MAYBE
TRS:
 {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                   mark(tt()) -> active(tt()),
                   mark(s(X)) -> active(s(mark(X))),
           mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
        mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                    mark(0()) -> active(0()),
                 mark(U31(X)) -> active(U31(mark(X))),
              mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
        mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
            mark(and(X1, X2)) -> active(and(mark(X1), X2)),
               mark(isNat(X)) -> active(isNat(X)),
         active(U11(tt(), N)) -> mark(N),
        active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
         active(plus(N, 0())) -> mark(U11(isNat(N), N)),
      active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
            active(U31(tt())) -> mark(0()),
           active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
            active(x(N, 0())) -> mark(U31(isNat(N))),
      active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
         active(and(tt(), X)) -> mark(X),
         active(isNat(s(V1))) -> mark(isNat(V1)),
  active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
           active(isNat(0())) -> mark(tt()),
     active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
            U11(X1, mark(X2)) -> U11(X1, X2),
          U11(X1, active(X2)) -> U11(X1, X2),
            U11(mark(X1), X2) -> U11(X1, X2),
          U11(active(X1), X2) -> U11(X1, X2),
                   s(mark(X)) -> s(X),
                 s(active(X)) -> s(X),
           plus(X1, mark(X2)) -> plus(X1, X2),
         plus(X1, active(X2)) -> plus(X1, X2),
           plus(mark(X1), X2) -> plus(X1, X2),
         plus(active(X1), X2) -> plus(X1, X2),
        U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
      U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
        U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
      U21(X1, active(X2), X3) -> U21(X1, X2, X3),
        U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
      U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                 U31(mark(X)) -> U31(X),
               U31(active(X)) -> U31(X),
              x(X1, mark(X2)) -> x(X1, X2),
            x(X1, active(X2)) -> x(X1, X2),
              x(mark(X1), X2) -> x(X1, X2),
            x(active(X1), X2) -> x(X1, X2),
        U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
      U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
        U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
      U41(X1, active(X2), X3) -> U41(X1, X2, X3),
        U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
      U41(active(X1), X2, X3) -> U41(X1, X2, X3),
            and(X1, mark(X2)) -> and(X1, X2),
          and(X1, active(X2)) -> and(X1, X2),
            and(mark(X1), X2) -> and(X1, X2),
          and(active(X1), X2) -> and(X1, X2),
               isNat(mark(X)) -> isNat(X),
             isNat(active(X)) -> isNat(X)}
 DP:
  Strict:
   {          mark#(U11(X1, X2)) -> mark#(X1),
              mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)),
              mark#(U11(X1, X2)) -> U11#(mark(X1), X2),
                     mark#(tt()) -> active#(tt()),
                     mark#(s(X)) -> mark#(X),
                     mark#(s(X)) -> active#(s(mark(X))),
                     mark#(s(X)) -> s#(mark(X)),
             mark#(plus(X1, X2)) -> mark#(X1),
             mark#(plus(X1, X2)) -> mark#(X2),
             mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))),
             mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)),
          mark#(U21(X1, X2, X3)) -> mark#(X1),
          mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)),
          mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3),
                      mark#(0()) -> active#(0()),
                   mark#(U31(X)) -> mark#(X),
                   mark#(U31(X)) -> active#(U31(mark(X))),
                   mark#(U31(X)) -> U31#(mark(X)),
                mark#(x(X1, X2)) -> mark#(X1),
                mark#(x(X1, X2)) -> mark#(X2),
                mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))),
                mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)),
          mark#(U41(X1, X2, X3)) -> mark#(X1),
          mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)),
          mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3),
              mark#(and(X1, X2)) -> mark#(X1),
              mark#(and(X1, X2)) -> active#(and(mark(X1), X2)),
              mark#(and(X1, X2)) -> and#(mark(X1), X2),
                 mark#(isNat(X)) -> active#(isNat(X)),
           active#(U11(tt(), N)) -> mark#(N),
          active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)),
          active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N),
          active#(plus(N, s(M))) -> and#(isNat(M), isNat(N)),
          active#(plus(N, s(M))) -> isNat#(N),
          active#(plus(N, s(M))) -> isNat#(M),
           active#(plus(N, 0())) -> mark#(U11(isNat(N), N)),
           active#(plus(N, 0())) -> U11#(isNat(N), N),
           active#(plus(N, 0())) -> isNat#(N),
        active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))),
        active#(U21(tt(), M, N)) -> s#(plus(N, M)),
        active#(U21(tt(), M, N)) -> plus#(N, M),
              active#(U31(tt())) -> mark#(0()),
             active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)),
             active#(x(N, s(M))) -> U41#(and(isNat(M), isNat(N)), M, N),
             active#(x(N, s(M))) -> and#(isNat(M), isNat(N)),
             active#(x(N, s(M))) -> isNat#(N),
             active#(x(N, s(M))) -> isNat#(M),
              active#(x(N, 0())) -> mark#(U31(isNat(N))),
              active#(x(N, 0())) -> U31#(isNat(N)),
              active#(x(N, 0())) -> isNat#(N),
        active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)),
        active#(U41(tt(), M, N)) -> plus#(x(N, M), N),
        active#(U41(tt(), M, N)) -> x#(N, M),
           active#(and(tt(), X)) -> mark#(X),
           active#(isNat(s(V1))) -> mark#(isNat(V1)),
           active#(isNat(s(V1))) -> isNat#(V1),
    active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))),
    active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)),
    active#(isNat(plus(V1, V2))) -> isNat#(V1),
    active#(isNat(plus(V1, V2))) -> isNat#(V2),
             active#(isNat(0())) -> mark#(tt()),
       active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))),
       active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)),
       active#(isNat(x(V1, V2))) -> isNat#(V1),
       active#(isNat(x(V1, V2))) -> isNat#(V2),
              U11#(X1, mark(X2)) -> U11#(X1, X2),
            U11#(X1, active(X2)) -> U11#(X1, X2),
              U11#(mark(X1), X2) -> U11#(X1, X2),
            U11#(active(X1), X2) -> U11#(X1, X2),
                     s#(mark(X)) -> s#(X),
                   s#(active(X)) -> s#(X),
             plus#(X1, mark(X2)) -> plus#(X1, X2),
           plus#(X1, active(X2)) -> plus#(X1, X2),
             plus#(mark(X1), X2) -> plus#(X1, X2),
           plus#(active(X1), X2) -> plus#(X1, X2),
          U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3),
        U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3),
          U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
        U21#(X1, active(X2), X3) -> U21#(X1, X2, X3),
          U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3),
        U21#(active(X1), X2, X3) -> U21#(X1, X2, X3),
                   U31#(mark(X)) -> U31#(X),
                 U31#(active(X)) -> U31#(X),
                x#(X1, mark(X2)) -> x#(X1, X2),
              x#(X1, active(X2)) -> x#(X1, X2),
                x#(mark(X1), X2) -> x#(X1, X2),
              x#(active(X1), X2) -> x#(X1, X2),
          U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3),
        U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3),
          U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
        U41#(X1, active(X2), X3) -> U41#(X1, X2, X3),
          U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3),
        U41#(active(X1), X2, X3) -> U41#(X1, X2, X3),
              and#(X1, mark(X2)) -> and#(X1, X2),
            and#(X1, active(X2)) -> and#(X1, X2),
              and#(mark(X1), X2) -> and#(X1, X2),
            and#(active(X1), X2) -> and#(X1, X2),
                 isNat#(mark(X)) -> isNat#(X),
               isNat#(active(X)) -> isNat#(X)}
  Weak:
  {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                    mark(tt()) -> active(tt()),
                    mark(s(X)) -> active(s(mark(X))),
            mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
         mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                     mark(0()) -> active(0()),
                  mark(U31(X)) -> active(U31(mark(X))),
               mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
         mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
             mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                mark(isNat(X)) -> active(isNat(X)),
          active(U11(tt(), N)) -> mark(N),
         active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
          active(plus(N, 0())) -> mark(U11(isNat(N), N)),
       active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
             active(U31(tt())) -> mark(0()),
            active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
             active(x(N, 0())) -> mark(U31(isNat(N))),
       active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
          active(and(tt(), X)) -> mark(X),
          active(isNat(s(V1))) -> mark(isNat(V1)),
   active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
            active(isNat(0())) -> mark(tt()),
      active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
             U11(X1, mark(X2)) -> U11(X1, X2),
           U11(X1, active(X2)) -> U11(X1, X2),
             U11(mark(X1), X2) -> U11(X1, X2),
           U11(active(X1), X2) -> U11(X1, X2),
                    s(mark(X)) -> s(X),
                  s(active(X)) -> s(X),
            plus(X1, mark(X2)) -> plus(X1, X2),
          plus(X1, active(X2)) -> plus(X1, X2),
            plus(mark(X1), X2) -> plus(X1, X2),
          plus(active(X1), X2) -> plus(X1, X2),
         U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
       U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
         U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
       U21(X1, active(X2), X3) -> U21(X1, X2, X3),
         U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
       U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                  U31(mark(X)) -> U31(X),
                U31(active(X)) -> U31(X),
               x(X1, mark(X2)) -> x(X1, X2),
             x(X1, active(X2)) -> x(X1, X2),
               x(mark(X1), X2) -> x(X1, X2),
             x(active(X1), X2) -> x(X1, X2),
         U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
       U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
         U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
       U41(X1, active(X2), X3) -> U41(X1, X2, X3),
         U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
       U41(active(X1), X2, X3) -> U41(X1, X2, X3),
             and(X1, mark(X2)) -> and(X1, X2),
           and(X1, active(X2)) -> and(X1, X2),
             and(mark(X1), X2) -> and(X1, X2),
           and(active(X1), X2) -> and(X1, X2),
                isNat(mark(X)) -> isNat(X),
              isNat(active(X)) -> isNat(X)}
  EDG:
   {
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(isNat(x(V1, V2))) -> isNat#(V2))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(isNat(x(V1, V2))) -> isNat#(V1))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(isNat(0())) -> mark#(tt()))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(isNat(plus(V1, V2))) -> isNat#(V2))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(isNat(plus(V1, V2))) -> isNat#(V1))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(isNat(s(V1))) -> isNat#(V1))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(isNat(s(V1))) -> mark#(isNat(V1)))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(and(tt(), X)) -> mark#(X))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(U41(tt(), M, N)) -> x#(N, M))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(U41(tt(), M, N)) -> plus#(x(N, M), N))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(x(N, 0())) -> isNat#(N))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(x(N, 0())) -> U31#(isNat(N)))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(x(N, 0())) -> mark#(U31(isNat(N))))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(x(N, s(M))) -> isNat#(M))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(x(N, s(M))) -> isNat#(N))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(x(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(x(N, s(M))) -> U41#(and(isNat(M), isNat(N)), M, N))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(U31(tt())) -> mark#(0()))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(U21(tt(), M, N)) -> plus#(N, M))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(U21(tt(), M, N)) -> s#(plus(N, M)))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(plus(N, 0())) -> isNat#(N))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(plus(N, 0())) -> U11#(isNat(N), N))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(plus(N, s(M))) -> isNat#(M))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(plus(N, s(M))) -> isNat#(N))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(plus(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
    (mark#(U31(X)) -> active#(U31(mark(X))), active#(U11(tt(), N)) -> mark#(N))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(isNat(X)) -> active#(isNat(X)))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(and(X1, X2)) -> and#(mark(X1), X2))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(and(X1, X2)) -> mark#(X1))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U41(X1, X2, X3)) -> mark#(X1))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(x(X1, X2)) -> mark#(X2))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(x(X1, X2)) -> mark#(X1))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U31(X)) -> U31#(mark(X)))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U31(X)) -> active#(U31(mark(X))))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U31(X)) -> mark#(X))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U21(X1, X2, X3)) -> mark#(X1))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(plus(X1, X2)) -> mark#(X2))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(plus(X1, X2)) -> mark#(X1))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(s(X)) -> s#(mark(X)))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(s(X)) -> active#(s(mark(X))))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(s(X)) -> mark#(X))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U11(X1, X2)) -> U11#(mark(X1), X2))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
    (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U11(X1, X2)) -> mark#(X1))
    (active#(isNat(plus(V1, V2))) -> isNat#(V1), isNat#(active(X)) -> isNat#(X))
    (active#(isNat(plus(V1, V2))) -> isNat#(V1), isNat#(mark(X)) -> isNat#(X))
    (mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
    (mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
    (mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
    (mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
    (mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3), U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3))
    (mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3), U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3))
    (U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
    (U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
    (U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
    (U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
    (U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3), U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3))
    (U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3), U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3))
    (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
    (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
    (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
    (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
    (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3))
    (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3))
    (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
    (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
    (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
    (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
    (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3))
    (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3))
    (U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3), U41#(active(X1), X2, X3) -> U41#(X1, X2, X3))
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    (U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
    (U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3), U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3))
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    (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(active(X1), X2, X3) -> U41#(X1, X2, X3))
    (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
    (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
    (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
    (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3))
    (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
    (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(active(X1), X2, X3) -> U41#(X1, X2, X3))
    (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
    (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
    (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
    (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3))
    (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(isNat(x(V1, V2))) -> isNat#(V2))
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    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(isNat(0())) -> mark#(tt()))
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    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(isNat(s(V1))) -> isNat#(V1))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(isNat(s(V1))) -> mark#(isNat(V1)))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(and(tt(), X)) -> mark#(X))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(U41(tt(), M, N)) -> x#(N, M))
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    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(x(N, 0())) -> isNat#(N))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(x(N, 0())) -> U31#(isNat(N)))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(x(N, 0())) -> mark#(U31(isNat(N))))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(x(N, s(M))) -> isNat#(M))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(x(N, s(M))) -> isNat#(N))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(x(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(x(N, s(M))) -> U41#(and(isNat(M), isNat(N)), M, N))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(U31(tt())) -> mark#(0()))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(U21(tt(), M, N)) -> plus#(N, M))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(U21(tt(), M, N)) -> s#(plus(N, M)))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(plus(N, 0())) -> isNat#(N))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(plus(N, 0())) -> U11#(isNat(N), N))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(plus(N, s(M))) -> isNat#(M))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(plus(N, s(M))) -> isNat#(N))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(plus(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
    (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(U11(tt(), N)) -> mark#(N))
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    (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
    (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(and(X1, X2)) -> mark#(X1))
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    (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
    (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(U41(X1, X2, X3)) -> mark#(X1))
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    (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(x(X1, X2)) -> mark#(X1))
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    (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
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    (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(plus(X1, X2)) -> mark#(X1))
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    (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(s(X)) -> mark#(X))
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    (mark#(U31(X)) -> mark#(X), mark#(and(X1, X2)) -> and#(mark(X1), X2))
    (mark#(U31(X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
    (mark#(U31(X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
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    (mark#(U31(X)) -> mark#(X), mark#(U41(X1, X2, X3)) -> mark#(X1))
    (mark#(U31(X)) -> mark#(X), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
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    (mark#(U31(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
    (mark#(U31(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
    (mark#(U31(X)) -> mark#(X), mark#(U31(X)) -> U31#(mark(X)))
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    (mark#(U31(X)) -> mark#(X), mark#(0()) -> active#(0()))
    (mark#(U31(X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3))
    (mark#(U31(X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
    (mark#(U31(X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> mark#(X1))
    (mark#(U31(X)) -> mark#(X), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
    (mark#(U31(X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
    (mark#(U31(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
    (mark#(U31(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
    (mark#(U31(X)) -> mark#(X), mark#(s(X)) -> s#(mark(X)))
    (mark#(U31(X)) -> mark#(X), mark#(s(X)) -> active#(s(mark(X))))
    (mark#(U31(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
    (mark#(U31(X)) -> mark#(X), mark#(tt()) -> active#(tt()))
    (mark#(U31(X)) -> mark#(X), mark#(U11(X1, X2)) -> U11#(mark(X1), X2))
    (mark#(U31(X)) -> mark#(X), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
    (mark#(U31(X)) -> mark#(X), mark#(U11(X1, X2)) -> mark#(X1))
    (s#(mark(X)) -> s#(X), s#(active(X)) -> s#(X))
    (s#(mark(X)) -> s#(X), s#(mark(X)) -> s#(X))
    (U31#(mark(X)) -> U31#(X), U31#(active(X)) -> U31#(X))
    (U31#(mark(X)) -> U31#(X), U31#(mark(X)) -> U31#(X))
    (isNat#(mark(X)) -> isNat#(X), isNat#(active(X)) -> isNat#(X))
    (isNat#(mark(X)) -> isNat#(X), isNat#(mark(X)) -> isNat#(X))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(isNat(X)) -> active#(isNat(X)))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(and(X1, X2)) -> and#(mark(X1), X2))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(and(X1, X2)) -> mark#(X1))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U41(X1, X2, X3)) -> mark#(X1))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(x(X1, X2)) -> mark#(X2))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(x(X1, X2)) -> mark#(X1))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U31(X)) -> U31#(mark(X)))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U31(X)) -> active#(U31(mark(X))))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U31(X)) -> mark#(X))
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    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U21(X1, X2, X3)) -> mark#(X1))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(plus(X1, X2)) -> mark#(X2))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(plus(X1, X2)) -> mark#(X1))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(s(X)) -> s#(mark(X)))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(s(X)) -> active#(s(mark(X))))
    (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(s(X)) -> mark#(X))
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    (mark#(U31(X)) -> U31#(mark(X)), U31#(active(X)) -> U31#(X))
    (mark#(U31(X)) -> U31#(mark(X)), U31#(mark(X)) -> U31#(X))
    (active#(x(N, 0())) -> U31#(isNat(N)), U31#(active(X)) -> U31#(X))
    (active#(x(N, 0())) -> U31#(isNat(N)), U31#(mark(X)) -> U31#(X))
    (mark#(x(X1, X2)) -> mark#(X2), mark#(isNat(X)) -> active#(isNat(X)))
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    (mark#(x(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X1))
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    (mark#(x(X1, X2)) -> mark#(X2), mark#(U31(X)) -> mark#(X))
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    (mark#(x(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X1))
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    (mark#(x(X1, X2)) -> mark#(X2), mark#(U11(X1, X2)) -> mark#(X1))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> isNat#(V2))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> isNat#(V1))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
