MAYBE Problem: app(app(plus(),0()),y) -> y app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y)) app(inc(),xs) -> app(app(map(),app(plus(),app(s(),0()))),xs) app(app(map(),f),nil()) -> nil() app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) Proof: DP Processor: DPs: app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) app#(inc(),xs) -> app#(s(),0()) app#(inc(),xs) -> app#(plus(),app(s(),0())) app#(inc(),xs) -> app#(map(),app(plus(),app(s(),0()))) app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) TRS: app(app(plus(),0()),y) -> y app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y)) app(inc(),xs) -> app(app(map(),app(plus(),app(s(),0()))),xs) app(app(map(),f),nil()) -> nil() app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) EDG Processor: DPs: app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) app#(inc(),xs) -> app#(s(),0()) app#(inc(),xs) -> app#(plus(),app(s(),0())) app#(inc(),xs) -> app#(map(),app(plus(),app(s(),0()))) app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) TRS: app(app(plus(),0()),y) -> y app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y)) app(inc(),xs) -> app(app(map(),app(plus(),app(s(),0()))),xs) app(app(map(),f),nil()) -> nil() app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) graph: app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(inc(),xs) -> app#(s(),0()) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(inc(),xs) -> app#(plus(),app(s(),0())) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(inc(),xs) -> app#(map(),app(plus(),app(s(),0()))) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x)) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) -> app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs)) app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) -> app#(app(plus(),app(s(),x)),y) -> app#(plus(),x) app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) -> app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) -> app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y)) SCC Processor: #sccs: 2 #rules: 4 #arcs: 22/121 DPs: app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) TRS: app(app(plus(),0()),y) -> y app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y)) app(inc(),xs) -> app(app(map(),app(plus(),app(s(),0()))),xs) app(app(map(),f),nil()) -> nil() app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) Open DPs: app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) TRS: app(app(plus(),0()),y) -> y app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y)) app(inc(),xs) -> app(app(map(),app(plus(),app(s(),0()))),xs) app(app(map(),f),nil()) -> nil() app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs)) Open