1,X2) 20: activate(n__cons(X1,X2)) -> cons(X1,X2) 21: activate(n__repItems(X)) -> repItems(X) 22: activate(X) -> X Number of strict rules: 22 Direct Order(PosReal,>,Poly) ... removes: 4 10 7 9 6 repItems(x1) weight: (/ 97553 4) + 2 * x1 incr(x1) weight: 2 * x1 s(x1) weight: x1 activate(x1) weight: x1 take(x1,x2) weight: (/ 148133 4) + x1 + 2 * x2 pair(x1,x2) weight: x1 + x2 tail(x1) weight: (/ 1 2) + x1 0() weight: 0 n__take(x1,x2) weight: (/ 148133 4) + x1 + 2 * x2 n__cons(x1,x2) weight: x1 + x2 nil() weight: 0 n__zip(x1,x2) weight: (/ 103137 4) + x1 + x2 pairNs() weight: 0 oddNs() weight: 0 n__repItems(x1) weight: (/ 97553 4) + 2 * x1 cons(x1,x2) weight: x1 + x2 n__incr(x1) weight: 2 * x1 zip(x1,x2) weight: (/ 103137 4) + x1 + x2 Number of strict rules: 17 Direct Order(PosReal,>,Poly) ... removes: 18 8 16 21 19 5 14 11 13 repItems(x1) weight: (/ 96499 8) + 2 * x1 incr(x1) weight: 2 * x1 s(x1) weight: x1 activate(x1) weight: 2 * x1 take(x1,x2) weight: (/ 3 8) + x1 + 2 * x2 pair(x1,x2) weight: (/ 1 8) + x1 + 2 * x2 tail(x1) weight: (/ 1 4) + x1 0() weight: 0 n__take(x1,x2) weight: (/ 1 4) + x1 + x2 n__cons(x1,x2) weight: x1 + x2 nil() weight: 0 n__zip(x1,x2) weight: (/ 54491 8) + x1 + x2 pairNs() weight: 0 oddNs() weight: 0 n__repItems(x1) weight: (/ 48249 4) + x1 cons(x1,x2) weight: x1 + x2 n__incr(x1) weight: x1 zip(x1,x2) weight: (/ 54493 8) + 2 * x1 + 2 * x2 Number of strict rules: 8 Direct Order(PosReal,>,Poly) ... failed. Freezing ... failed. Dependency Pairs: #1: #oddNs() -> #incr(pairNs()) #2: #oddNs() -> #pairNs() #3: #activate(n__cons(X1,X2)) -> #cons(X1,X2) #4: #activate(n__incr(X)) -> #incr(X) #5: #incr(cons(X,XS)) -> #cons(s(X),n__incr(activate(XS))) #6: #incr(cons(X,XS)) -> #activate(XS) #7: #pairNs() -> #cons(0(),n__incr(oddNs())) #8: #pairNs() -> #oddNs() Number of SCCs: 2, DPs: 4, edges: 4 SCC { #2 #8 } 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... found. #pairNs() -#8-> #oddNs() --->* #oddNs() -#2-> #pairNs() --->* #pairNs() Looping with: [ ] NO