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    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> isNat#(V1))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(s(V1))) -> isNat#(V1))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(s(V1))) -> mark#(isNat(V1)))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(and(tt(), X)) -> mark#(X))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U41(tt(), M, N)) -> x#(N, M))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U41(tt(), M, N)) -> plus#(x(N, M), N))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, 0())) -> isNat#(N))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, 0())) -> U31#(isNat(N)))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, 0())) -> mark#(U31(isNat(N))))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> isNat#(M))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> isNat#(N))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> and#(isNat(M), isNat(N)))
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    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, 0())) -> isNat#(N))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, 0())) -> U11#(isNat(N), N))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> isNat#(M))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> isNat#(N))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> and#(isNat(M), isNat(N)))
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    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
    (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U11(tt(), N)) -> mark#(N))
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    (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(and(X1, X2)) -> and#(mark(X1), X2))
    (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
    (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(and(X1, X2)) -> mark#(X1))
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    (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
    (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U41(X1, X2, X3)) -> mark#(X1))
    (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
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    (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U21(X1, X2, X3)) -> mark#(X1))
    (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
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    (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(plus(X1, X2)) -> mark#(X2))
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    (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
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    (active#(x(N, s(M))) -> isNat#(M), isNat#(mark(X)) -> isNat#(X))
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    (mark#(plus(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> and#(mark(X1), X2))
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    (mark#(plus(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> mark#(X1))
    (mark#(plus(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
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    (mark#(plus(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
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    (mark#(plus(X1, X2)) -> mark#(X1), mark#(U31(X)) -> mark#(X))
    (mark#(plus(X1, X2)) -> mark#(X1), mark#(0()) -> active#(0()))
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    (mark#(plus(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> mark#(X1))
    (mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
    (mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
    (mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
    (mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
    (mark#(plus(X1, X2)) -> mark#(X1), mark#(s(X)) -> s#(mark(X)))
    (mark#(plus(X1, X2)) -> mark#(X1), mark#(s(X)) -> active#(s(mark(X))))
    (mark#(plus(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
    (mark#(plus(X1, X2)) -> mark#(X1), mark#(tt()) -> active#(tt()))
    (mark#(plus(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> U11#(mark(X1), X2))
    (mark#(plus(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
    (mark#(plus(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> mark#(X1))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> and#(mark(X1), X2))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> mark#(X1))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(U31(X)) -> U31#(mark(X)))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(U31(X)) -> active#(U31(mark(X))))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(U31(X)) -> mark#(X))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(0()) -> active#(0()))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> mark#(X1))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(s(X)) -> s#(mark(X)))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(s(X)) -> active#(s(mark(X))))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(tt()) -> active#(tt()))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> U11#(mark(X1), X2))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
    (mark#(x(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> mark#(X1))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> and#(mark(X1), X2))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> mark#(X1))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(U31(X)) -> U31#(mark(X)))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(U31(X)) -> active#(U31(mark(X))))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(U31(X)) -> mark#(X))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(0()) -> active#(0()))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3))
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    (mark#(and(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> mark#(X1))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(s(X)) -> s#(mark(X)))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(s(X)) -> active#(s(mark(X))))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(tt()) -> active#(tt()))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> U11#(mark(X1), X2))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
    (mark#(and(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> mark#(X1))
    (active#(U41(tt(), M, N)) -> plus#(x(N, M), N), plus#(active(X1), X2) -> plus#(X1, X2))
    (active#(U41(tt(), M, N)) -> plus#(x(N, M), N), plus#(mark(X1), X2) -> plus#(X1, X2))
    (active#(U41(tt(), M, N)) -> plus#(x(N, M), N), plus#(X1, active(X2)) -> plus#(X1, X2))
    (active#(U41(tt(), M, N)) -> plus#(x(N, M), N), plus#(X1, mark(X2)) -> plus#(X1, X2))
    (active#(plus(N, s(M))) -> isNat#(N), isNat#(active(X)) -> isNat#(X))
    (active#(plus(N, s(M))) -> isNat#(N), isNat#(mark(X)) -> isNat#(X))
    (active#(x(N, s(M))) -> isNat#(N), isNat#(active(X)) -> isNat#(X))
    (active#(x(N, s(M))) -> isNat#(N), isNat#(mark(X)) -> isNat#(X))
    (mark#(U11(X1, X2)) -> U11#(mark(X1), X2), U11#(active(X1), X2) -> U11#(X1, X2))
    (mark#(U11(X1, X2)) -> U11#(mark(X1), X2), U11#(mark(X1), X2) -> U11#(X1, X2))
    (mark#(U11(X1, X2)) -> U11#(mark(X1), X2), U11#(X1, active(X2)) -> U11#(X1, X2))
    (mark#(U11(X1, X2)) -> U11#(mark(X1), X2), U11#(X1, mark(X2)) -> U11#(X1, X2))
    (active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
    (active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
    (active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
    (active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
    (active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N), U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3))
    (active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N), U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> isNat#(V2))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> isNat#(V1))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(isNat(0())) -> mark#(tt()))
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    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> isNat#(V1))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(isNat(s(V1))) -> isNat#(V1))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(isNat(s(V1))) -> mark#(isNat(V1)))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(and(tt(), X)) -> mark#(X))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(U41(tt(), M, N)) -> x#(N, M))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(U41(tt(), M, N)) -> plus#(x(N, M), N))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(x(N, 0())) -> isNat#(N))
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    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(x(N, 0())) -> mark#(U31(isNat(N))))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNat#(M))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNat#(N))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(x(N, s(M))) -> U41#(and(isNat(M), isNat(N)), M, N))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(U31(tt())) -> mark#(0()))
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    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(U21(tt(), M, N)) -> s#(plus(N, M)))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(plus(N, 0())) -> isNat#(N))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(plus(N, 0())) -> U11#(isNat(N), N))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNat#(M))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNat#(N))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
    (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(U11(tt(), N)) -> mark#(N))
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    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(and(X1, X2)) -> mark#(X1))
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    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U41(X1, X2, X3)) -> mark#(X1))
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    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(x(X1, X2)) -> mark#(X1))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U31(X)) -> U31#(mark(X)))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U31(X)) -> active#(U31(mark(X))))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U31(X)) -> mark#(X))
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    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U21(X1, X2, X3)) -> mark#(X1))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> mark#(X2))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> mark#(X1))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(s(X)) -> s#(mark(X)))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(s(X)) -> active#(s(mark(X))))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(s(X)) -> mark#(X))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U11(X1, X2)) -> U11#(mark(X1), X2))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
    (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U11(X1, X2)) -> mark#(X1))
    (active#(isNat(plus(V1, V2))) -> isNat#(V2), isNat#(active(X)) -> isNat#(X))
    (active#(isNat(plus(V1, V2))) -> isNat#(V2), isNat#(mark(X)) -> isNat#(X))
    (U11#(X1, mark(X2)) -> U11#(X1, X2), U11#(active(X1), X2) -> U11#(X1, X2))
    (U11#(X1, mark(X2)) -> U11#(X1, X2), U11#(mark(X1), X2) -> U11#(X1, X2))
    (U11#(X1, mark(X2)) -> U11#(X1, X2), U11#(X1, active(X2)) -> U11#(X1, X2))
    (U11#(X1, mark(X2)) -> U11#(X1, X2), U11#(X1, mark(X2)) -> U11#(X1, X2))
    (U11#(mark(X1), X2) -> U11#(X1, X2), U11#(active(X1), X2) -> U11#(X1, X2))
    (U11#(mark(X1), X2) -> U11#(X1, X2), U11#(mark(X1), X2) -> U11#(X1, X2))
    (U11#(mark(X1), X2) -> U11#(X1, X2), U11#(X1, active(X2)) -> U11#(X1, X2))
    (U11#(mark(X1), X2) -> U11#(X1, X2), U11#(X1, mark(X2)) -> U11#(X1, X2))
    (plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(active(X1), X2) -> plus#(X1, X2))
    (plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))
    (plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
    (plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
    (plus#(mark(X1), X2) -> plus#(X1, X2), plus#(active(X1), X2) -> plus#(X1, X2))
    (plus#(mark(X1), X2) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))
    (plus#(mark(X1), X2) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
    (plus#(mark(X1), X2) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
    (x#(X1, mark(X2)) -> x#(X1, X2), x#(active(X1), X2) -> x#(X1, X2))
    (x#(X1, mark(X2)) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))
    (x#(X1, mark(X2)) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
    (x#(X1, mark(X2)) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
    (x#(mark(X1), X2) -> x#(X1, X2), x#(active(X1), X2) -> x#(X1, X2))
    (x#(mark(X1), X2) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))
    (x#(mark(X1), X2) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
    (x#(mark(X1), X2) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
    (and#(X1, mark(X2)) -> and#(X1, X2), and#(active(X1), X2) -> and#(X1, X2))
    (and#(X1, mark(X2)) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))
    (and#(X1, mark(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
    (and#(X1, mark(X2)) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
    (and#(mark(X1), X2) -> and#(X1, X2), and#(active(X1), X2) -> and#(X1, X2))
    (and#(mark(X1), X2) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))
    (and#(mark(X1), X2) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
    (and#(mark(X1), X2) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
    (mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)), plus#(active(X1), X2) -> plus#(X1, X2))
    (mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)), plus#(mark(X1), X2) -> plus#(X1, X2))
    (mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)), plus#(X1, active(X2)) -> plus#(X1, X2))
    (mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)), plus#(X1, mark(X2)) -> plus#(X1, X2))
    (active#(plus(N, s(M))) -> and#(isNat(M), isNat(N)), and#(active(X1), X2) -> and#(X1, X2))
    (active#(plus(N, s(M))) -> and#(isNat(M), isNat(N)), and#(mark(X1), X2) -> and#(X1, X2))
    (active#(plus(N, s(M))) -> and#(isNat(M), isNat(N)), and#(X1, active(X2)) -> and#(X1, X2))
    (active#(plus(N, s(M))) -> and#(isNat(M), isNat(N)), and#(X1, mark(X2)) -> and#(X1, X2))
    (active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)), and#(active(X1), X2) -> and#(X1, X2))
    (active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)), and#(mark(X1), X2) -> and#(X1, X2))
    (active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)), and#(X1, active(X2)) -> and#(X1, X2))
    (active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)), and#(X1, mark(X2)) -> and#(X1, X2))
    (active#(U21(tt(), M, N)) -> plus#(N, M), plus#(active(X1), X2) -> plus#(X1, X2))
    (active#(U21(tt(), M, N)) -> plus#(N, M), plus#(mark(X1), X2) -> plus#(X1, X2))
    (active#(U21(tt(), M, N)) -> plus#(N, M), plus#(X1, active(X2)) -> plus#(X1, X2))
    (active#(U21(tt(), M, N)) -> plus#(N, M), plus#(X1, mark(X2)) -> plus#(X1, X2))
    (active#(U31(tt())) -> mark#(0()), mark#(0()) -> active#(0()))
    (active#(isNat(0())) -> mark#(tt()), mark#(tt()) -> active#(tt()))
    (active#(U41(tt(), M, N)) -> x#(N, M), x#(X1, mark(X2)) -> x#(X1, X2))
    (active#(U41(tt(), M, N)) -> x#(N, M), x#(X1, active(X2)) -> x#(X1, X2))
    (active#(U41(tt(), M, N)) -> x#(N, M), x#(mark(X1), X2) -> x#(X1, X2))
    (active#(U41(tt(), M, N)) -> x#(N, M), x#(active(X1), X2) -> x#(X1, X2))
    (active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)), and#(X1, mark(X2)) -> and#(X1, X2))
    (active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)), and#(X1, active(X2)) -> and#(X1, X2))
    (active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)), and#(mark(X1), X2) -> and#(X1, X2))
    (active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)), and#(active(X1), X2) -> and#(X1, X2))
    (active#(x(N, s(M))) -> and#(isNat(M), isNat(N)), and#(X1, mark(X2)) -> and#(X1, X2))
    (active#(x(N, s(M))) -> and#(isNat(M), isNat(N)), and#(X1, active(X2)) -> and#(X1, X2))
    (active#(x(N, s(M))) -> and#(isNat(M), isNat(N)), and#(mark(X1), X2) -> and#(X1, X2))
    (active#(x(N, s(M))) -> and#(isNat(M), isNat(N)), and#(active(X1), X2) -> and#(X1, X2))
    (mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)), x#(X1, mark(X2)) -> x#(X1, X2))
    (mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)), x#(X1, active(X2)) -> x#(X1, X2))
    (mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)), x#(mark(X1), X2) -> x#(X1, X2))
    (mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)), x#(active(X1), X2) -> x#(X1, X2))
    (and#(active(X1), X2) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
    (and#(active(X1), X2) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
    (and#(active(X1), X2) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))
    (and#(active(X1), X2) -> and#(X1, X2), and#(active(X1), X2) -> and#(X1, X2))
    (and#(X1, active(X2)) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
    (and#(X1, active(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
    (and#(X1, active(X2)) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))
    (and#(X1, active(X2)) -> and#(X1, X2), and#(active(X1), X2) -> and#(X1, X2))
    (x#(active(X1), X2) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
    (x#(active(X1), X2) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
    (x#(active(X1), X2) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))
    (x#(active(X1), X2) -> x#(X1, X2), x#(active(X1), X2) -> x#(X1, X2))
    (x#(X1, active(X2)) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
    (x#(X1, active(X2)) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
    (x#(X1, active(X2)) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))
    (x#(X1, active(X2)) -> x#(X1, X2), x#(active(X1), X2) -> x#(X1, X2))
    (plus#(active(X1), X2) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
    (plus#(active(X1), X2) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
    (plus#(active(X1), X2) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))
    (plus#(active(X1), X2) -> plus#(X1, X2), plus#(active(X1), X2) -> plus#(X1, X2))
    (plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
    (plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
    (plus#(X1, active(X2)) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))
    (plus#(X1, active(X2)) -> plus#(X1, X2), plus#(active(X1), X2) -> plus#(X1, X2))
    (U11#(active(X1), X2) -> U11#(X1, X2), U11#(X1, mark(X2)) -> U11#(X1, X2))
    (U11#(active(X1), X2) -> U11#(X1, X2), U11#(X1, active(X2)) -> U11#(X1, X2))
    (U11#(active(X1), X2) -> U11#(X1, X2), U11#(mark(X1), X2) -> U11#(X1, X2))
    (U11#(active(X1), X2) -> U11#(X1, X2), U11#(active(X1), X2) -> U11#(X1, X2))
    (U11#(X1, active(X2)) -> U11#(X1, X2), U11#(X1, mark(X2)) -> U11#(X1, X2))
    (U11#(X1, active(X2)) -> U11#(X1, X2), U11#(X1, active(X2)) -> U11#(X1, X2))
    (U11#(X1, active(X2)) -> U11#(X1, X2), U11#(mark(X1), X2) -> U11#(X1, X2))
    (U11#(X1, active(X2)) -> U11#(X1, X2), U11#(active(X1), X2) -> U11#(X1, X2))
    (active#(isNat(x(V1, V2))) -> isNat#(V2), isNat#(mark(X)) -> isNat#(X))
    (active#(isNat(x(V1, V2))) -> isNat#(V2), isNat#(active(X)) -> isNat#(X))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U11(X1, X2)) -> mark#(X1))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U11(X1, X2)) -> U11#(mark(X1), X2))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(s(X)) -> mark#(X))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(s(X)) -> active#(s(mark(X))))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(s(X)) -> s#(mark(X)))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> mark#(X1))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> mark#(X2))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U21(X1, X2, X3)) -> mark#(X1))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U31(X)) -> mark#(X))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U31(X)) -> active#(U31(mark(X))))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U31(X)) -> U31#(mark(X)))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(x(X1, X2)) -> mark#(X1))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(x(X1, X2)) -> mark#(X2))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U41(X1, X2, X3)) -> mark#(X1))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(and(X1, X2)) -> mark#(X1))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(and(X1, X2)) -> and#(mark(X1), X2))
    (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(isNat(X)) -> active#(isNat(X)))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(U11(tt(), N)) -> mark#(N))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(plus(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNat#(N))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(plus(N, s(M))) -> isNat#(M))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(plus(N, 0())) -> U11#(isNat(N), N))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(plus(N, 0())) -> isNat#(N))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(U21(tt(), M, N)) -> s#(plus(N, M)))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(U21(tt(), M, N)) -> plus#(N, M))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(U31(tt())) -> mark#(0()))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(x(N, s(M))) -> U41#(and(isNat(M), isNat(N)), M, N))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(x(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNat#(N))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(x(N, s(M))) -> isNat#(M))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(x(N, 0())) -> mark#(U31(isNat(N))))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(x(N, 0())) -> U31#(isNat(N)))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(x(N, 0())) -> isNat#(N))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(U41(tt(), M, N)) -> plus#(x(N, M), N))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(U41(tt(), M, N)) -> x#(N, M))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(and(tt(), X)) -> mark#(X))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(s(V1))) -> mark#(isNat(V1)))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(s(V1))) -> isNat#(V1))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> isNat#(V1))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> isNat#(V2))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(0())) -> mark#(tt()))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> isNat#(V1))
    (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> isNat#(V2))
    (active#(x(N, s(M))) -> U41#(and(isNat(M), isNat(N)), M, N), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
    (active#(x(N, s(M))) -> U41#(and(isNat(M), isNat(N)), M, N), U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3))
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    (active#(U11(tt(), N)) -> mark#(N), mark#(plus(X1, X2)) -> mark#(X1))
    (active#(U11(tt(), N)) -> mark#(N), mark#(plus(X1, X2)) -> mark#(X2))
    (active#(U11(tt(), N)) -> mark#(N), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
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    (active#(U11(tt(), N)) -> mark#(N), mark#(U21(X1, X2, X3)) -> mark#(X1))
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    (active#(U11(tt(), N)) -> mark#(N), mark#(0()) -> active#(0()))
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    (active#(U11(tt(), N)) -> mark#(N), mark#(U31(X)) -> U31#(mark(X)))
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    (active#(U11(tt(), N)) -> mark#(N), mark#(x(X1, X2)) -> mark#(X2))
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    (active#(plus(N, 0())) -> U11#(isNat(N), N), U11#(mark(X1), X2) -> U11#(X1, X2))
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    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, s(M))) -> isNat#(N))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, s(M))) -> isNat#(M))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, 0())) -> U11#(isNat(N), N))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, 0())) -> isNat#(N))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U21(tt(), M, N)) -> s#(plus(N, M)))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U21(tt(), M, N)) -> plus#(N, M))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U31(tt())) -> mark#(0()))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> U41#(and(isNat(M), isNat(N)), M, N))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> isNat#(N))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> isNat#(M))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, 0())) -> mark#(U31(isNat(N))))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, 0())) -> U31#(isNat(N)))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, 0())) -> isNat#(N))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U41(tt(), M, N)) -> plus#(x(N, M), N))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U41(tt(), M, N)) -> x#(N, M))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(and(tt(), X)) -> mark#(X))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(s(V1))) -> mark#(isNat(V1)))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(s(V1))) -> isNat#(V1))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> isNat#(V1))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> isNat#(V2))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(0())) -> mark#(tt()))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> isNat#(V1))
