MAYBE
MAYBE
TRS:
 {
                  __(X1, mark(X2)) -> mark(__(X1, X2)),
                  __(mark(X1), X2) -> mark(__(X1, X2)),
                __(ok(X1), ok(X2)) -> ok(__(X1, X2)),
              active(__(X, nil())) -> mark(X),
                active(__(X1, X2)) -> __(X1, active(X2)),
                active(__(X1, X2)) -> __(active(X1), X2),
           active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))),
              active(__(nil(), X)) -> mark(X),
                    active(U11(X)) -> U11(active(X)),
                 active(U11(tt())) -> mark(tt()),
                    active(U22(X)) -> U22(active(X)),
                 active(U22(tt())) -> mark(tt()),
                 active(isList(V)) -> mark(U11(isNeList(V))),
        active(isList(__(V1, V2))) -> mark(U21(isList(V1), V2)),
             active(isList(nil())) -> mark(tt()),
               active(U21(X1, X2)) -> U21(active(X1), X2),
             active(U21(tt(), V2)) -> mark(U22(isList(V2))),
                    active(U31(X)) -> U31(active(X)),
                 active(U31(tt())) -> mark(tt()),
                    active(U42(X)) -> U42(active(X)),
                 active(U42(tt())) -> mark(tt()),
               active(isNeList(V)) -> mark(U31(isQid(V))),
      active(isNeList(__(V1, V2))) -> mark(U41(isList(V1), V2)),
      active(isNeList(__(V1, V2))) -> mark(U51(isNeList(V1), V2)),
               active(U41(X1, X2)) -> U41(active(X1), X2),
             active(U41(tt(), V2)) -> mark(U42(isNeList(V2))),
                    active(U52(X)) -> U52(active(X)),
                 active(U52(tt())) -> mark(tt()),
               active(U51(X1, X2)) -> U51(active(X1), X2),
             active(U51(tt(), V2)) -> mark(U52(isList(V2))),
                    active(U61(X)) -> U61(active(X)),
                 active(U61(tt())) -> mark(tt()),
                    active(U72(X)) -> U72(active(X)),
                 active(U72(tt())) -> mark(tt()),
                  active(isPal(V)) -> mark(U81(isNePal(V))),
              active(isPal(nil())) -> mark(tt()),
               active(U71(X1, X2)) -> U71(active(X1), X2),
              active(U71(tt(), P)) -> mark(U72(isPal(P))),
                    active(U81(X)) -> U81(active(X)),
                 active(U81(tt())) -> mark(tt()),
                active(isQid(a())) -> mark(tt()),
                active(isQid(e())) -> mark(tt()),
                active(isQid(i())) -> mark(tt()),
                active(isQid(o())) -> mark(tt()),
                active(isQid(u())) -> mark(tt()),
                active(isNePal(V)) -> mark(U61(isQid(V))),
  active(isNePal(__(I, __(P, I)))) -> mark(U71(isQid(I), P)),
                      U11(mark(X)) -> mark(U11(X)),
                        U11(ok(X)) -> ok(U11(X)),
                      U22(mark(X)) -> mark(U22(X)),
                        U22(ok(X)) -> ok(U22(X)),
                     isList(ok(X)) -> ok(isList(X)),
                 U21(mark(X1), X2) -> mark(U21(X1, X2)),
               U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)),
                      U31(mark(X)) -> mark(U31(X)),
                        U31(ok(X)) -> ok(U31(X)),
                      U42(mark(X)) -> mark(U42(X)),
                        U42(ok(X)) -> ok(U42(X)),
                   isNeList(ok(X)) -> ok(isNeList(X)),
                 U41(mark(X1), X2) -> mark(U41(X1, X2)),
               U41(ok(X1), ok(X2)) -> ok(U41(X1, X2)),
                      U52(mark(X)) -> mark(U52(X)),
                        U52(ok(X)) -> ok(U52(X)),
                 U51(mark(X1), X2) -> mark(U51(X1, X2)),
               U51(ok(X1), ok(X2)) -> ok(U51(X1, X2)),
                      U61(mark(X)) -> mark(U61(X)),
                        U61(ok(X)) -> ok(U61(X)),
                      U72(mark(X)) -> mark(U72(X)),
                        U72(ok(X)) -> ok(U72(X)),
                      isPal(ok(X)) -> ok(isPal(X)),
