MAYBE * Step 1: Failure MAYBE + Considered Problem: - Strict TRS: eqEdge(E(e11,e12),E(e21,e22)) -> eqEdge[Ite](and(!EQ(e11,e21),!EQ(e12,e22)),e21,e22,e11,e12) getNodeFromEdge(0(),E(x,y)) -> x getNodeFromEdge(S(0()),E(x,y)) -> x getNodeFromEdge(S(S(x')),E(x,y)) -> y goal(u,v,edges) -> reach(u,v,edges) member(x,Nil()) -> False() member(x',Cons(x,xs)) -> member[Ite](eqEdge(x',x),x',Cons(x,xs)) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() reach(u,v,edges) -> reach[Ite](member(E(u,v),edges),u,v,edges) via(u,v,Cons(E(x,y),xs),edges) -> via[Ite](!EQ(u,x),u,v,Cons(E(x,y),xs),edges) via(u,v,Nil(),edges) -> Nil() - Weak TRS: !EQ(0(),0()) -> True() !EQ(0(),S(y)) -> False() !EQ(S(x),0()) -> False() !EQ(S(x),S(y)) -> !EQ(x,y) and(False(),False()) -> False() and(False(),True()) -> False() and(True(),False()) -> False() and(True(),True()) -> True() eqEdge[Ite](False(),e21,e22,e11,e12) -> False() eqEdge[Ite](True(),e21,e22,e11,e12) -> True() member[Ite](False(),x',Cons(x,xs)) -> member(x',xs) member[Ite](True(),x,xs) -> True() reach[Ite](False(),u,v,edges) -> via(u,v,edges,edges) reach[Ite](True(),u,v,edges) -> Cons(E(u,v),Nil()) via[Ite](False(),u,v,Cons(x,xs),edges) -> via(u,v,xs,edges) via[Ite](True(),u,v,Cons(E(x,y),xs),edges) -> via[Let](u,v,Cons(E(x,y),xs),edges,reach(y,v,edges)) via[Let](u,v,Cons(x,xs),edges,Cons(x',xs')) -> Cons(x,Cons(x',xs')) via[Let](u,v,Cons(x,xs),edges,Nil()) -> via(u,v,xs,edges) - Signature: {!EQ/2,and/2,eqEdge/2,eqEdge[Ite]/5,getNodeFromEdge/2,goal/3,member/2,member[Ite]/3,notEmpty/1,reach/3 ,reach[Ite]/4,via/4,via[Ite]/5,via[Let]/5} / {0/0,Cons/2,E/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {!EQ,and,eqEdge,eqEdge[Ite],getNodeFromEdge,goal,member ,member[Ite],notEmpty,reach,reach[Ite],via,via[Ite],via[Let]} and constructors {0,Cons,E,False,Nil,S,True} + Applied Processor: NaturalMI {miDimension = 3, miDegree = 3, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: Incompatible MAYBE