    (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> isNat#(V2))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(U11(X1, X2)) -> mark#(X1))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(U11(X1, X2)) -> U11#(mark(X1), X2))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(tt()) -> active#(tt()))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(s(X)) -> mark#(X))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(s(X)) -> active#(s(mark(X))))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(s(X)) -> s#(mark(X)))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X1))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X2))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(U21(X1, X2, X3)) -> mark#(X1))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(0()) -> active#(0()))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(U31(X)) -> mark#(X))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(U31(X)) -> active#(U31(mark(X))))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(U31(X)) -> U31#(mark(X)))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X1))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X2))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(U41(X1, X2, X3)) -> mark#(X1))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> mark#(X1))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> and#(mark(X1), X2))
    (mark#(plus(X1, X2)) -> mark#(X2), mark#(isNat(X)) -> active#(isNat(X)))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(U11(tt(), N)) -> mark#(N))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> isNat#(N))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> isNat#(M))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, 0())) -> U11#(isNat(N), N))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, 0())) -> isNat#(N))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(U21(tt(), M, N)) -> s#(plus(N, M)))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(U21(tt(), M, N)) -> plus#(N, M))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(U31(tt())) -> mark#(0()))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> U41#(and(isNat(M), isNat(N)), M, N))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> isNat#(N))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> isNat#(M))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, 0())) -> mark#(U31(isNat(N))))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, 0())) -> U31#(isNat(N)))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, 0())) -> isNat#(N))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(U41(tt(), M, N)) -> plus#(x(N, M), N))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(U41(tt(), M, N)) -> x#(N, M))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(and(tt(), X)) -> mark#(X))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(s(V1))) -> mark#(isNat(V1)))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(s(V1))) -> isNat#(V1))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(plus(V1, V2))) -> isNat#(V1))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(plus(V1, V2))) -> isNat#(V2))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(0())) -> mark#(tt()))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(x(V1, V2))) -> isNat#(V1))
    (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(x(V1, V2))) -> isNat#(V2))
    (mark#(s(X)) -> s#(mark(X)), s#(mark(X)) -> s#(X))
    (mark#(s(X)) -> s#(mark(X)), s#(active(X)) -> s#(X))
    (isNat#(active(X)) -> isNat#(X), isNat#(mark(X)) -> isNat#(X))
    (isNat#(active(X)) -> isNat#(X), isNat#(active(X)) -> isNat#(X))
    (U31#(active(X)) -> U31#(X), U31#(mark(X)) -> U31#(X))
    (U31#(active(X)) -> U31#(X), U31#(active(X)) -> U31#(X))
    (s#(active(X)) -> s#(X), s#(mark(X)) -> s#(X))
    (s#(active(X)) -> s#(X), s#(active(X)) -> s#(X))
    (active#(and(tt(), X)) -> mark#(X), mark#(U11(X1, X2)) -> mark#(X1))
    (active#(and(tt(), X)) -> mark#(X), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
    (active#(and(tt(), X)) -> mark#(X), mark#(U11(X1, X2)) -> U11#(mark(X1), X2))
    (active#(and(tt(), X)) -> mark#(X), mark#(tt()) -> active#(tt()))
    (active#(and(tt(), X)) -> mark#(X), mark#(s(X)) -> mark#(X))
    (active#(and(tt(), X)) -> mark#(X), mark#(s(X)) -> active#(s(mark(X))))
    (active#(and(tt(), X)) -> mark#(X), mark#(s(X)) -> s#(mark(X)))
    (active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
    (active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
    (active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
    (active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
    (active#(and(tt(), X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> mark#(X1))
    (active#(and(tt(), X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
    (active#(and(tt(), X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3))
    (active#(and(tt(), X)) -> mark#(X), mark#(0()) -> active#(0()))
    (active#(and(tt(), X)) -> mark#(X), mark#(U31(X)) -> mark#(X))
    (active#(and(tt(), X)) -> mark#(X), mark#(U31(X)) -> active#(U31(mark(X))))
    (active#(and(tt(), X)) -> mark#(X), mark#(U31(X)) -> U31#(mark(X)))
    (active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
    (active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
    (active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
    (active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
    (active#(and(tt(), X)) -> mark#(X), mark#(U41(X1, X2, X3)) -> mark#(X1))
    (active#(and(tt(), X)) -> mark#(X), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
    (active#(and(tt(), X)) -> mark#(X), mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3))
    (active#(and(tt(), X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
    (active#(and(tt(), X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
    (active#(and(tt(), X)) -> mark#(X), mark#(and(X1, X2)) -> and#(mark(X1), X2))
    (active#(and(tt(), X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
    (mark#(s(X)) -> mark#(X), mark#(U11(X1, X2)) -> mark#(X1))
    (mark#(s(X)) -> mark#(X), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
    (mark#(s(X)) -> mark#(X), mark#(U11(X1, X2)) -> U11#(mark(X1), X2))
    (mark#(s(X)) -> mark#(X), mark#(tt()) -> active#(tt()))
    (mark#(s(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
    (mark#(s(X)) -> mark#(X), mark#(s(X)) -> active#(s(mark(X))))
    (mark#(s(X)) -> mark#(X), mark#(s(X)) -> s#(mark(X)))
    (mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
    (mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
    (mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
    (mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
    (mark#(s(X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> mark#(X1))
    (mark#(s(X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
    (mark#(s(X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3))
    (mark#(s(X)) -> mark#(X), mark#(0()) -> active#(0()))
    (mark#(s(X)) -> mark#(X), mark#(U31(X)) -> mark#(X))
    (mark#(s(X)) -> mark#(X), mark#(U31(X)) -> active#(U31(mark(X))))
    (mark#(s(X)) -> mark#(X), mark#(U31(X)) -> U31#(mark(X)))
    (mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
    (mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
    (mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
    (mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
    (mark#(s(X)) -> mark#(X), mark#(U41(X1, X2, X3)) -> mark#(X1))
    (mark#(s(X)) -> mark#(X), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
    (mark#(s(X)) -> mark#(X), mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3))
    (mark#(s(X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
    (mark#(s(X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
    (mark#(s(X)) -> mark#(X), mark#(and(X1, X2)) -> and#(mark(X1), X2))
    (mark#(s(X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
    (active#(U21(tt(), M, N)) -> s#(plus(N, M)), s#(mark(X)) -> s#(X))
    (active#(U21(tt(), M, N)) -> s#(plus(N, M)), s#(active(X)) -> s#(X))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U11(tt(), N)) -> mark#(N))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(plus(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(plus(N, s(M))) -> isNat#(N))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(plus(N, s(M))) -> isNat#(M))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(plus(N, 0())) -> U11#(isNat(N), N))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(plus(N, 0())) -> isNat#(N))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U21(tt(), M, N)) -> s#(plus(N, M)))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U21(tt(), M, N)) -> plus#(N, M))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U31(tt())) -> mark#(0()))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(x(N, s(M))) -> U41#(and(isNat(M), isNat(N)), M, N))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(x(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(x(N, s(M))) -> isNat#(N))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(x(N, s(M))) -> isNat#(M))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(x(N, 0())) -> mark#(U31(isNat(N))))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(x(N, 0())) -> U31#(isNat(N)))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(x(N, 0())) -> isNat#(N))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U41(tt(), M, N)) -> plus#(x(N, M), N))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U41(tt(), M, N)) -> x#(N, M))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(and(tt(), X)) -> mark#(X))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(s(V1))) -> mark#(isNat(V1)))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(s(V1))) -> isNat#(V1))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> isNat#(V1))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> isNat#(V2))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(0())) -> mark#(tt()))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(x(V1, V2))) -> isNat#(V1))
    (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(x(V1, V2))) -> isNat#(V2))
    (U41#(active(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
    (U41#(active(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3))
    (U41#(active(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
    (U41#(active(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
    (U41#(active(X1), X2, X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
    (U41#(active(X1), X2, X3) -> U41#(X1, X2, X3), U41#(active(X1), X2, X3) -> U41#(X1, X2, X3))
    (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
    (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3))
    (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
    (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
    (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
    (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(active(X1), X2, X3) -> U41#(X1, X2, X3))
    (U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
    (U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3), U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3))
    (U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
    (U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
    (U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
    (U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3), U41#(active(X1), X2, X3) -> U41#(X1, X2, X3))
    (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3))
    (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3))
    (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
    (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
    (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
    (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
    (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3))
    (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3))
    (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
    (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
    (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
    (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
    (U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3), U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3))
    (U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3), U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3))
    (U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
    (U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
    (U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
    (U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
    (mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
    (mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3), U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3))
    (mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
    (mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
    (mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
    (mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3), U41#(active(X1), X2, X3) -> U41#(X1, X2, X3))
    (active#(isNat(x(V1, V2))) -> isNat#(V1), isNat#(mark(X)) -> isNat#(X))
    (active#(isNat(x(V1, V2))) -> isNat#(V1), isNat#(active(X)) -> isNat#(X))
    (active#(isNat(s(V1))) -> isNat#(V1), isNat#(mark(X)) -> isNat#(X))
    (active#(isNat(s(V1))) -> isNat#(V1), isNat#(active(X)) -> isNat#(X))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U11(X1, X2)) -> mark#(X1))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U11(X1, X2)) -> U11#(mark(X1), X2))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(s(X)) -> mark#(X))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(s(X)) -> active#(s(mark(X))))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(s(X)) -> s#(mark(X)))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> mark#(X1))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> mark#(X2))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> plus#(mark(X1), mark(X2)))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U21(X1, X2, X3)) -> mark#(X1))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U21(X1, X2, X3)) -> U21#(mark(X1), X2, X3))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U31(X)) -> mark#(X))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U31(X)) -> active#(U31(mark(X))))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U31(X)) -> U31#(mark(X)))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> mark#(X1))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> mark#(X2))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> x#(mark(X1), mark(X2)))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U41(X1, X2, X3)) -> mark#(X1))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U41(X1, X2, X3)) -> U41#(mark(X1), X2, X3))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(and(X1, X2)) -> mark#(X1))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(and(X1, X2)) -> and#(mark(X1), X2))
    (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(isNat(X)) -> active#(isNat(X)))
    (mark#(s(X)) -> active#(s(mark(X))), active#(U11(tt(), N)) -> mark#(N))
    (mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
    (mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> U21#(and(isNat(M), isNat(N)), M, N))
    (mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> isNat#(N))
    (mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, s(M))) -> isNat#(M))
    (mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
    (mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, 0())) -> U11#(isNat(N), N))
    (mark#(s(X)) -> active#(s(mark(X))), active#(plus(N, 0())) -> isNat#(N))
    (mark#(s(X)) -> active#(s(mark(X))), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
    (mark#(s(X)) -> active#(s(mark(X))), active#(U21(tt(), M, N)) -> s#(plus(N, M)))
    (mark#(s(X)) -> active#(s(mark(X))), active#(U21(tt(), M, N)) -> plus#(N, M))
    (mark#(s(X)) -> active#(s(mark(X))), active#(U31(tt())) -> mark#(0()))
    (mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
    (mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> U41#(and(isNat(M), isNat(N)), M, N))
    (mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> and#(isNat(M), isNat(N)))
    (mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> isNat#(N))
    (mark#(s(X)) -> active#(s(mark(X))), active#(x(N, s(M))) -> isNat#(M))
    (mark#(s(X)) -> active#(s(mark(X))), active#(x(N, 0())) -> mark#(U31(isNat(N))))
    (mark#(s(X)) -> active#(s(mark(X))), active#(x(N, 0())) -> U31#(isNat(N)))
    (mark#(s(X)) -> active#(s(mark(X))), active#(x(N, 0())) -> isNat#(N))
    (mark#(s(X)) -> active#(s(mark(X))), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
    (mark#(s(X)) -> active#(s(mark(X))), active#(U41(tt(), M, N)) -> plus#(x(N, M), N))
    (mark#(s(X)) -> active#(s(mark(X))), active#(U41(tt(), M, N)) -> x#(N, M))
    (mark#(s(X)) -> active#(s(mark(X))), active#(and(tt(), X)) -> mark#(X))
    (mark#(s(X)) -> active#(s(mark(X))), active#(isNat(s(V1))) -> mark#(isNat(V1)))
    (mark#(s(X)) -> active#(s(mark(X))), active#(isNat(s(V1))) -> isNat#(V1))
    (mark#(s(X)) -> active#(s(mark(X))), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(s(X)) -> active#(s(mark(X))), active#(isNat(plus(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(s(X)) -> active#(s(mark(X))), active#(isNat(plus(V1, V2))) -> isNat#(V1))
    (mark#(s(X)) -> active#(s(mark(X))), active#(isNat(plus(V1, V2))) -> isNat#(V2))
    (mark#(s(X)) -> active#(s(mark(X))), active#(isNat(0())) -> mark#(tt()))
    (mark#(s(X)) -> active#(s(mark(X))), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
    (mark#(s(X)) -> active#(s(mark(X))), active#(isNat(x(V1, V2))) -> and#(isNat(V1), isNat(V2)))
    (mark#(s(X)) -> active#(s(mark(X))), active#(isNat(x(V1, V2))) -> isNat#(V1))
    (mark#(s(X)) -> active#(s(mark(X))), active#(isNat(x(V1, V2))) -> isNat#(V2))
   }
   SCCS:
    Scc:
     {  isNat#(mark(X)) -> isNat#(X),
      isNat#(active(X)) -> isNat#(X)}
    Scc:
     {  and#(X1, mark(X2)) -> and#(X1, X2),
      and#(X1, active(X2)) -> and#(X1, X2),
        and#(mark(X1), X2) -> and#(X1, X2),
      and#(active(X1), X2) -> and#(X1, X2)}
    Scc:
     {  U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3),
      U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3),
        U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
      U41#(X1, active(X2), X3) -> U41#(X1, X2, X3),
        U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3),
      U41#(active(X1), X2, X3) -> U41#(X1, X2, X3)}
    Scc:
     {  x#(X1, mark(X2)) -> x#(X1, X2),
      x#(X1, active(X2)) -> x#(X1, X2),
        x#(mark(X1), X2) -> x#(X1, X2),
      x#(active(X1), X2) -> x#(X1, X2)}
    Scc:
     {  U31#(mark(X)) -> U31#(X),
      U31#(active(X)) -> U31#(X)}
    Scc:
     {  U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3),
      U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3),
        U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
      U21#(X1, active(X2), X3) -> U21#(X1, X2, X3),
        U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3),
      U21#(active(X1), X2, X3) -> U21#(X1, X2, X3)}
    Scc:
     {  plus#(X1, mark(X2)) -> plus#(X1, X2),
      plus#(X1, active(X2)) -> plus#(X1, X2),
        plus#(mark(X1), X2) -> plus#(X1, X2),
      plus#(active(X1), X2) -> plus#(X1, X2)}
    Scc:
     {  s#(mark(X)) -> s#(X),
      s#(active(X)) -> s#(X)}
    Scc:
     {  U11#(X1, mark(X2)) -> U11#(X1, X2),
      U11#(X1, active(X2)) -> U11#(X1, X2),
        U11#(mark(X1), X2) -> U11#(X1, X2),
      U11#(active(X1), X2) -> U11#(X1, X2)}
    Scc:
     {          mark#(U11(X1, X2)) -> mark#(X1),
                mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)),
                       mark#(s(X)) -> mark#(X),
                       mark#(s(X)) -> active#(s(mark(X))),
               mark#(plus(X1, X2)) -> mark#(X1),
               mark#(plus(X1, X2)) -> mark#(X2),
               mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))),
            mark#(U21(X1, X2, X3)) -> mark#(X1),
            mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)),
                     mark#(U31(X)) -> mark#(X),
                     mark#(U31(X)) -> active#(U31(mark(X))),
                  mark#(x(X1, X2)) -> mark#(X1),
                  mark#(x(X1, X2)) -> mark#(X2),
                  mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))),
            mark#(U41(X1, X2, X3)) -> mark#(X1),
            mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)),
                mark#(and(X1, X2)) -> mark#(X1),
                mark#(and(X1, X2)) -> active#(and(mark(X1), X2)),
                   mark#(isNat(X)) -> active#(isNat(X)),
             active#(U11(tt(), N)) -> mark#(N),
            active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)),
             active#(plus(N, 0())) -> mark#(U11(isNat(N), N)),
          active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))),
               active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)),
                active#(x(N, 0())) -> mark#(U31(isNat(N))),
          active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)),
             active#(and(tt(), X)) -> mark#(X),
             active#(isNat(s(V1))) -> mark#(isNat(V1)),
      active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))),
         active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2)))}
    SCC:
     Strict:
      {  isNat#(mark(X)) -> isNat#(X),
       isNat#(active(X)) -> isNat#(X)}
     Weak:
     {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                       mark(tt()) -> active(tt()),
                       mark(s(X)) -> active(s(mark(X))),
               mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
            mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                        mark(0()) -> active(0()),
                     mark(U31(X)) -> active(U31(mark(X))),
                  mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
            mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                   mark(isNat(X)) -> active(isNat(X)),
             active(U11(tt(), N)) -> mark(N),
            active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
             active(plus(N, 0())) -> mark(U11(isNat(N), N)),
          active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                active(U31(tt())) -> mark(0()),
               active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                active(x(N, 0())) -> mark(U31(isNat(N))),
          active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
             active(and(tt(), X)) -> mark(X),
             active(isNat(s(V1))) -> mark(isNat(V1)),
      active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
               active(isNat(0())) -> mark(tt()),
         active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                U11(X1, mark(X2)) -> U11(X1, X2),
              U11(X1, active(X2)) -> U11(X1, X2),
                U11(mark(X1), X2) -> U11(X1, X2),
              U11(active(X1), X2) -> U11(X1, X2),
                       s(mark(X)) -> s(X),
                     s(active(X)) -> s(X),
               plus(X1, mark(X2)) -> plus(X1, X2),
             plus(X1, active(X2)) -> plus(X1, X2),
               plus(mark(X1), X2) -> plus(X1, X2),
             plus(active(X1), X2) -> plus(X1, X2),
            U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
          U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
            U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
          U21(X1, active(X2), X3) -> U21(X1, X2, X3),
            U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
          U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                     U31(mark(X)) -> U31(X),
                   U31(active(X)) -> U31(X),
                  x(X1, mark(X2)) -> x(X1, X2),
                x(X1, active(X2)) -> x(X1, X2),
                  x(mark(X1), X2) -> x(X1, X2),
                x(active(X1), X2) -> x(X1, X2),
            U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
          U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
            U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
          U41(X1, active(X2), X3) -> U41(X1, X2, X3),
            U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
          U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                and(X1, mark(X2)) -> and(X1, X2),
              and(X1, active(X2)) -> and(X1, X2),
                and(mark(X1), X2) -> and(X1, X2),
              and(active(X1), X2) -> and(X1, X2),
                   isNat(mark(X)) -> isNat(X),
                 isNat(active(X)) -> isNat(X)}
     SPSC:
      Simple Projection:
       pi(isNat#) = 0
      Strict:
       {isNat#(active(X)) -> isNat#(X)}
      EDG:
       {(isNat#(active(X)) -> isNat#(X), isNat#(active(X)) -> isNat#(X))}
       SCCS:
        Scc:
         {isNat#(active(X)) -> isNat#(X)}
        SCC:
         Strict:
          {isNat#(active(X)) -> isNat#(X)}
         Weak:
         {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                           mark(tt()) -> active(tt()),
                           mark(s(X)) -> active(s(mark(X))),
                   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                            mark(0()) -> active(0()),
                         mark(U31(X)) -> active(U31(mark(X))),
                      mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                    mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                       mark(isNat(X)) -> active(isNat(X)),
                 active(U11(tt(), N)) -> mark(N),
                active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                 active(plus(N, 0())) -> mark(U11(isNat(N), N)),
              active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                    active(U31(tt())) -> mark(0()),