                 U71(mark(X1), X2) -> mark(U71(X1, X2)),
               U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)),
                      U81(mark(X)) -> mark(U81(X)),
                        U81(ok(X)) -> ok(U81(X)),
                      isQid(ok(X)) -> ok(isQid(X)),
                    isNePal(ok(X)) -> ok(isNePal(X)),
                proper(__(X1, X2)) -> __(proper(X1), proper(X2)),
                     proper(nil()) -> ok(nil()),
                      proper(tt()) -> ok(tt()),
                    proper(U11(X)) -> U11(proper(X)),
                    proper(U22(X)) -> U22(proper(X)),
                 proper(isList(X)) -> isList(proper(X)),
               proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)),
                    proper(U31(X)) -> U31(proper(X)),
                    proper(U42(X)) -> U42(proper(X)),
               proper(isNeList(X)) -> isNeList(proper(X)),
               proper(U41(X1, X2)) -> U41(proper(X1), proper(X2)),
                    proper(U52(X)) -> U52(proper(X)),
               proper(U51(X1, X2)) -> U51(proper(X1), proper(X2)),
                    proper(U61(X)) -> U61(proper(X)),
                    proper(U72(X)) -> U72(proper(X)),
                  proper(isPal(X)) -> isPal(proper(X)),
               proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)),
                    proper(U81(X)) -> U81(proper(X)),
                  proper(isQid(X)) -> isQid(proper(X)),
                proper(isNePal(X)) -> isNePal(proper(X)),
                       proper(a()) -> ok(a()),
                       proper(e()) -> ok(e()),
                       proper(i()) -> ok(i()),
                       proper(o()) -> ok(o()),
                       proper(u()) -> ok(u()),
                      top(mark(X)) -> top(proper(X)),
                        top(ok(X)) -> top(active(X))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
                    __(X1, mark(X2)) -> mark(__(X1, X2)),
                    __(mark(X1), X2) -> mark(__(X1, X2)),
                  __(ok(X1), ok(X2)) -> ok(__(X1, X2)),
                active(__(X, nil())) -> mark(X),
                  active(__(X1, X2)) -> __(X1, active(X2)),
                  active(__(X1, X2)) -> __(active(X1), X2),
             active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))),
                active(__(nil(), X)) -> mark(X),
                      active(U11(X)) -> U11(active(X)),
                   active(U11(tt())) -> mark(tt()),
                      active(U22(X)) -> U22(active(X)),
                   active(U22(tt())) -> mark(tt()),
                   active(isList(V)) -> mark(U11(isNeList(V))),
          active(isList(__(V1, V2))) -> mark(U21(isList(V1), V2)),
               active(isList(nil())) -> mark(tt()),
                 active(U21(X1, X2)) -> U21(active(X1), X2),
               active(U21(tt(), V2)) -> mark(U22(isList(V2))),
                      active(U31(X)) -> U31(active(X)),
                   active(U31(tt())) -> mark(tt()),
                      active(U42(X)) -> U42(active(X)),
                   active(U42(tt())) -> mark(tt()),
                 active(isNeList(V)) -> mark(U31(isQid(V))),
        active(isNeList(__(V1, V2))) -> mark(U41(isList(V1), V2)),
        active(isNeList(__(V1, V2))) -> mark(U51(isNeList(V1), V2)),
                 active(U41(X1, X2)) -> U41(active(X1), X2),
               active(U41(tt(), V2)) -> mark(U42(isNeList(V2))),
                      active(U52(X)) -> U52(active(X)),
                   active(U52(tt())) -> mark(tt()),
                 active(U51(X1, X2)) -> U51(active(X1), X2),
               active(U51(tt(), V2)) -> mark(U52(isList(V2))),
                      active(U61(X)) -> U61(active(X)),
                   active(U61(tt())) -> mark(tt()),
                      active(U72(X)) -> U72(active(X)),
                   active(U72(tt())) -> mark(tt()),
