MAYBE * Step 1: Failure MAYBE + Considered Problem: - Strict TRS: EQEDGE(E(z0,z1),E(z2,z3)) -> c25(EQEDGE[ITE](and(!EQ(z0,z2),!EQ(z1,z3)),z2,z3,z0,z1) ,AND(!EQ(z0,z2),!EQ(z1,z3)) ,!EQ'(z0,z2)) EQEDGE(E(z0,z1),E(z2,z3)) -> c26(EQEDGE[ITE](and(!EQ(z0,z2),!EQ(z1,z3)),z2,z3,z0,z1) ,AND(!EQ(z0,z2),!EQ(z1,z3)) ,!EQ'(z1,z3)) GETNODEFROMEDGE(0(),E(z0,z1)) -> c20() GETNODEFROMEDGE(S(0()),E(z0,z1)) -> c19() GETNODEFROMEDGE(S(S(z0)),E(z1,z2)) -> c18() GOAL(z0,z1,z2) -> c30(REACH(z0,z1,z2)) MEMBER(z0,Cons(z1,z2)) -> c23(MEMBER[ITE](eqEdge(z0,z1),z0,Cons(z1,z2)),EQEDGE(z0,z1)) MEMBER(z0,Nil()) -> c24() NOTEMPTY(Cons(z0,z1)) -> c27() NOTEMPTY(Nil()) -> c28() REACH(z0,z1,z2) -> c29(REACH[ITE](member(E(z0,z1),z2),z0,z1,z2),MEMBER(E(z0,z1),z2)) VIA(z0,z1,Cons(E(z2,z3),z4),z5) -> c21(VIA[ITE](!EQ(z0,z2),z0,z1,Cons(E(z2,z3),z4),z5),!EQ'(z0,z2)) VIA(z0,z1,Nil(),z2) -> c22() - Weak TRS: !EQ(0(),0()) -> True() !EQ(0(),S(z0)) -> False() !EQ(S(z0),0()) -> False() !EQ(S(z0),S(z1)) -> !EQ(z0,z1) !EQ'(0(),0()) -> c3() !EQ'(0(),S(z0)) -> c1() !EQ'(S(z0),0()) -> c2() !EQ'(S(z0),S(z1)) -> c(!EQ'(z0,z1)) AND(False(),False()) -> c4() AND(False(),True()) -> c6() AND(True(),False()) -> c5() AND(True(),True()) -> c7() EQEDGE[ITE](False(),z0,z1,z2,z3) -> c16() EQEDGE[ITE](True(),z0,z1,z2,z3) -> c17() MEMBER[ITE](False(),z0,Cons(z1,z2)) -> c12(MEMBER(z0,z2)) MEMBER[ITE](True(),z0,z1) -> c13() REACH[ITE](False(),z0,z1,z2) -> c14(VIA(z0,z1,z2,z2)) REACH[ITE](True(),z0,z1,z2) -> c15() VIA[ITE](False(),z0,z1,Cons(z2,z3),z4) -> c9(VIA(z0,z1,z3,z4)) VIA[ITE](True(),z0,z1,Cons(E(z2,z3),z4),z5) -> c8(VIA[LET](z0,z1,Cons(E(z2,z3),z4),z5,reach(z3,z1,z5)) ,REACH(z3,z1,z5)) VIA[LET](z0,z1,Cons(z2,z3),z4,Cons(z5,z6)) -> c11() VIA[LET](z0,z1,Cons(z2,z3),z4,Nil()) -> c10(VIA(z0,z1,z3,z4)) and(False(),False()) -> False() and(False(),True()) -> False() and(True(),False()) -> False() and(True(),True()) -> True() eqEdge(E(z0,z1),E(z2,z3)) -> eqEdge[Ite](and(!EQ(z0,z2),!EQ(z1,z3)),z2,z3,z0,z1) eqEdge[Ite](False(),z0,z1,z2,z3) -> False() eqEdge[Ite](True(),z0,z1,z2,z3) -> True() getNodeFromEdge(0(),E(z0,z1)) -> z0 getNodeFromEdge(S(0()),E(z0,z1)) -> z0 getNodeFromEdge(S(S(z0)),E(z1,z2)) -> z2 goal(z0,z1,z2) -> reach(z0,z1,z2) member(z0,Cons(z1,z2)) -> member[Ite](eqEdge(z0,z1),z0,Cons(z1,z2)) member(z0,Nil()) -> False() member[Ite](False(),z0,Cons(z1,z2)) -> member(z0,z2) member[Ite](True(),z0,z1) -> True() notEmpty(Cons(z0,z1)) -> True() notEmpty(Nil()) -> False() reach(z0,z1,z2) -> reach[Ite](member(E(z0,z1),z2),z0,z1,z2) reach[Ite](False(),z0,z1,z2) -> via(z0,z1,z2,z2) reach[Ite](True(),z0,z1,z2) -> Cons(E(z0,z1),Nil()) via(z0,z1,Cons(E(z2,z3),z4),z5) -> via[Ite](!EQ(z0,z2),z0,z1,Cons(E(z2,z3),z4),z5) via(z0,z1,Nil(),z2) -> Nil() via[Ite](False(),z0,z1,Cons(z2,z3),z4) -> via(z0,z1,z3,z4) via[Ite](True(),z0,z1,Cons(E(z2,z3),z4),z5) -> via[Let](z0,z1,Cons(E(z2,z3),z4),z5,reach(z3,z1,z5)) via[Let](z0,z1,Cons(z2,z3),z4,Cons(z5,z6)) -> Cons(z2,Cons(z5,z6)) via[Let](z0,z1,Cons(z2,z3),z4,Nil()) -> via(z0,z1,z3,z4) - Signature: {!EQ/2,!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,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,c/1,c1/0,c10/1,c11/0,c12/1,c13/0,c14/1,c15/0,c16/0,c17/0,c18/0,c19/0,c2/0,c20/0 ,c21/2,c22/0,c23/2,c24/0,c25/3,c26/3,c27/0,c28/0,c29/2,c3/0,c30/1,c4/0,c5/0,c6/0,c7/0,c8/2,c9/1} - Obligation: innermost runtime complexity wrt. defined symbols {!EQ,!EQ',AND,EQEDGE,EQEDGE[ITE],GETNODEFROMEDGE,GOAL ,MEMBER,MEMBER[ITE],NOTEMPTY,REACH,REACH[ITE],VIA,VIA[ITE],VIA[LET],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,c,c1,c10,c11,c12,c13,c14,c15,c16,c17,c18,c19,c2,c20,c21,c22,c23,c24,c25,c26,c27,c28,c29,c3,c30 ,c4,c5,c6,c7,c8,c9} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: None MAYBE