                   active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                    active(x(N, 0())) -> mark(U31(isNat(N))),
              active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                 active(and(tt(), X)) -> mark(X),
                 active(isNat(s(V1))) -> mark(isNat(V1)),
          active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                   active(isNat(0())) -> mark(tt()),
             active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                    U11(X1, mark(X2)) -> U11(X1, X2),
                  U11(X1, active(X2)) -> U11(X1, X2),
                    U11(mark(X1), X2) -> U11(X1, X2),
                  U11(active(X1), X2) -> U11(X1, X2),
                           s(mark(X)) -> s(X),
                         s(active(X)) -> s(X),
                   plus(X1, mark(X2)) -> plus(X1, X2),
                 plus(X1, active(X2)) -> plus(X1, X2),
                   plus(mark(X1), X2) -> plus(X1, X2),
                 plus(active(X1), X2) -> plus(X1, X2),
                U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
              U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
              U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
              U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                         U31(mark(X)) -> U31(X),
                       U31(active(X)) -> U31(X),
                      x(X1, mark(X2)) -> x(X1, X2),
                    x(X1, active(X2)) -> x(X1, X2),
                      x(mark(X1), X2) -> x(X1, X2),
                    x(active(X1), X2) -> x(X1, X2),
                U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
              U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
              U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
              U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                    and(X1, mark(X2)) -> and(X1, X2),
                  and(X1, active(X2)) -> and(X1, X2),
                    and(mark(X1), X2) -> and(X1, X2),
                  and(active(X1), X2) -> and(X1, X2),
                       isNat(mark(X)) -> isNat(X),
                     isNat(active(X)) -> isNat(X)}
         SPSC:
          Simple Projection:
           pi(isNat#) = 0
          Strict:
           {}
          Qed
    SCC:
     Strict:
      {  and#(X1, mark(X2)) -> and#(X1, X2),
       and#(X1, active(X2)) -> and#(X1, X2),
         and#(mark(X1), X2) -> and#(X1, X2),
       and#(active(X1), X2) -> and#(X1, X2)}
     Weak:
     {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                       mark(tt()) -> active(tt()),
                       mark(s(X)) -> active(s(mark(X))),
               mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
            mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                        mark(0()) -> active(0()),
                     mark(U31(X)) -> active(U31(mark(X))),
                  mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
            mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                   mark(isNat(X)) -> active(isNat(X)),
             active(U11(tt(), N)) -> mark(N),
            active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
             active(plus(N, 0())) -> mark(U11(isNat(N), N)),
          active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                active(U31(tt())) -> mark(0()),
               active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                active(x(N, 0())) -> mark(U31(isNat(N))),
          active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
             active(and(tt(), X)) -> mark(X),
             active(isNat(s(V1))) -> mark(isNat(V1)),
      active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
               active(isNat(0())) -> mark(tt()),
         active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                U11(X1, mark(X2)) -> U11(X1, X2),
              U11(X1, active(X2)) -> U11(X1, X2),
                U11(mark(X1), X2) -> U11(X1, X2),
              U11(active(X1), X2) -> U11(X1, X2),
                       s(mark(X)) -> s(X),
                     s(active(X)) -> s(X),
               plus(X1, mark(X2)) -> plus(X1, X2),
             plus(X1, active(X2)) -> plus(X1, X2),
               plus(mark(X1), X2) -> plus(X1, X2),
             plus(active(X1), X2) -> plus(X1, X2),
            U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
          U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
            U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
          U21(X1, active(X2), X3) -> U21(X1, X2, X3),
            U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
          U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                     U31(mark(X)) -> U31(X),
                   U31(active(X)) -> U31(X),
                  x(X1, mark(X2)) -> x(X1, X2),
                x(X1, active(X2)) -> x(X1, X2),
                  x(mark(X1), X2) -> x(X1, X2),
                x(active(X1), X2) -> x(X1, X2),
            U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
          U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
            U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
          U41(X1, active(X2), X3) -> U41(X1, X2, X3),
            U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
          U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                and(X1, mark(X2)) -> and(X1, X2),
              and(X1, active(X2)) -> and(X1, X2),
                and(mark(X1), X2) -> and(X1, X2),
              and(active(X1), X2) -> and(X1, X2),
                   isNat(mark(X)) -> isNat(X),
                 isNat(active(X)) -> isNat(X)}
     SPSC:
      Simple Projection:
       pi(and#) = 0
      Strict:
       {  and#(X1, mark(X2)) -> and#(X1, X2),
        and#(X1, active(X2)) -> and#(X1, X2),
          and#(mark(X1), X2) -> and#(X1, X2)}
      EDG:
       {(and#(X1, active(X2)) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))
        (and#(X1, active(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
        (and#(X1, active(X2)) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
        (and#(mark(X1), X2) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
        (and#(mark(X1), X2) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
        (and#(mark(X1), X2) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))
        (and#(X1, mark(X2)) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
        (and#(X1, mark(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
        (and#(X1, mark(X2)) -> and#(X1, X2), and#(mark(X1), X2) -> and#(X1, X2))}
       SCCS:
        Scc:
         {  and#(X1, mark(X2)) -> and#(X1, X2),
          and#(X1, active(X2)) -> and#(X1, X2),
            and#(mark(X1), X2) -> and#(X1, X2)}
        SCC:
         Strict:
          {  and#(X1, mark(X2)) -> and#(X1, X2),
           and#(X1, active(X2)) -> and#(X1, X2),
             and#(mark(X1), X2) -> and#(X1, X2)}
         Weak:
         {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                           mark(tt()) -> active(tt()),
                           mark(s(X)) -> active(s(mark(X))),
                   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                            mark(0()) -> active(0()),
                         mark(U31(X)) -> active(U31(mark(X))),
                      mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                    mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                       mark(isNat(X)) -> active(isNat(X)),
                 active(U11(tt(), N)) -> mark(N),
                active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                 active(plus(N, 0())) -> mark(U11(isNat(N), N)),
              active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                    active(U31(tt())) -> mark(0()),
                   active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                    active(x(N, 0())) -> mark(U31(isNat(N))),
              active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                 active(and(tt(), X)) -> mark(X),
                 active(isNat(s(V1))) -> mark(isNat(V1)),
          active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                   active(isNat(0())) -> mark(tt()),
             active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                    U11(X1, mark(X2)) -> U11(X1, X2),
                  U11(X1, active(X2)) -> U11(X1, X2),
                    U11(mark(X1), X2) -> U11(X1, X2),
                  U11(active(X1), X2) -> U11(X1, X2),
                           s(mark(X)) -> s(X),
                         s(active(X)) -> s(X),
                   plus(X1, mark(X2)) -> plus(X1, X2),
                 plus(X1, active(X2)) -> plus(X1, X2),
                   plus(mark(X1), X2) -> plus(X1, X2),
                 plus(active(X1), X2) -> plus(X1, X2),
                U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
              U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
              U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
              U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                         U31(mark(X)) -> U31(X),
                       U31(active(X)) -> U31(X),
                      x(X1, mark(X2)) -> x(X1, X2),
                    x(X1, active(X2)) -> x(X1, X2),
                      x(mark(X1), X2) -> x(X1, X2),
                    x(active(X1), X2) -> x(X1, X2),
                U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
              U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
              U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
              U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                    and(X1, mark(X2)) -> and(X1, X2),
                  and(X1, active(X2)) -> and(X1, X2),
                    and(mark(X1), X2) -> and(X1, X2),
                  and(active(X1), X2) -> and(X1, X2),
                       isNat(mark(X)) -> isNat(X),
                     isNat(active(X)) -> isNat(X)}
         SPSC:
          Simple Projection:
           pi(and#) = 0
          Strict:
           {  and#(X1, mark(X2)) -> and#(X1, X2),
            and#(X1, active(X2)) -> and#(X1, X2)}
          EDG:
           {(and#(X1, active(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))
            (and#(X1, active(X2)) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
            (and#(X1, mark(X2)) -> and#(X1, X2), and#(X1, mark(X2)) -> and#(X1, X2))
            (and#(X1, mark(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))}
           SCCS:
            Scc:
             {  and#(X1, mark(X2)) -> and#(X1, X2),
              and#(X1, active(X2)) -> and#(X1, X2)}
            SCC:
             Strict:
              {  and#(X1, mark(X2)) -> and#(X1, X2),
               and#(X1, active(X2)) -> and#(X1, X2)}
             Weak:
             {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                               mark(tt()) -> active(tt()),
                               mark(s(X)) -> active(s(mark(X))),
                       mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                    mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                mark(0()) -> active(0()),
                             mark(U31(X)) -> active(U31(mark(X))),
                          mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                    mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                        mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                           mark(isNat(X)) -> active(isNat(X)),
                     active(U11(tt(), N)) -> mark(N),
                    active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                     active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                  active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                        active(U31(tt())) -> mark(0()),
                       active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                        active(x(N, 0())) -> mark(U31(isNat(N))),
                  active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                     active(and(tt(), X)) -> mark(X),
                     active(isNat(s(V1))) -> mark(isNat(V1)),
              active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                       active(isNat(0())) -> mark(tt()),
                 active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                        U11(X1, mark(X2)) -> U11(X1, X2),
                      U11(X1, active(X2)) -> U11(X1, X2),
                        U11(mark(X1), X2) -> U11(X1, X2),
                      U11(active(X1), X2) -> U11(X1, X2),
                               s(mark(X)) -> s(X),
                             s(active(X)) -> s(X),
                       plus(X1, mark(X2)) -> plus(X1, X2),
                     plus(X1, active(X2)) -> plus(X1, X2),
                       plus(mark(X1), X2) -> plus(X1, X2),
                     plus(active(X1), X2) -> plus(X1, X2),
                    U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                  U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                    U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                  U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                    U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                  U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                             U31(mark(X)) -> U31(X),
                           U31(active(X)) -> U31(X),
                          x(X1, mark(X2)) -> x(X1, X2),
                        x(X1, active(X2)) -> x(X1, X2),
                          x(mark(X1), X2) -> x(X1, X2),
                        x(active(X1), X2) -> x(X1, X2),
                    U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                  U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                    U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                  U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                    U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                  U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                        and(X1, mark(X2)) -> and(X1, X2),
                      and(X1, active(X2)) -> and(X1, X2),
                        and(mark(X1), X2) -> and(X1, X2),
                      and(active(X1), X2) -> and(X1, X2),
                           isNat(mark(X)) -> isNat(X),
                         isNat(active(X)) -> isNat(X)}
             SPSC:
              Simple Projection:
               pi(and#) = 1
              Strict:
               {and#(X1, active(X2)) -> and#(X1, X2)}
              EDG:
               {(and#(X1, active(X2)) -> and#(X1, X2), and#(X1, active(X2)) -> and#(X1, X2))}
               SCCS:
                Scc:
                 {and#(X1, active(X2)) -> and#(X1, X2)}
                SCC:
                 Strict:
                  {and#(X1, active(X2)) -> and#(X1, X2)}
                 Weak:
                 {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                                   mark(tt()) -> active(tt()),
                                   mark(s(X)) -> active(s(mark(X))),
                           mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                        mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                    mark(0()) -> active(0()),
                                 mark(U31(X)) -> active(U31(mark(X))),
                              mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                        mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                            mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                               mark(isNat(X)) -> active(isNat(X)),
                         active(U11(tt(), N)) -> mark(N),
                        active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                         active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                      active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                            active(U31(tt())) -> mark(0()),
                           active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                            active(x(N, 0())) -> mark(U31(isNat(N))),
                      active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                         active(and(tt(), X)) -> mark(X),
                         active(isNat(s(V1))) -> mark(isNat(V1)),
                  active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                           active(isNat(0())) -> mark(tt()),
                     active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                            U11(X1, mark(X2)) -> U11(X1, X2),
                          U11(X1, active(X2)) -> U11(X1, X2),
                            U11(mark(X1), X2) -> U11(X1, X2),
                          U11(active(X1), X2) -> U11(X1, X2),
                                   s(mark(X)) -> s(X),
                                 s(active(X)) -> s(X),
                           plus(X1, mark(X2)) -> plus(X1, X2),
                         plus(X1, active(X2)) -> plus(X1, X2),
                           plus(mark(X1), X2) -> plus(X1, X2),
                         plus(active(X1), X2) -> plus(X1, X2),
                        U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                      U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                        U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                      U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                        U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                      U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                                 U31(mark(X)) -> U31(X),
                               U31(active(X)) -> U31(X),
                              x(X1, mark(X2)) -> x(X1, X2),
                            x(X1, active(X2)) -> x(X1, X2),
                              x(mark(X1), X2) -> x(X1, X2),
                            x(active(X1), X2) -> x(X1, X2),
                        U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                      U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                        U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                      U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                        U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                      U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                            and(X1, mark(X2)) -> and(X1, X2),
                          and(X1, active(X2)) -> and(X1, X2),
                            and(mark(X1), X2) -> and(X1, X2),
                          and(active(X1), X2) -> and(X1, X2),
                               isNat(mark(X)) -> isNat(X),
                             isNat(active(X)) -> isNat(X)}
                 SPSC:
                  Simple Projection:
                   pi(and#) = 1
                  Strict:
                   {}
                  Qed
    SCC:
     Strict:
      {  U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3),
       U41#(X1, X2, active(X3)) -> U41#(X1, X2, X3),
         U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
       U41#(X1, active(X2), X3) -> U41#(X1, X2, X3),
         U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3),
       U41#(active(X1), X2, X3) -> U41#(X1, X2, X3)}
     Weak:
     {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                       mark(tt()) -> active(tt()),
                       mark(s(X)) -> active(s(mark(X))),
               mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
            mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                        mark(0()) -> active(0()),
                     mark(U31(X)) -> active(U31(mark(X))),
                  mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
            mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                   mark(isNat(X)) -> active(isNat(X)),
             active(U11(tt(), N)) -> mark(N),
            active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
             active(plus(N, 0())) -> mark(U11(isNat(N), N)),
          active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                active(U31(tt())) -> mark(0()),
               active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                active(x(N, 0())) -> mark(U31(isNat(N))),
          active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
             active(and(tt(), X)) -> mark(X),
             active(isNat(s(V1))) -> mark(isNat(V1)),
      active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
               active(isNat(0())) -> mark(tt()),
         active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                U11(X1, mark(X2)) -> U11(X1, X2),
              U11(X1, active(X2)) -> U11(X1, X2),
                U11(mark(X1), X2) -> U11(X1, X2),
              U11(active(X1), X2) -> U11(X1, X2),
                       s(mark(X)) -> s(X),
                     s(active(X)) -> s(X),
               plus(X1, mark(X2)) -> plus(X1, X2),
             plus(X1, active(X2)) -> plus(X1, X2),
               plus(mark(X1), X2) -> plus(X1, X2),
             plus(active(X1), X2) -> plus(X1, X2),
            U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
          U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
            U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
          U21(X1, active(X2), X3) -> U21(X1, X2, X3),
            U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
          U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                     U31(mark(X)) -> U31(X),
                   U31(active(X)) -> U31(X),
                  x(X1, mark(X2)) -> x(X1, X2),
                x(X1, active(X2)) -> x(X1, X2),
                  x(mark(X1), X2) -> x(X1, X2),
                x(active(X1), X2) -> x(X1, X2),
            U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
          U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
            U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
          U41(X1, active(X2), X3) -> U41(X1, X2, X3),
            U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
          U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                and(X1, mark(X2)) -> and(X1, X2),
              and(X1, active(X2)) -> and(X1, X2),
                and(mark(X1), X2) -> and(X1, X2),
              and(active(X1), X2) -> and(X1, X2),
                   isNat(mark(X)) -> isNat(X),
                 isNat(active(X)) -> isNat(X)}
     SPSC:
      Simple Projection:
       pi(U41#) = 2
      Strict:
       {  U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3),
          U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
        U41#(X1, active(X2), X3) -> U41#(X1, X2, X3),
          U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3),
        U41#(active(X1), X2, X3) -> U41#(X1, X2, X3)}
      EDG:
       {(U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(active(X1), X2, X3) -> U41#(X1, X2, X3))
        (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
        (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
        (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
        (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
        (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(active(X1), X2, X3) -> U41#(X1, X2, X3))
        (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
        (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
        (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
        (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
        (U41#(active(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
        (U41#(active(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
        (U41#(active(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
        (U41#(active(X1), X2, X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
        (U41#(active(X1), X2, X3) -> U41#(X1, X2, X3), U41#(active(X1), X2, X3) -> U41#(X1, X2, X3))
        (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
        (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
        (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
        (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
        (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(active(X1), X2, X3) -> U41#(X1, X2, X3))
        (U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
        (U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
        (U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
        (U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
        (U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3), U41#(active(X1), X2, X3) -> U41#(X1, X2, X3))}
       SCCS:
        Scc:
         {  U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3),
            U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
          U41#(X1, active(X2), X3) -> U41#(X1, X2, X3),
            U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3),
          U41#(active(X1), X2, X3) -> U41#(X1, X2, X3)}
        SCC:
         Strict:
          {  U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3),
             U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