                    active(isPal(V)) -> mark(U81(isNePal(V))),
                active(isPal(nil())) -> mark(tt()),
                 active(U71(X1, X2)) -> U71(active(X1), X2),
                active(U71(tt(), P)) -> mark(U72(isPal(P))),
                      active(U81(X)) -> U81(active(X)),
                   active(U81(tt())) -> mark(tt()),
                  active(isQid(a())) -> mark(tt()),
                  active(isQid(e())) -> mark(tt()),
                  active(isQid(i())) -> mark(tt()),
                  active(isQid(o())) -> mark(tt()),
                  active(isQid(u())) -> mark(tt()),
                  active(isNePal(V)) -> mark(U61(isQid(V))),
    active(isNePal(__(I, __(P, I)))) -> mark(U71(isQid(I), P)),
                        U11(mark(X)) -> mark(U11(X)),
                          U11(ok(X)) -> ok(U11(X)),
                        U22(mark(X)) -> mark(U22(X)),
                          U22(ok(X)) -> ok(U22(X)),
                       isList(ok(X)) -> ok(isList(X)),
                   U21(mark(X1), X2) -> mark(U21(X1, X2)),
                 U21(ok(X1), ok(X2)) -> ok(U21(X1, X2)),
                        U31(mark(X)) -> mark(U31(X)),
                          U31(ok(X)) -> ok(U31(X)),
                        U42(mark(X)) -> mark(U42(X)),
                          U42(ok(X)) -> ok(U42(X)),
                     isNeList(ok(X)) -> ok(isNeList(X)),
                   U41(mark(X1), X2) -> mark(U41(X1, X2)),
                 U41(ok(X1), ok(X2)) -> ok(U41(X1, X2)),
                        U52(mark(X)) -> mark(U52(X)),
                          U52(ok(X)) -> ok(U52(X)),
                   U51(mark(X1), X2) -> mark(U51(X1, X2)),
                 U51(ok(X1), ok(X2)) -> ok(U51(X1, X2)),
                        U61(mark(X)) -> mark(U61(X)),
                          U61(ok(X)) -> ok(U61(X)),
                        U72(mark(X)) -> mark(U72(X)),
                          U72(ok(X)) -> ok(U72(X)),
                        isPal(ok(X)) -> ok(isPal(X)),
                   U71(mark(X1), X2) -> mark(U71(X1, X2)),
                 U71(ok(X1), ok(X2)) -> ok(U71(X1, X2)),
                        U81(mark(X)) -> mark(U81(X)),
                          U81(ok(X)) -> ok(U81(X)),
                        isQid(ok(X)) -> ok(isQid(X)),
                      isNePal(ok(X)) -> ok(isNePal(X)),
                  proper(__(X1, X2)) -> __(proper(X1), proper(X2)),
                       proper(nil()) -> ok(nil()),
                        proper(tt()) -> ok(tt()),
                      proper(U11(X)) -> U11(proper(X)),
                      proper(U22(X)) -> U22(proper(X)),
                   proper(isList(X)) -> isList(proper(X)),
                 proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)),
                      proper(U31(X)) -> U31(proper(X)),
                      proper(U42(X)) -> U42(proper(X)),
                 proper(isNeList(X)) -> isNeList(proper(X)),
                 proper(U41(X1, X2)) -> U41(proper(X1), proper(X2)),
                      proper(U52(X)) -> U52(proper(X)),
                 proper(U51(X1, X2)) -> U51(proper(X1), proper(X2)),
                      proper(U61(X)) -> U61(proper(X)),
                      proper(U72(X)) -> U72(proper(X)),
                    proper(isPal(X)) -> isPal(proper(X)),
                 proper(U71(X1, X2)) -> U71(proper(X1), proper(X2)),
                      proper(U81(X)) -> U81(proper(X)),
                    proper(isQid(X)) -> isQid(proper(X)),
                  proper(isNePal(X)) -> isNePal(proper(X)),
                         proper(a()) -> ok(a()),
                         proper(e()) -> ok(e()),
                         proper(i()) -> ok(i()),
                         proper(o()) -> ok(o()),
                         proper(u()) -> ok(u()),
                        top(mark(X)) -> top(proper(X)),
                          top(ok(X)) -> top(active(X))
   }
  Fail