MAYBE Problem: intlist(nil()) -> nil() intlist(cons(x,y)) -> cons(s(x),intlist(y)) int(0(),0()) -> cons(0(),nil()) int(0(),s(y)) -> cons(0(),int(s(0()),s(y))) int(s(x),0()) -> nil() int(s(x),s(y)) -> intlist(int(x,y)) Proof: DP Processor: DPs: intlist#(cons(x,y)) -> intlist#(y) int#(0(),s(y)) -> int#(s(0()),s(y)) int#(s(x),s(y)) -> int#(x,y) int#(s(x),s(y)) -> intlist#(int(x,y)) TRS: intlist(nil()) -> nil() intlist(cons(x,y)) -> cons(s(x),intlist(y)) int(0(),0()) -> cons(0(),nil()) int(0(),s(y)) -> cons(0(),int(s(0()),s(y))) int(s(x),0()) -> nil() int(s(x),s(y)) -> intlist(int(x,y)) TDG Processor: DPs: intlist#(cons(x,y)) -> intlist#(y) int#(0(),s(y)) -> int#(s(0()),s(y)) int#(s(x),s(y)) -> int#(x,y) int#(s(x),s(y)) -> intlist#(int(x,y)) TRS: intlist(nil()) -> nil() intlist(cons(x,y)) -> cons(s(x),intlist(y)) int(0(),0()) -> cons(0(),nil()) int(0(),s(y)) -> cons(0(),int(s(0()),s(y))) int(s(x),0()) -> nil() int(s(x),s(y)) -> intlist(int(x,y)) graph: int#(0(),s(y)) -> int#(s(0()),s(y)) -> int#(s(x),s(y)) -> intlist#(int(x,y)) int#(0(),s(y)) -> int#(s(0()),s(y)) -> int#(s(x),s(y)) -> int#(x,y) int#(0(),s(y)) -> int#(s(0()),s(y)) -> int#(0(),s(y)) -> int#(s(0()),s(y)) int#(s(x),s(y)) -> int#(x,y) -> int#(s(x),s(y)) -> intlist#(int(x,y)) int#(s(x),s(y)) -> int#(x,y) -> int#(s(x),s(y)) -> int#(x,y) int#(s(x),s(y)) -> int#(x,y) -> int#(0(),s(y)) -> int#(s(0()),s(y)) int#(s(x),s(y)) -> intlist#(int(x,y)) -> intlist#(cons(x,y)) -> intlist#(y) intlist#(cons(x,y)) -> intlist#(y) -> intlist#(cons(x,y)) -> intlist#(y) EDG Processor: DPs: intlist#(cons(x,y)) -> intlist#(y) int#(0(),s(y)) -> int#(s(0()),s(y)) int#(s(x),s(y)) -> int#(x,y) int#(s(x),s(y)) -> intlist#(int(x,y)) TRS: intlist(nil()) -> nil() intlist(cons(x,y)) -> cons(s(x),intlist(y)) int(0(),0()) -> cons(0(),nil()) int(0(),s(y)) -> cons(0(),int(s(0()),s(y))) int(s(x),0()) -> nil() int(s(x),s(y)) -> intlist(int(x,y)) graph: int#(0(),s(y)) -> int#(s(0()),s(y)) -> int#(s(x),s(y)) -> int#(x,y) int#(0(),s(y)) -> int#(s(0()),s(y)) -> int#(s(x),s(y)) -> intlist#(int(x,y)) int#(s(x),s(y)) -> int#(x,y) -> int#(0(),s(y)) -> int#(s(0()),s(y)) int#(s(x),s(y)) -> int#(x,y) -> int#(s(x),s(y)) -> int#(x,y) int#(s(x),s(y)) -> int#(x,y) -> int#(s(x),s(y)) -> intlist#(int(x,y)) int#(s(x),s(y)) -> intlist#(int(x,y)) -> intlist#(cons(x,y)) -> intlist#(y) intlist#(cons(x,y)) -> intlist#(y) -> intlist#(cons(x,y)) -> intlist#(y) Restore Modifier: DPs: intlist#(cons(x,y)) -> intlist#(y) int#(0(),s(y)) -> int#(s(0()),s(y)) int#(s(x),s(y)) -> int#(x,y) int#(s(x),s(y)) -> intlist#(int(x,y)) TRS: intlist(nil()) -> nil() intlist(cons(x,y)) -> cons(s(x),intlist(y)) int(0(),0()) -> cons(0(),nil()) int(0(),s(y)) -> cons(0(),int(s(0()),s(y))) int(s(x),0()) -> nil() int(s(x),s(y)) -> intlist(int(x,y)) SCC Processor: #sccs: 2 #rules: 3 #arcs: 7/16 DPs: int#(0(),s(y)) -> int#(s(0()),s(y)) int#(s(x),s(y)) -> int#(x,y) TRS: intlist(nil()) -> nil() intlist(cons(x,y)) -> cons(s(x),intlist(y)) int(0(),0()) -> cons(0(),nil()) int(0(),s(y)) -> cons(0(),int(s(0()),s(y))) int(s(x),0()) -> nil() int(s(x),s(y)) -> intlist(int(x,y)) Matrix Interpretation Processor: dimension: 1 interpretation: [int#](x0, x1) = x1 + 1, [int](x0, x1) = 0, [0] = 1, [s](x0) = x0 + 1, [cons](x0, x1) = 0, [intlist](x0) = 0, [nil] = 0 orientation: int#(0(),s(y)) = y + 2 >= y + 2 = int#(s(0()),s(y)) int#(s(x),s(y)) = y + 2 >= y + 1 = int#(x,y) intlist(nil()) = 0 >= 0 = nil() intlist(cons(x,y)) = 0 >= 0 = cons(s(x),intlist(y)) int(0(),0()) = 0 >= 0 = cons(0(),nil()) int(0(),s(y)) = 0 >= 0 = cons(0(),int(s(0()),s(y))) int(s(x),0()) = 0 >= 0 = nil() int(s(x),s(y)) = 0 >= 0 = intlist(int(x,y)) problem: DPs: int#(0(),s(y)) -> int#(s(0()),s(y)) TRS: intlist(nil()) -> nil() intlist(cons(x,y)) -> cons(s(x),intlist(y)) int(0(),0()) -> cons(0(),nil()) int(0(),s(y)) -> cons(0(),int(s(0()),s(y))) int(s(x),0()) -> nil() int(s(x),s(y)) -> intlist(int(x,y)) Matrix Interpretation Processor: dimension: 1 interpretation: [int#](x0, x1) = x0, [int](x0, x1) = x0 + 1, [0] = 1, [s](x0) = 0, [cons](x0, x1) = x0 + 1, [intlist](x0) = 1, [nil] = 1 orientation: int#(0(),s(y)) = 1 >= 0 = int#(s(0()),s(y)) intlist(nil()) = 1 >= 1 = nil() intlist(cons(x,y)) = 1 >= 1 = cons(s(x),intlist(y)) int(0(),0()) = 2 >= 2 = cons(0(),nil()) int(0(),s(y)) = 2 >= 2 = cons(0(),int(s(0()),s(y))) int(s(x),0()) = 1 >= 1 = nil() int(s(x),s(y)) = 1 >= 1 = intlist(int(x,y)) problem: DPs: TRS: intlist(nil()) -> nil() intlist(cons(x,y)) -> cons(s(x),intlist(y)) int(0(),0()) -> cons(0(),nil()) int(0(),s(y)) -> cons(0(),int(s(0()),s(y))) int(s(x),0()) -> nil() int(s(x),s(y)) -> intlist(int(x,y)) Qed DPs: intlist#(cons(x,y)) -> intlist#(y) TRS: intlist(nil()) -> nil() intlist(cons(x,y)) -> cons(s(x),intlist(y)) int(0(),0()) -> cons(0(),nil()) int(0(),s(y)) -> cons(0(),int(s(0()),s(y))) int(s(x),0()) -> nil() int(s(x),s(y)) -> intlist(int(x,y)) Open