           U41#(X1, active(X2), X3) -> U41#(X1, X2, X3),
             U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3),
           U41#(active(X1), X2, X3) -> U41#(X1, X2, X3)}
         Weak:
         {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                           mark(tt()) -> active(tt()),
                           mark(s(X)) -> active(s(mark(X))),
                   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                            mark(0()) -> active(0()),
                         mark(U31(X)) -> active(U31(mark(X))),
                      mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                    mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                       mark(isNat(X)) -> active(isNat(X)),
                 active(U11(tt(), N)) -> mark(N),
                active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                 active(plus(N, 0())) -> mark(U11(isNat(N), N)),
              active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                    active(U31(tt())) -> mark(0()),
                   active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                    active(x(N, 0())) -> mark(U31(isNat(N))),
              active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                 active(and(tt(), X)) -> mark(X),
                 active(isNat(s(V1))) -> mark(isNat(V1)),
          active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                   active(isNat(0())) -> mark(tt()),
             active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                    U11(X1, mark(X2)) -> U11(X1, X2),
                  U11(X1, active(X2)) -> U11(X1, X2),
                    U11(mark(X1), X2) -> U11(X1, X2),
                  U11(active(X1), X2) -> U11(X1, X2),
                           s(mark(X)) -> s(X),
                         s(active(X)) -> s(X),
                   plus(X1, mark(X2)) -> plus(X1, X2),
                 plus(X1, active(X2)) -> plus(X1, X2),
                   plus(mark(X1), X2) -> plus(X1, X2),
                 plus(active(X1), X2) -> plus(X1, X2),
                U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
              U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
              U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
              U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                         U31(mark(X)) -> U31(X),
                       U31(active(X)) -> U31(X),
                      x(X1, mark(X2)) -> x(X1, X2),
                    x(X1, active(X2)) -> x(X1, X2),
                      x(mark(X1), X2) -> x(X1, X2),
                    x(active(X1), X2) -> x(X1, X2),
                U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
              U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
              U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
              U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                    and(X1, mark(X2)) -> and(X1, X2),
                  and(X1, active(X2)) -> and(X1, X2),
                    and(mark(X1), X2) -> and(X1, X2),
                  and(active(X1), X2) -> and(X1, X2),
                       isNat(mark(X)) -> isNat(X),
                     isNat(active(X)) -> isNat(X)}
         SPSC:
          Simple Projection:
           pi(U41#) = 0
          Strict:
           {  U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3),
              U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
            U41#(X1, active(X2), X3) -> U41#(X1, X2, X3),
              U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3)}
          EDG:
           {(U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
            (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
            (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
            (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
            (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
            (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
            (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
            (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
            (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
            (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
            (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
            (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
            (U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3), U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3))
            (U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
            (U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
            (U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))}
           SCCS:
            Scc:
             {  U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3),
                U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
              U41#(X1, active(X2), X3) -> U41#(X1, X2, X3),
                U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3)}
            SCC:
             Strict:
              {  U41#(X1, X2, mark(X3)) -> U41#(X1, X2, X3),
                 U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
               U41#(X1, active(X2), X3) -> U41#(X1, X2, X3),
                 U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3)}
             Weak:
             {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                               mark(tt()) -> active(tt()),
                               mark(s(X)) -> active(s(mark(X))),
                       mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                    mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                mark(0()) -> active(0()),
                             mark(U31(X)) -> active(U31(mark(X))),
                          mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                    mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                        mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                           mark(isNat(X)) -> active(isNat(X)),
                     active(U11(tt(), N)) -> mark(N),
                    active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                     active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                  active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                        active(U31(tt())) -> mark(0()),
                       active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                        active(x(N, 0())) -> mark(U31(isNat(N))),
                  active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                     active(and(tt(), X)) -> mark(X),
                     active(isNat(s(V1))) -> mark(isNat(V1)),
              active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                       active(isNat(0())) -> mark(tt()),
                 active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                        U11(X1, mark(X2)) -> U11(X1, X2),
                      U11(X1, active(X2)) -> U11(X1, X2),
                        U11(mark(X1), X2) -> U11(X1, X2),
                      U11(active(X1), X2) -> U11(X1, X2),
                               s(mark(X)) -> s(X),
                             s(active(X)) -> s(X),
                       plus(X1, mark(X2)) -> plus(X1, X2),
                     plus(X1, active(X2)) -> plus(X1, X2),
                       plus(mark(X1), X2) -> plus(X1, X2),
                     plus(active(X1), X2) -> plus(X1, X2),
                    U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                  U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                    U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                  U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                    U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                  U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                             U31(mark(X)) -> U31(X),
                           U31(active(X)) -> U31(X),
                          x(X1, mark(X2)) -> x(X1, X2),
                        x(X1, active(X2)) -> x(X1, X2),
                          x(mark(X1), X2) -> x(X1, X2),
                        x(active(X1), X2) -> x(X1, X2),
                    U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                  U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                    U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                  U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                    U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                  U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                        and(X1, mark(X2)) -> and(X1, X2),
                      and(X1, active(X2)) -> and(X1, X2),
                        and(mark(X1), X2) -> and(X1, X2),
                      and(active(X1), X2) -> and(X1, X2),
                           isNat(mark(X)) -> isNat(X),
                         isNat(active(X)) -> isNat(X)}
             SPSC:
              Simple Projection:
               pi(U41#) = 2
              Strict:
               {  U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
                U41#(X1, active(X2), X3) -> U41#(X1, X2, X3),
                  U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3)}
              EDG:
               {(U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
                (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
                (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
                (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
                (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
                (U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))
                (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
                (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
                (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3))}
               SCCS:
                Scc:
                 {  U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
                  U41#(X1, active(X2), X3) -> U41#(X1, X2, X3),
                    U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3)}
                SCC:
                 Strict:
                  {  U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
                   U41#(X1, active(X2), X3) -> U41#(X1, X2, X3),
                     U41#(mark(X1), X2, X3) -> U41#(X1, X2, X3)}
                 Weak:
                 {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                                   mark(tt()) -> active(tt()),
                                   mark(s(X)) -> active(s(mark(X))),
                           mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                        mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                    mark(0()) -> active(0()),
                                 mark(U31(X)) -> active(U31(mark(X))),
                              mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                        mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                            mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                               mark(isNat(X)) -> active(isNat(X)),
                         active(U11(tt(), N)) -> mark(N),
                        active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                         active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                      active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                            active(U31(tt())) -> mark(0()),
                           active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                            active(x(N, 0())) -> mark(U31(isNat(N))),
                      active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                         active(and(tt(), X)) -> mark(X),
                         active(isNat(s(V1))) -> mark(isNat(V1)),
                  active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                           active(isNat(0())) -> mark(tt()),
                     active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                            U11(X1, mark(X2)) -> U11(X1, X2),
                          U11(X1, active(X2)) -> U11(X1, X2),
                            U11(mark(X1), X2) -> U11(X1, X2),
                          U11(active(X1), X2) -> U11(X1, X2),
                                   s(mark(X)) -> s(X),
                                 s(active(X)) -> s(X),
                           plus(X1, mark(X2)) -> plus(X1, X2),
                         plus(X1, active(X2)) -> plus(X1, X2),
                           plus(mark(X1), X2) -> plus(X1, X2),
                         plus(active(X1), X2) -> plus(X1, X2),
                        U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                      U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                        U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                      U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                        U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                      U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                                 U31(mark(X)) -> U31(X),
                               U31(active(X)) -> U31(X),
                              x(X1, mark(X2)) -> x(X1, X2),
                            x(X1, active(X2)) -> x(X1, X2),
                              x(mark(X1), X2) -> x(X1, X2),
                            x(active(X1), X2) -> x(X1, X2),
                        U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                      U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                        U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                      U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                        U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                      U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                            and(X1, mark(X2)) -> and(X1, X2),
                          and(X1, active(X2)) -> and(X1, X2),
                            and(mark(X1), X2) -> and(X1, X2),
                          and(active(X1), X2) -> and(X1, X2),
                               isNat(mark(X)) -> isNat(X),
                             isNat(active(X)) -> isNat(X)}
                 SPSC:
                  Simple Projection:
                   pi(U41#) = 0
                  Strict:
                   {  U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
                    U41#(X1, active(X2), X3) -> U41#(X1, X2, X3)}
                  EDG:
                   {(U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))
                    (U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
                    (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3))
                    (U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))}
                   SCCS:
                    Scc:
                     {  U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
                      U41#(X1, active(X2), X3) -> U41#(X1, X2, X3)}
                    SCC:
                     Strict:
                      {  U41#(X1, mark(X2), X3) -> U41#(X1, X2, X3),
                       U41#(X1, active(X2), X3) -> U41#(X1, X2, X3)}
                     Weak:
                     {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                                       mark(tt()) -> active(tt()),
                                       mark(s(X)) -> active(s(mark(X))),
                               mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                            mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                        mark(0()) -> active(0()),
                                     mark(U31(X)) -> active(U31(mark(X))),
                                  mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                            mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                                mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                                   mark(isNat(X)) -> active(isNat(X)),
                             active(U11(tt(), N)) -> mark(N),
                            active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                             active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                          active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                                active(U31(tt())) -> mark(0()),
                               active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                                active(x(N, 0())) -> mark(U31(isNat(N))),
                          active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                             active(and(tt(), X)) -> mark(X),
                             active(isNat(s(V1))) -> mark(isNat(V1)),
                      active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                               active(isNat(0())) -> mark(tt()),
                         active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                                U11(X1, mark(X2)) -> U11(X1, X2),
                              U11(X1, active(X2)) -> U11(X1, X2),
                                U11(mark(X1), X2) -> U11(X1, X2),
                              U11(active(X1), X2) -> U11(X1, X2),
                                       s(mark(X)) -> s(X),
                                     s(active(X)) -> s(X),
                               plus(X1, mark(X2)) -> plus(X1, X2),
                             plus(X1, active(X2)) -> plus(X1, X2),
                               plus(mark(X1), X2) -> plus(X1, X2),
                             plus(active(X1), X2) -> plus(X1, X2),
                            U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                          U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                            U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                          U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                            U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                          U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                                     U31(mark(X)) -> U31(X),
                                   U31(active(X)) -> U31(X),
                                  x(X1, mark(X2)) -> x(X1, X2),
                                x(X1, active(X2)) -> x(X1, X2),
                                  x(mark(X1), X2) -> x(X1, X2),
                                x(active(X1), X2) -> x(X1, X2),
                            U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                          U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                            U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                          U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                            U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                          U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                                and(X1, mark(X2)) -> and(X1, X2),
                              and(X1, active(X2)) -> and(X1, X2),
                                and(mark(X1), X2) -> and(X1, X2),
                              and(active(X1), X2) -> and(X1, X2),
                                   isNat(mark(X)) -> isNat(X),
                                 isNat(active(X)) -> isNat(X)}
                     SPSC:
                      Simple Projection:
                       pi(U41#) = 1
                      Strict:
                       {U41#(X1, active(X2), X3) -> U41#(X1, X2, X3)}
                      EDG:
                       {(U41#(X1, active(X2), X3) -> U41#(X1, X2, X3), U41#(X1, active(X2), X3) -> U41#(X1, X2, X3))}
                       SCCS:
                        Scc:
                         {U41#(X1, active(X2), X3) -> U41#(X1, X2, X3)}
                        SCC:
                         Strict:
                          {U41#(X1, active(X2), X3) -> U41#(X1, X2, X3)}
                         Weak:
                         {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                                           mark(tt()) -> active(tt()),
                                           mark(s(X)) -> active(s(mark(X))),
                                   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                                mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                            mark(0()) -> active(0()),
                                         mark(U31(X)) -> active(U31(mark(X))),
                                      mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                                mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                                    mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                                       mark(isNat(X)) -> active(isNat(X)),
                                 active(U11(tt(), N)) -> mark(N),
                                active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                                 active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                              active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                                    active(U31(tt())) -> mark(0()),
                                   active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                                    active(x(N, 0())) -> mark(U31(isNat(N))),
                              active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                                 active(and(tt(), X)) -> mark(X),
                                 active(isNat(s(V1))) -> mark(isNat(V1)),
                          active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                                   active(isNat(0())) -> mark(tt()),
                             active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                                    U11(X1, mark(X2)) -> U11(X1, X2),
                                  U11(X1, active(X2)) -> U11(X1, X2),
                                    U11(mark(X1), X2) -> U11(X1, X2),
                                  U11(active(X1), X2) -> U11(X1, X2),
                                           s(mark(X)) -> s(X),
                                         s(active(X)) -> s(X),
                                   plus(X1, mark(X2)) -> plus(X1, X2),
                                 plus(X1, active(X2)) -> plus(X1, X2),
                                   plus(mark(X1), X2) -> plus(X1, X2),
                                 plus(active(X1), X2) -> plus(X1, X2),
                                U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                              U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                                U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                              U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                                U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                              U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                                         U31(mark(X)) -> U31(X),
                                       U31(active(X)) -> U31(X),
                                      x(X1, mark(X2)) -> x(X1, X2),
                                    x(X1, active(X2)) -> x(X1, X2),
                                      x(mark(X1), X2) -> x(X1, X2),
                                    x(active(X1), X2) -> x(X1, X2),
                                U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                              U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                                U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                              U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                                U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                              U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                                    and(X1, mark(X2)) -> and(X1, X2),
                                  and(X1, active(X2)) -> and(X1, X2),
                                    and(mark(X1), X2) -> and(X1, X2),
                                  and(active(X1), X2) -> and(X1, X2),
                                       isNat(mark(X)) -> isNat(X),
                                     isNat(active(X)) -> isNat(X)}
                         SPSC:
                          Simple Projection:
                           pi(U41#) = 1
                          Strict:
                           {}
                          Qed
    SCC:
     Strict:
      {  x#(X1, mark(X2)) -> x#(X1, X2),
       x#(X1, active(X2)) -> x#(X1, X2),
         x#(mark(X1), X2) -> x#(X1, X2),
       x#(active(X1), X2) -> x#(X1, X2)}
     Weak:
     {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                       mark(tt()) -> active(tt()),
                       mark(s(X)) -> active(s(mark(X))),
               mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
            mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                        mark(0()) -> active(0()),
                     mark(U31(X)) -> active(U31(mark(X))),
                  mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
            mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                   mark(isNat(X)) -> active(isNat(X)),
             active(U11(tt(), N)) -> mark(N),
            active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
             active(plus(N, 0())) -> mark(U11(isNat(N), N)),
          active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                active(U31(tt())) -> mark(0()),
               active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                active(x(N, 0())) -> mark(U31(isNat(N))),
          active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
             active(and(tt(), X)) -> mark(X),
             active(isNat(s(V1))) -> mark(isNat(V1)),
      active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
               active(isNat(0())) -> mark(tt()),
         active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                U11(X1, mark(X2)) -> U11(X1, X2),
              U11(X1, active(X2)) -> U11(X1, X2),
                U11(mark(X1), X2) -> U11(X1, X2),
              U11(active(X1), X2) -> U11(X1, X2),
                       s(mark(X)) -> s(X),
                     s(active(X)) -> s(X),
               plus(X1, mark(X2)) -> plus(X1, X2),
             plus(X1, active(X2)) -> plus(X1, X2),
               plus(mark(X1), X2) -> plus(X1, X2),
             plus(active(X1), X2) -> plus(X1, X2),
            U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
          U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
            U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
          U21(X1, active(X2), X3) -> U21(X1, X2, X3),
            U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
          U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                     U31(mark(X)) -> U31(X),
                   U31(active(X)) -> U31(X),
                  x(X1, mark(X2)) -> x(X1, X2),
                x(X1, active(X2)) -> x(X1, X2),
                  x(mark(X1), X2) -> x(X1, X2),
                x(active(X1), X2) -> x(X1, X2),
            U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
          U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
            U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
          U41(X1, active(X2), X3) -> U41(X1, X2, X3),
            U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
          U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                and(X1, mark(X2)) -> and(X1, X2),
              and(X1, active(X2)) -> and(X1, X2),
                and(mark(X1), X2) -> and(X1, X2),
              and(active(X1), X2) -> and(X1, X2),
                   isNat(mark(X)) -> isNat(X),
                 isNat(active(X)) -> isNat(X)}
     SPSC:
      Simple Projection:
       pi(x#) = 0
      Strict:
       {  x#(X1, mark(X2)) -> x#(X1, X2),
        x#(X1, active(X2)) -> x#(X1, X2),
          x#(mark(X1), X2) -> x#(X1, X2)}
      EDG:
       {(x#(X1, active(X2)) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))
        (x#(X1, active(X2)) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
        (x#(X1, active(X2)) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
        (x#(mark(X1), X2) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
        (x#(mark(X1), X2) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
        (x#(mark(X1), X2) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))
        (x#(X1, mark(X2)) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
        (x#(X1, mark(X2)) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
        (x#(X1, mark(X2)) -> x#(X1, X2), x#(mark(X1), X2) -> x#(X1, X2))}
       SCCS:
        Scc:
         {  x#(X1, mark(X2)) -> x#(X1, X2),
          x#(X1, active(X2)) -> x#(X1, X2),
            x#(mark(X1), X2) -> x#(X1, X2)}
        SCC:
         Strict:
          {  x#(X1, mark(X2)) -> x#(X1, X2),
           x#(X1, active(X2)) -> x#(X1, X2),
             x#(mark(X1), X2) -> x#(X1, X2)}
         Weak:
         {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                           mark(tt()) -> active(tt()),
                           mark(s(X)) -> active(s(mark(X))),
                   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                            mark(0()) -> active(0()),
                         mark(U31(X)) -> active(U31(mark(X))),
                      mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                    mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                       mark(isNat(X)) -> active(isNat(X)),
                 active(U11(tt(), N)) -> mark(N),
                active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                 active(plus(N, 0())) -> mark(U11(isNat(N), N)),
              active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                    active(U31(tt())) -> mark(0()),
                   active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                    active(x(N, 0())) -> mark(U31(isNat(N))),
              active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                 active(and(tt(), X)) -> mark(X),
                 active(isNat(s(V1))) -> mark(isNat(V1)),
          active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                   active(isNat(0())) -> mark(tt()),
             active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                    U11(X1, mark(X2)) -> U11(X1, X2),
                  U11(X1, active(X2)) -> U11(X1, X2),
                    U11(mark(X1), X2) -> U11(X1, X2),
                  U11(active(X1), X2) -> U11(X1, X2),
                           s(mark(X)) -> s(X),
                         s(active(X)) -> s(X),
                   plus(X1, mark(X2)) -> plus(X1, X2),
                 plus(X1, active(X2)) -> plus(X1, X2),
                   plus(mark(X1), X2) -> plus(X1, X2),
                 plus(active(X1), X2) -> plus(X1, X2),
                U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
              U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
              U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
              U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                         U31(mark(X)) -> U31(X),
                       U31(active(X)) -> U31(X),
                      x(X1, mark(X2)) -> x(X1, X2),
                    x(X1, active(X2)) -> x(X1, X2),
                      x(mark(X1), X2) -> x(X1, X2),
                    x(active(X1), X2) -> x(X1, X2),
                U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
              U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
              U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
              U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                    and(X1, mark(X2)) -> and(X1, X2),
                  and(X1, active(X2)) -> and(X1, X2),
                    and(mark(X1), X2) -> and(X1, X2),
                  and(active(X1), X2) -> and(X1, X2),
                       isNat(mark(X)) -> isNat(X),
                     isNat(active(X)) -> isNat(X)}
         SPSC:
          Simple Projection:
           pi(x#) = 0
          Strict:
           {  x#(X1, mark(X2)) -> x#(X1, X2),
            x#(X1, active(X2)) -> x#(X1, X2)}
          EDG:
           {(x#(X1, active(X2)) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))
            (x#(X1, active(X2)) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
            (x#(X1, mark(X2)) -> x#(X1, X2), x#(X1, mark(X2)) -> x#(X1, X2))
            (x#(X1, mark(X2)) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))}
           SCCS:
            Scc:
             {  x#(X1, mark(X2)) -> x#(X1, X2),
              x#(X1, active(X2)) -> x#(X1, X2)}
            SCC:
             Strict:
              {  x#(X1, mark(X2)) -> x#(X1, X2),
               x#(X1, active(X2)) -> x#(X1, X2)}
             Weak:
             {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                               mark(tt()) -> active(tt()),
                               mark(s(X)) -> active(s(mark(X))),
                       mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                    mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                mark(0()) -> active(0()),
                             mark(U31(X)) -> active(U31(mark(X))),
                          mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                    mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                        mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                           mark(isNat(X)) -> active(isNat(X)),
                     active(U11(tt(), N)) -> mark(N),
                    active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                     active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                  active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                        active(U31(tt())) -> mark(0()),
                       active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                        active(x(N, 0())) -> mark(U31(isNat(N))),
                  active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                     active(and(tt(), X)) -> mark(X),
                     active(isNat(s(V1))) -> mark(isNat(V1)),
              active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                       active(isNat(0())) -> mark(tt()),
                 active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                        U11(X1, mark(X2)) -> U11(X1, X2),
                      U11(X1, active(X2)) -> U11(X1, X2),
                        U11(mark(X1), X2) -> U11(X1, X2),
                      U11(active(X1), X2) -> U11(X1, X2),
                               s(mark(X)) -> s(X),
                             s(active(X)) -> s(X),
                       plus(X1, mark(X2)) -> plus(X1, X2),
                     plus(X1, active(X2)) -> plus(X1, X2),
                       plus(mark(X1), X2) -> plus(X1, X2),
                     plus(active(X1), X2) -> plus(X1, X2),
                    U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                  U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                    U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                  U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                    U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                  U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                             U31(mark(X)) -> U31(X),
                           U31(active(X)) -> U31(X),
                          x(X1, mark(X2)) -> x(X1, X2),
                        x(X1, active(X2)) -> x(X1, X2),
                          x(mark(X1), X2) -> x(X1, X2),
                        x(active(X1), X2) -> x(X1, X2),
                    U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                  U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                    U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                  U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                    U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                  U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                        and(X1, mark(X2)) -> and(X1, X2),
                      and(X1, active(X2)) -> and(X1, X2),
                        and(mark(X1), X2) -> and(X1, X2),
                      and(active(X1), X2) -> and(X1, X2),
                           isNat(mark(X)) -> isNat(X),
                         isNat(active(X)) -> isNat(X)}
             SPSC:
              Simple Projection:
               pi(x#) = 1
              Strict:
               {x#(X1, active(X2)) -> x#(X1, X2)}
              EDG:
               {(x#(X1, active(X2)) -> x#(X1, X2), x#(X1, active(X2)) -> x#(X1, X2))}
               SCCS:
                Scc:
                 {x#(X1, active(X2)) -> x#(X1, X2)}
                SCC:
                 Strict:
                  {x#(X1, active(X2)) -> x#(X1, X2)}
                 Weak:
                 {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                                   mark(tt()) -> active(tt()),
                                   mark(s(X)) -> active(s(mark(X))),
                           mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                        mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                    mark(0()) -> active(0()),
                                 mark(U31(X)) -> active(U31(mark(X))),
                              mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                        mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                            mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                               mark(isNat(X)) -> active(isNat(X)),
                         active(U11(tt(), N)) -> mark(N),
                        active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                         active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                      active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                            active(U31(tt())) -> mark(0()),
                           active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                            active(x(N, 0())) -> mark(U31(isNat(N))),
                      active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                         active(and(tt(), X)) -> mark(X),
                         active(isNat(s(V1))) -> mark(isNat(V1)),
                  active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                           active(isNat(0())) -> mark(tt()),
                     active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                            U11(X1, mark(X2)) -> U11(X1, X2),
                          U11(X1, active(X2)) -> U11(X1, X2),
                            U11(mark(X1), X2) -> U11(X1, X2),
                          U11(active(X1), X2) -> U11(X1, X2),
                                   s(mark(X)) -> s(X),
                                 s(active(X)) -> s(X),
                           plus(X1, mark(X2)) -> plus(X1, X2),
                         plus(X1, active(X2)) -> plus(X1, X2),
                           plus(mark(X1), X2) -> plus(X1, X2),
                         plus(active(X1), X2) -> plus(X1, X2),
                        U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                      U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                        U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                      U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                        U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                      U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                                 U31(mark(X)) -> U31(X),
                               U31(active(X)) -> U31(X),
                              x(X1, mark(X2)) -> x(X1, X2),
                            x(X1, active(X2)) -> x(X1, X2),
                              x(mark(X1), X2) -> x(X1, X2),
                            x(active(X1), X2) -> x(X1, X2),
                        U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                      U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                        U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                      U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                        U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                      U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                            and(X1, mark(X2)) -> and(X1, X2),
                          and(X1, active(X2)) -> and(X1, X2),
                            and(mark(X1), X2) -> and(X1, X2),
                          and(active(X1), X2) -> and(X1, X2),
                               isNat(mark(X)) -> isNat(X),
                             isNat(active(X)) -> isNat(X)}
                 SPSC:
                  Simple Projection:
                   pi(x#) = 1
                  Strict:
                   {}
                  Qed
    SCC:
     Strict:
      {  U31#(mark(X)) -> U31#(X),
       U31#(active(X)) -> U31#(X)}
     Weak:
     {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                       mark(tt()) -> active(tt()),
                       mark(s(X)) -> active(s(mark(X))),
               mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
            mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                        mark(0()) -> active(0()),
                     mark(U31(X)) -> active(U31(mark(X))),
                  mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
            mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                   mark(isNat(X)) -> active(isNat(X)),
             active(U11(tt(), N)) -> mark(N),
            active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
             active(plus(N, 0())) -> mark(U11(isNat(N), N)),
          active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                active(U31(tt())) -> mark(0()),
               active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                active(x(N, 0())) -> mark(U31(isNat(N))),
          active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
             active(and(tt(), X)) -> mark(X),
             active(isNat(s(V1))) -> mark(isNat(V1)),
      active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
               active(isNat(0())) -> mark(tt()),
         active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                U11(X1, mark(X2)) -> U11(X1, X2),
              U11(X1, active(X2)) -> U11(X1, X2),
                U11(mark(X1), X2) -> U11(X1, X2),
              U11(active(X1), X2) -> U11(X1, X2),
                       s(mark(X)) -> s(X),
                     s(active(X)) -> s(X),
               plus(X1, mark(X2)) -> plus(X1, X2),
             plus(X1, active(X2)) -> plus(X1, X2),
               plus(mark(X1), X2) -> plus(X1, X2),
             plus(active(X1), X2) -> plus(X1, X2),
            U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
          U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
            U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
          U21(X1, active(X2), X3) -> U21(X1, X2, X3),
            U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
          U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                     U31(mark(X)) -> U31(X),
                   U31(active(X)) -> U31(X),
                  x(X1, mark(X2)) -> x(X1, X2),
                x(X1, active(X2)) -> x(X1, X2),
                  x(mark(X1), X2) -> x(X1, X2),
                x(active(X1), X2) -> x(X1, X2),
            U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
          U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
            U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
          U41(X1, active(X2), X3) -> U41(X1, X2, X3),
            U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
          U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                and(X1, mark(X2)) -> and(X1, X2),
              and(X1, active(X2)) -> and(X1, X2),
                and(mark(X1), X2) -> and(X1, X2),
              and(active(X1), X2) -> and(X1, X2),
                   isNat(mark(X)) -> isNat(X),
                 isNat(active(X)) -> isNat(X)}
     SPSC:
      Simple Projection:
       pi(U31#) = 0
      Strict:
       {U31#(active(X)) -> U31#(X)}
      EDG:
       {(U31#(active(X)) -> U31#(X), U31#(active(X)) -> U31#(X))}
       SCCS:
        Scc:
         {U31#(active(X)) -> U31#(X)}
        SCC:
         Strict:
          {U31#(active(X)) -> U31#(X)}
         Weak:
         {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                           mark(tt()) -> active(tt()),
                           mark(s(X)) -> active(s(mark(X))),
                   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                            mark(0()) -> active(0()),
                         mark(U31(X)) -> active(U31(mark(X))),
                      mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                    mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                       mark(isNat(X)) -> active(isNat(X)),
                 active(U11(tt(), N)) -> mark(N),
                active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                 active(plus(N, 0())) -> mark(U11(isNat(N), N)),
              active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                    active(U31(tt())) -> mark(0()),
                   active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                    active(x(N, 0())) -> mark(U31(isNat(N))),
              active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                 active(and(tt(), X)) -> mark(X),
                 active(isNat(s(V1))) -> mark(isNat(V1)),
          active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                   active(isNat(0())) -> mark(tt()),
             active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                    U11(X1, mark(X2)) -> U11(X1, X2),
                  U11(X1, active(X2)) -> U11(X1, X2),
                    U11(mark(X1), X2) -> U11(X1, X2),
                  U11(active(X1), X2) -> U11(X1, X2),
                           s(mark(X)) -> s(X),
                         s(active(X)) -> s(X),
                   plus(X1, mark(X2)) -> plus(X1, X2),
                 plus(X1, active(X2)) -> plus(X1, X2),
                   plus(mark(X1), X2) -> plus(X1, X2),
                 plus(active(X1), X2) -> plus(X1, X2),
                U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
              U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
              U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
              U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                         U31(mark(X)) -> U31(X),
                       U31(active(X)) -> U31(X),
                      x(X1, mark(X2)) -> x(X1, X2),
                    x(X1, active(X2)) -> x(X1, X2),
                      x(mark(X1), X2) -> x(X1, X2),
                    x(active(X1), X2) -> x(X1, X2),
                U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
              U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
              U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
              U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                    and(X1, mark(X2)) -> and(X1, X2),
                  and(X1, active(X2)) -> and(X1, X2),
                    and(mark(X1), X2) -> and(X1, X2),
                  and(active(X1), X2) -> and(X1, X2),
                       isNat(mark(X)) -> isNat(X),
                     isNat(active(X)) -> isNat(X)}
         SPSC:
          Simple Projection:
           pi(U31#) = 0
          Strict:
           {}
          Qed
    SCC:
     Strict:
      {  U21#(X1, X2, mark(X3)) -> U21#(X1, X2, X3),
       U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3),
         U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
       U21#(X1, active(X2), X3) -> U21#(X1, X2, X3),
         U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3),
       U21#(active(X1), X2, X3) -> U21#(X1, X2, X3)}
     Weak:
     {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                       mark(tt()) -> active(tt()),
                       mark(s(X)) -> active(s(mark(X))),
               mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
            mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                        mark(0()) -> active(0()),
                     mark(U31(X)) -> active(U31(mark(X))),
                  mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
            mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                   mark(isNat(X)) -> active(isNat(X)),
             active(U11(tt(), N)) -> mark(N),
            active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
             active(plus(N, 0())) -> mark(U11(isNat(N), N)),
          active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                active(U31(tt())) -> mark(0()),
               active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                active(x(N, 0())) -> mark(U31(isNat(N))),
          active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
             active(and(tt(), X)) -> mark(X),
             active(isNat(s(V1))) -> mark(isNat(V1)),
      active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
               active(isNat(0())) -> mark(tt()),
         active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                U11(X1, mark(X2)) -> U11(X1, X2),
              U11(X1, active(X2)) -> U11(X1, X2),
                U11(mark(X1), X2) -> U11(X1, X2),
              U11(active(X1), X2) -> U11(X1, X2),
                       s(mark(X)) -> s(X),
                     s(active(X)) -> s(X),
               plus(X1, mark(X2)) -> plus(X1, X2),
             plus(X1, active(X2)) -> plus(X1, X2),
               plus(mark(X1), X2) -> plus(X1, X2),
             plus(active(X1), X2) -> plus(X1, X2),
            U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
          U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
            U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
          U21(X1, active(X2), X3) -> U21(X1, X2, X3),
            U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
          U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                     U31(mark(X)) -> U31(X),
                   U31(active(X)) -> U31(X),
                  x(X1, mark(X2)) -> x(X1, X2),
                x(X1, active(X2)) -> x(X1, X2),
                  x(mark(X1), X2) -> x(X1, X2),
                x(active(X1), X2) -> x(X1, X2),
            U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
          U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
            U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
          U41(X1, active(X2), X3) -> U41(X1, X2, X3),
            U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
          U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                and(X1, mark(X2)) -> and(X1, X2),
              and(X1, active(X2)) -> and(X1, X2),
                and(mark(X1), X2) -> and(X1, X2),
              and(active(X1), X2) -> and(X1, X2),
                   isNat(mark(X)) -> isNat(X),
                 isNat(active(X)) -> isNat(X)}
     SPSC:
      Simple Projection:
       pi(U21#) = 2
      Strict:
       {U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3),
          U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
        U21#(X1, active(X2), X3) -> U21#(X1, X2, X3),
          U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3),
        U21#(active(X1), X2, X3) -> U21#(X1, X2, X3)}
      EDG:
       {(U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
        (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
        (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
        (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
        (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3))
        (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
        (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
        (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
        (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
        (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3))
        (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3))
        (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
        (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
        (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
        (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
        (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3))
        (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
        (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
        (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
        (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
        (U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3), U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3))
        (U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
        (U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
        (U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
        (U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))}
       SCCS:
        Scc:
         {U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3),
            U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
          U21#(X1, active(X2), X3) -> U21#(X1, X2, X3),
            U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3),
          U21#(active(X1), X2, X3) -> U21#(X1, X2, X3)}
        SCC:
         Strict:
          {U21#(X1, X2, active(X3)) -> U21#(X1, X2, X3),
             U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
           U21#(X1, active(X2), X3) -> U21#(X1, X2, X3),
             U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3),
           U21#(active(X1), X2, X3) -> U21#(X1, X2, X3)}
         Weak:
         {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                           mark(tt()) -> active(tt()),
                           mark(s(X)) -> active(s(mark(X))),
                   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                            mark(0()) -> active(0()),
                         mark(U31(X)) -> active(U31(mark(X))),
                      mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                    mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                       mark(isNat(X)) -> active(isNat(X)),
                 active(U11(tt(), N)) -> mark(N),
                active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                 active(plus(N, 0())) -> mark(U11(isNat(N), N)),
              active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                    active(U31(tt())) -> mark(0()),
                   active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                    active(x(N, 0())) -> mark(U31(isNat(N))),
              active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                 active(and(tt(), X)) -> mark(X),
                 active(isNat(s(V1))) -> mark(isNat(V1)),
          active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                   active(isNat(0())) -> mark(tt()),
             active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                    U11(X1, mark(X2)) -> U11(X1, X2),
                  U11(X1, active(X2)) -> U11(X1, X2),
                    U11(mark(X1), X2) -> U11(X1, X2),
                  U11(active(X1), X2) -> U11(X1, X2),
                           s(mark(X)) -> s(X),
                         s(active(X)) -> s(X),
                   plus(X1, mark(X2)) -> plus(X1, X2),
                 plus(X1, active(X2)) -> plus(X1, X2),
                   plus(mark(X1), X2) -> plus(X1, X2),
                 plus(active(X1), X2) -> plus(X1, X2),
                U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
              U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
              U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
              U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                         U31(mark(X)) -> U31(X),
                       U31(active(X)) -> U31(X),
                      x(X1, mark(X2)) -> x(X1, X2),
                    x(X1, active(X2)) -> x(X1, X2),
                      x(mark(X1), X2) -> x(X1, X2),
                    x(active(X1), X2) -> x(X1, X2),
                U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
              U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
              U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
              U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                    and(X1, mark(X2)) -> and(X1, X2),
                  and(X1, active(X2)) -> and(X1, X2),
                    and(mark(X1), X2) -> and(X1, X2),
                  and(active(X1), X2) -> and(X1, X2),
                       isNat(mark(X)) -> isNat(X),
                     isNat(active(X)) -> isNat(X)}
         SPSC:
          Simple Projection:
           pi(U21#) = 2
          Strict:
           {  U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
            U21#(X1, active(X2), X3) -> U21#(X1, X2, X3),
              U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3),
            U21#(active(X1), X2, X3) -> U21#(X1, X2, X3)}
          EDG:
           {(U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
            (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
            (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
            (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
            (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
            (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
            (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
            (U21#(active(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
            (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
            (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
            (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
            (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))
            (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
            (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
            (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
            (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(active(X1), X2, X3) -> U21#(X1, X2, X3))}
           SCCS:
            Scc:
             {  U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
              U21#(X1, active(X2), X3) -> U21#(X1, X2, X3),
                U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3),
              U21#(active(X1), X2, X3) -> U21#(X1, X2, X3)}
            SCC:
             Strict:
              {  U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
               U21#(X1, active(X2), X3) -> U21#(X1, X2, X3),
                 U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3),
               U21#(active(X1), X2, X3) -> U21#(X1, X2, X3)}
             Weak:
             {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                               mark(tt()) -> active(tt()),
                               mark(s(X)) -> active(s(mark(X))),
                       mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                    mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                mark(0()) -> active(0()),
                             mark(U31(X)) -> active(U31(mark(X))),
                          mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                    mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                        mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                           mark(isNat(X)) -> active(isNat(X)),
                     active(U11(tt(), N)) -> mark(N),
                    active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                     active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                  active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                        active(U31(tt())) -> mark(0()),
                       active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                        active(x(N, 0())) -> mark(U31(isNat(N))),
                  active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                     active(and(tt(), X)) -> mark(X),
                     active(isNat(s(V1))) -> mark(isNat(V1)),
              active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                       active(isNat(0())) -> mark(tt()),
                 active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                        U11(X1, mark(X2)) -> U11(X1, X2),
                      U11(X1, active(X2)) -> U11(X1, X2),
                        U11(mark(X1), X2) -> U11(X1, X2),
                      U11(active(X1), X2) -> U11(X1, X2),
                               s(mark(X)) -> s(X),
                             s(active(X)) -> s(X),
                       plus(X1, mark(X2)) -> plus(X1, X2),
                     plus(X1, active(X2)) -> plus(X1, X2),
                       plus(mark(X1), X2) -> plus(X1, X2),
                     plus(active(X1), X2) -> plus(X1, X2),
                    U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                  U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                    U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                  U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                    U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                  U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                             U31(mark(X)) -> U31(X),
                           U31(active(X)) -> U31(X),
                          x(X1, mark(X2)) -> x(X1, X2),
                        x(X1, active(X2)) -> x(X1, X2),
                          x(mark(X1), X2) -> x(X1, X2),
                        x(active(X1), X2) -> x(X1, X2),
                    U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                  U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                    U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                  U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                    U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                  U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                        and(X1, mark(X2)) -> and(X1, X2),
                      and(X1, active(X2)) -> and(X1, X2),
                        and(mark(X1), X2) -> and(X1, X2),
                      and(active(X1), X2) -> and(X1, X2),
                           isNat(mark(X)) -> isNat(X),
                         isNat(active(X)) -> isNat(X)}
             SPSC:
              Simple Projection:
               pi(U21#) = 0
              Strict:
               {  U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
                U21#(X1, active(X2), X3) -> U21#(X1, X2, X3),
                  U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3)}
              EDG:
               {(U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
                (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
                (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
                (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
                (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
                (U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))
                (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
                (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
                (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3))}
               SCCS:
                Scc:
                 {  U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
                  U21#(X1, active(X2), X3) -> U21#(X1, X2, X3),
                    U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3)}
                SCC:
                 Strict:
                  {  U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
                   U21#(X1, active(X2), X3) -> U21#(X1, X2, X3),
                     U21#(mark(X1), X2, X3) -> U21#(X1, X2, X3)}
                 Weak:
                 {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                                   mark(tt()) -> active(tt()),
                                   mark(s(X)) -> active(s(mark(X))),
                           mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                        mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                    mark(0()) -> active(0()),
                                 mark(U31(X)) -> active(U31(mark(X))),
                              mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                        mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                            mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                               mark(isNat(X)) -> active(isNat(X)),
                         active(U11(tt(), N)) -> mark(N),
                        active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                         active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                      active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                            active(U31(tt())) -> mark(0()),
                           active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                            active(x(N, 0())) -> mark(U31(isNat(N))),
                      active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                         active(and(tt(), X)) -> mark(X),
                         active(isNat(s(V1))) -> mark(isNat(V1)),
                  active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                           active(isNat(0())) -> mark(tt()),
                     active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                            U11(X1, mark(X2)) -> U11(X1, X2),
                          U11(X1, active(X2)) -> U11(X1, X2),
                            U11(mark(X1), X2) -> U11(X1, X2),
                          U11(active(X1), X2) -> U11(X1, X2),
                                   s(mark(X)) -> s(X),
                                 s(active(X)) -> s(X),
                           plus(X1, mark(X2)) -> plus(X1, X2),
                         plus(X1, active(X2)) -> plus(X1, X2),
                           plus(mark(X1), X2) -> plus(X1, X2),
                         plus(active(X1), X2) -> plus(X1, X2),
                        U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                      U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                        U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                      U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                        U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                      U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                                 U31(mark(X)) -> U31(X),
                               U31(active(X)) -> U31(X),
                              x(X1, mark(X2)) -> x(X1, X2),
                            x(X1, active(X2)) -> x(X1, X2),
                              x(mark(X1), X2) -> x(X1, X2),
                            x(active(X1), X2) -> x(X1, X2),
                        U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                      U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                        U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                      U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                        U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                      U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                            and(X1, mark(X2)) -> and(X1, X2),
                          and(X1, active(X2)) -> and(X1, X2),
                            and(mark(X1), X2) -> and(X1, X2),
                          and(active(X1), X2) -> and(X1, X2),
                               isNat(mark(X)) -> isNat(X),
                             isNat(active(X)) -> isNat(X)}
                 SPSC:
                  Simple Projection:
                   pi(U21#) = 0
                  Strict:
                   {  U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
                    U21#(X1, active(X2), X3) -> U21#(X1, X2, X3)}
                  EDG:
                   {(U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))
                    (U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
                    (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3))
                    (U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))}
                   SCCS:
                    Scc:
                     {  U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
                      U21#(X1, active(X2), X3) -> U21#(X1, X2, X3)}
                    SCC:
                     Strict:
                      {  U21#(X1, mark(X2), X3) -> U21#(X1, X2, X3),
                       U21#(X1, active(X2), X3) -> U21#(X1, X2, X3)}
                     Weak:
                     {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                                       mark(tt()) -> active(tt()),
                                       mark(s(X)) -> active(s(mark(X))),
                               mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                            mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                        mark(0()) -> active(0()),
                                     mark(U31(X)) -> active(U31(mark(X))),
                                  mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                            mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                                mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                                   mark(isNat(X)) -> active(isNat(X)),
                             active(U11(tt(), N)) -> mark(N),
                            active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                             active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                          active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                                active(U31(tt())) -> mark(0()),
                               active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                                active(x(N, 0())) -> mark(U31(isNat(N))),
                          active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                             active(and(tt(), X)) -> mark(X),
                             active(isNat(s(V1))) -> mark(isNat(V1)),
                      active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                               active(isNat(0())) -> mark(tt()),
                         active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                                U11(X1, mark(X2)) -> U11(X1, X2),
                              U11(X1, active(X2)) -> U11(X1, X2),
                                U11(mark(X1), X2) -> U11(X1, X2),
                              U11(active(X1), X2) -> U11(X1, X2),
                                       s(mark(X)) -> s(X),
                                     s(active(X)) -> s(X),
                               plus(X1, mark(X2)) -> plus(X1, X2),
                             plus(X1, active(X2)) -> plus(X1, X2),
                               plus(mark(X1), X2) -> plus(X1, X2),
                             plus(active(X1), X2) -> plus(X1, X2),
                            U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                          U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                            U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                          U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                            U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                          U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                                     U31(mark(X)) -> U31(X),
                                   U31(active(X)) -> U31(X),
                                  x(X1, mark(X2)) -> x(X1, X2),
                                x(X1, active(X2)) -> x(X1, X2),
                                  x(mark(X1), X2) -> x(X1, X2),
                                x(active(X1), X2) -> x(X1, X2),
                            U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                          U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                            U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                          U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                            U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                          U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                                and(X1, mark(X2)) -> and(X1, X2),
                              and(X1, active(X2)) -> and(X1, X2),
                                and(mark(X1), X2) -> and(X1, X2),
                              and(active(X1), X2) -> and(X1, X2),
                                   isNat(mark(X)) -> isNat(X),
                                 isNat(active(X)) -> isNat(X)}
                     SPSC:
                      Simple Projection:
                       pi(U21#) = 1
                      Strict:
                       {U21#(X1, active(X2), X3) -> U21#(X1, X2, X3)}
                      EDG:
                       {(U21#(X1, active(X2), X3) -> U21#(X1, X2, X3), U21#(X1, active(X2), X3) -> U21#(X1, X2, X3))}
                       SCCS:
                        Scc:
                         {U21#(X1, active(X2), X3) -> U21#(X1, X2, X3)}
                        SCC:
                         Strict:
                          {U21#(X1, active(X2), X3) -> U21#(X1, X2, X3)}
                         Weak:
                         {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                                           mark(tt()) -> active(tt()),
                                           mark(s(X)) -> active(s(mark(X))),
                                   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                                mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                            mark(0()) -> active(0()),
                                         mark(U31(X)) -> active(U31(mark(X))),
                                      mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                                mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                                    mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                                       mark(isNat(X)) -> active(isNat(X)),
                                 active(U11(tt(), N)) -> mark(N),
                                active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                                 active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                              active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                                    active(U31(tt())) -> mark(0()),
                                   active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                                    active(x(N, 0())) -> mark(U31(isNat(N))),
                              active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                                 active(and(tt(), X)) -> mark(X),
                                 active(isNat(s(V1))) -> mark(isNat(V1)),
                          active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                                   active(isNat(0())) -> mark(tt()),
                             active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                                    U11(X1, mark(X2)) -> U11(X1, X2),
                                  U11(X1, active(X2)) -> U11(X1, X2),
                                    U11(mark(X1), X2) -> U11(X1, X2),
                                  U11(active(X1), X2) -> U11(X1, X2),
                                           s(mark(X)) -> s(X),
                                         s(active(X)) -> s(X),
                                   plus(X1, mark(X2)) -> plus(X1, X2),
                                 plus(X1, active(X2)) -> plus(X1, X2),
                                   plus(mark(X1), X2) -> plus(X1, X2),
                                 plus(active(X1), X2) -> plus(X1, X2),
                                U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                              U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                                U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                              U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                                U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                              U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                                         U31(mark(X)) -> U31(X),
                                       U31(active(X)) -> U31(X),
                                      x(X1, mark(X2)) -> x(X1, X2),
                                    x(X1, active(X2)) -> x(X1, X2),
                                      x(mark(X1), X2) -> x(X1, X2),
                                    x(active(X1), X2) -> x(X1, X2),
                                U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                              U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                                U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                              U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                                U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                              U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                                    and(X1, mark(X2)) -> and(X1, X2),
                                  and(X1, active(X2)) -> and(X1, X2),
                                    and(mark(X1), X2) -> and(X1, X2),
                                  and(active(X1), X2) -> and(X1, X2),
                                       isNat(mark(X)) -> isNat(X),
                                     isNat(active(X)) -> isNat(X)}
                         SPSC:
                          Simple Projection:
                           pi(U21#) = 1
                          Strict:
                           {}
                          Qed
    SCC:
     Strict:
      {  plus#(X1, mark(X2)) -> plus#(X1, X2),
       plus#(X1, active(X2)) -> plus#(X1, X2),
         plus#(mark(X1), X2) -> plus#(X1, X2),
       plus#(active(X1), X2) -> plus#(X1, X2)}
     Weak:
     {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                       mark(tt()) -> active(tt()),
                       mark(s(X)) -> active(s(mark(X))),
               mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
            mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                        mark(0()) -> active(0()),
                     mark(U31(X)) -> active(U31(mark(X))),
                  mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
            mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                   mark(isNat(X)) -> active(isNat(X)),
             active(U11(tt(), N)) -> mark(N),
            active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
             active(plus(N, 0())) -> mark(U11(isNat(N), N)),
          active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                active(U31(tt())) -> mark(0()),
               active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                active(x(N, 0())) -> mark(U31(isNat(N))),
          active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
             active(and(tt(), X)) -> mark(X),
             active(isNat(s(V1))) -> mark(isNat(V1)),
      active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
               active(isNat(0())) -> mark(tt()),
         active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                U11(X1, mark(X2)) -> U11(X1, X2),
              U11(X1, active(X2)) -> U11(X1, X2),
                U11(mark(X1), X2) -> U11(X1, X2),
              U11(active(X1), X2) -> U11(X1, X2),
                       s(mark(X)) -> s(X),
                     s(active(X)) -> s(X),
               plus(X1, mark(X2)) -> plus(X1, X2),
             plus(X1, active(X2)) -> plus(X1, X2),
               plus(mark(X1), X2) -> plus(X1, X2),
             plus(active(X1), X2) -> plus(X1, X2),
            U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
          U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
            U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
          U21(X1, active(X2), X3) -> U21(X1, X2, X3),
            U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
          U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                     U31(mark(X)) -> U31(X),
                   U31(active(X)) -> U31(X),
                  x(X1, mark(X2)) -> x(X1, X2),
                x(X1, active(X2)) -> x(X1, X2),
                  x(mark(X1), X2) -> x(X1, X2),
                x(active(X1), X2) -> x(X1, X2),
            U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
          U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
            U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
          U41(X1, active(X2), X3) -> U41(X1, X2, X3),
            U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
          U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                and(X1, mark(X2)) -> and(X1, X2),
              and(X1, active(X2)) -> and(X1, X2),
                and(mark(X1), X2) -> and(X1, X2),
              and(active(X1), X2) -> and(X1, X2),
                   isNat(mark(X)) -> isNat(X),
                 isNat(active(X)) -> isNat(X)}
     SPSC:
      Simple Projection:
       pi(plus#) = 0
      Strict:
       {  plus#(X1, mark(X2)) -> plus#(X1, X2),
        plus#(X1, active(X2)) -> plus#(X1, X2),
          plus#(mark(X1), X2) -> plus#(X1, X2)}
      EDG:
       {(plus#(X1, active(X2)) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))
        (plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
        (plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
        (plus#(mark(X1), X2) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
        (plus#(mark(X1), X2) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
        (plus#(mark(X1), X2) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))
        (plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
        (plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
        (plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(mark(X1), X2) -> plus#(X1, X2))}
       SCCS:
        Scc:
         {  plus#(X1, mark(X2)) -> plus#(X1, X2),
          plus#(X1, active(X2)) -> plus#(X1, X2),
            plus#(mark(X1), X2) -> plus#(X1, X2)}
        SCC:
         Strict:
          {  plus#(X1, mark(X2)) -> plus#(X1, X2),
           plus#(X1, active(X2)) -> plus#(X1, X2),
             plus#(mark(X1), X2) -> plus#(X1, X2)}
         Weak:
         {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                           mark(tt()) -> active(tt()),
                           mark(s(X)) -> active(s(mark(X))),
                   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                            mark(0()) -> active(0()),
                         mark(U31(X)) -> active(U31(mark(X))),
                      mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                    mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                       mark(isNat(X)) -> active(isNat(X)),
                 active(U11(tt(), N)) -> mark(N),
                active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                 active(plus(N, 0())) -> mark(U11(isNat(N), N)),
              active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                    active(U31(tt())) -> mark(0()),
                   active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                    active(x(N, 0())) -> mark(U31(isNat(N))),
              active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                 active(and(tt(), X)) -> mark(X),
                 active(isNat(s(V1))) -> mark(isNat(V1)),
          active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                   active(isNat(0())) -> mark(tt()),
             active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                    U11(X1, mark(X2)) -> U11(X1, X2),
                  U11(X1, active(X2)) -> U11(X1, X2),
                    U11(mark(X1), X2) -> U11(X1, X2),
                  U11(active(X1), X2) -> U11(X1, X2),
                           s(mark(X)) -> s(X),
                         s(active(X)) -> s(X),
                   plus(X1, mark(X2)) -> plus(X1, X2),
                 plus(X1, active(X2)) -> plus(X1, X2),
                   plus(mark(X1), X2) -> plus(X1, X2),
                 plus(active(X1), X2) -> plus(X1, X2),
                U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
              U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
              U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
              U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                         U31(mark(X)) -> U31(X),
                       U31(active(X)) -> U31(X),
                      x(X1, mark(X2)) -> x(X1, X2),
                    x(X1, active(X2)) -> x(X1, X2),
                      x(mark(X1), X2) -> x(X1, X2),
                    x(active(X1), X2) -> x(X1, X2),
                U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
              U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
              U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
              U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                    and(X1, mark(X2)) -> and(X1, X2),
                  and(X1, active(X2)) -> and(X1, X2),
                    and(mark(X1), X2) -> and(X1, X2),
                  and(active(X1), X2) -> and(X1, X2),
                       isNat(mark(X)) -> isNat(X),
                     isNat(active(X)) -> isNat(X)}
         SPSC:
          Simple Projection:
           pi(plus#) = 0
          Strict:
           {  plus#(X1, mark(X2)) -> plus#(X1, X2),
            plus#(X1, active(X2)) -> plus#(X1, X2)}
          EDG:
           {(plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))
            (plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
            (plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(X1, mark(X2)) -> plus#(X1, X2))
            (plus#(X1, mark(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))}
           SCCS:
            Scc:
             {  plus#(X1, mark(X2)) -> plus#(X1, X2),
              plus#(X1, active(X2)) -> plus#(X1, X2)}
            SCC:
             Strict:
              {  plus#(X1, mark(X2)) -> plus#(X1, X2),
               plus#(X1, active(X2)) -> plus#(X1, X2)}
             Weak:
             {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                               mark(tt()) -> active(tt()),
                               mark(s(X)) -> active(s(mark(X))),
                       mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                    mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                mark(0()) -> active(0()),
                             mark(U31(X)) -> active(U31(mark(X))),
                          mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                    mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                        mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                           mark(isNat(X)) -> active(isNat(X)),
                     active(U11(tt(), N)) -> mark(N),
                    active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                     active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                  active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                        active(U31(tt())) -> mark(0()),
                       active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                        active(x(N, 0())) -> mark(U31(isNat(N))),
                  active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                     active(and(tt(), X)) -> mark(X),
                     active(isNat(s(V1))) -> mark(isNat(V1)),
              active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                       active(isNat(0())) -> mark(tt()),
                 active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                        U11(X1, mark(X2)) -> U11(X1, X2),
                      U11(X1, active(X2)) -> U11(X1, X2),
                        U11(mark(X1), X2) -> U11(X1, X2),
                      U11(active(X1), X2) -> U11(X1, X2),
                               s(mark(X)) -> s(X),
                             s(active(X)) -> s(X),
                       plus(X1, mark(X2)) -> plus(X1, X2),
                     plus(X1, active(X2)) -> plus(X1, X2),
                       plus(mark(X1), X2) -> plus(X1, X2),
                     plus(active(X1), X2) -> plus(X1, X2),
                    U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                  U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                    U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                  U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                    U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                  U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                             U31(mark(X)) -> U31(X),
                           U31(active(X)) -> U31(X),
                          x(X1, mark(X2)) -> x(X1, X2),
                        x(X1, active(X2)) -> x(X1, X2),
                          x(mark(X1), X2) -> x(X1, X2),
                        x(active(X1), X2) -> x(X1, X2),
                    U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                  U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                    U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                  U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                    U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                  U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                        and(X1, mark(X2)) -> and(X1, X2),
                      and(X1, active(X2)) -> and(X1, X2),
                        and(mark(X1), X2) -> and(X1, X2),
                      and(active(X1), X2) -> and(X1, X2),
                           isNat(mark(X)) -> isNat(X),
                         isNat(active(X)) -> isNat(X)}
             SPSC:
              Simple Projection:
               pi(plus#) = 1
              Strict:
               {plus#(X1, active(X2)) -> plus#(X1, X2)}
              EDG:
               {(plus#(X1, active(X2)) -> plus#(X1, X2), plus#(X1, active(X2)) -> plus#(X1, X2))}
               SCCS:
                Scc:
                 {plus#(X1, active(X2)) -> plus#(X1, X2)}
                SCC:
                 Strict:
                  {plus#(X1, active(X2)) -> plus#(X1, X2)}
                 Weak:
                 {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                                   mark(tt()) -> active(tt()),
                                   mark(s(X)) -> active(s(mark(X))),
                           mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                        mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                    mark(0()) -> active(0()),
                                 mark(U31(X)) -> active(U31(mark(X))),
                              mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                        mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                            mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                               mark(isNat(X)) -> active(isNat(X)),
                         active(U11(tt(), N)) -> mark(N),
                        active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                         active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                      active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                            active(U31(tt())) -> mark(0()),
                           active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                            active(x(N, 0())) -> mark(U31(isNat(N))),
                      active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                         active(and(tt(), X)) -> mark(X),
                         active(isNat(s(V1))) -> mark(isNat(V1)),
                  active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                           active(isNat(0())) -> mark(tt()),
                     active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                            U11(X1, mark(X2)) -> U11(X1, X2),
                          U11(X1, active(X2)) -> U11(X1, X2),
                            U11(mark(X1), X2) -> U11(X1, X2),
                          U11(active(X1), X2) -> U11(X1, X2),
                                   s(mark(X)) -> s(X),
                                 s(active(X)) -> s(X),
                           plus(X1, mark(X2)) -> plus(X1, X2),
                         plus(X1, active(X2)) -> plus(X1, X2),
                           plus(mark(X1), X2) -> plus(X1, X2),
                         plus(active(X1), X2) -> plus(X1, X2),
                        U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                      U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                        U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                      U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                        U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                      U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                                 U31(mark(X)) -> U31(X),
                               U31(active(X)) -> U31(X),
                              x(X1, mark(X2)) -> x(X1, X2),
                            x(X1, active(X2)) -> x(X1, X2),
                              x(mark(X1), X2) -> x(X1, X2),
                            x(active(X1), X2) -> x(X1, X2),
                        U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                      U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                        U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                      U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                        U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                      U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                            and(X1, mark(X2)) -> and(X1, X2),
                          and(X1, active(X2)) -> and(X1, X2),
                            and(mark(X1), X2) -> and(X1, X2),
                          and(active(X1), X2) -> and(X1, X2),
                               isNat(mark(X)) -> isNat(X),
                             isNat(active(X)) -> isNat(X)}
                 SPSC:
                  Simple Projection:
                   pi(plus#) = 1
                  Strict:
                   {}
                  Qed
    SCC:
     Strict:
      {  s#(mark(X)) -> s#(X),
       s#(active(X)) -> s#(X)}
     Weak:
     {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                       mark(tt()) -> active(tt()),
                       mark(s(X)) -> active(s(mark(X))),
               mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
            mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                        mark(0()) -> active(0()),
                     mark(U31(X)) -> active(U31(mark(X))),
                  mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
            mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                   mark(isNat(X)) -> active(isNat(X)),
             active(U11(tt(), N)) -> mark(N),
            active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
             active(plus(N, 0())) -> mark(U11(isNat(N), N)),
          active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                active(U31(tt())) -> mark(0()),
               active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                active(x(N, 0())) -> mark(U31(isNat(N))),
          active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
             active(and(tt(), X)) -> mark(X),
             active(isNat(s(V1))) -> mark(isNat(V1)),
      active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
               active(isNat(0())) -> mark(tt()),
         active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                U11(X1, mark(X2)) -> U11(X1, X2),
              U11(X1, active(X2)) -> U11(X1, X2),
                U11(mark(X1), X2) -> U11(X1, X2),
              U11(active(X1), X2) -> U11(X1, X2),
                       s(mark(X)) -> s(X),
                     s(active(X)) -> s(X),
               plus(X1, mark(X2)) -> plus(X1, X2),
             plus(X1, active(X2)) -> plus(X1, X2),
               plus(mark(X1), X2) -> plus(X1, X2),
             plus(active(X1), X2) -> plus(X1, X2),
            U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
          U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
            U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
          U21(X1, active(X2), X3) -> U21(X1, X2, X3),
            U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
          U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                     U31(mark(X)) -> U31(X),
                   U31(active(X)) -> U31(X),
                  x(X1, mark(X2)) -> x(X1, X2),
                x(X1, active(X2)) -> x(X1, X2),
                  x(mark(X1), X2) -> x(X1, X2),
                x(active(X1), X2) -> x(X1, X2),
            U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
          U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
            U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
          U41(X1, active(X2), X3) -> U41(X1, X2, X3),
            U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
          U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                and(X1, mark(X2)) -> and(X1, X2),
              and(X1, active(X2)) -> and(X1, X2),
                and(mark(X1), X2) -> and(X1, X2),
              and(active(X1), X2) -> and(X1, X2),
                   isNat(mark(X)) -> isNat(X),
                 isNat(active(X)) -> isNat(X)}
     SPSC:
      Simple Projection:
       pi(s#) = 0
      Strict:
       {s#(active(X)) -> s#(X)}
      EDG:
       {(s#(active(X)) -> s#(X), s#(active(X)) -> s#(X))}
       SCCS:
        Scc:
         {s#(active(X)) -> s#(X)}
        SCC:
         Strict:
          {s#(active(X)) -> s#(X)}
         Weak:
         {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                           mark(tt()) -> active(tt()),
                           mark(s(X)) -> active(s(mark(X))),
                   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                            mark(0()) -> active(0()),
                         mark(U31(X)) -> active(U31(mark(X))),
                      mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                    mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                       mark(isNat(X)) -> active(isNat(X)),
                 active(U11(tt(), N)) -> mark(N),
                active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                 active(plus(N, 0())) -> mark(U11(isNat(N), N)),
              active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                    active(U31(tt())) -> mark(0()),
                   active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                    active(x(N, 0())) -> mark(U31(isNat(N))),
              active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                 active(and(tt(), X)) -> mark(X),
                 active(isNat(s(V1))) -> mark(isNat(V1)),
          active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                   active(isNat(0())) -> mark(tt()),
             active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                    U11(X1, mark(X2)) -> U11(X1, X2),
                  U11(X1, active(X2)) -> U11(X1, X2),
                    U11(mark(X1), X2) -> U11(X1, X2),
                  U11(active(X1), X2) -> U11(X1, X2),
                           s(mark(X)) -> s(X),
                         s(active(X)) -> s(X),
                   plus(X1, mark(X2)) -> plus(X1, X2),
                 plus(X1, active(X2)) -> plus(X1, X2),
                   plus(mark(X1), X2) -> plus(X1, X2),
                 plus(active(X1), X2) -> plus(X1, X2),
                U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
              U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
              U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
              U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                         U31(mark(X)) -> U31(X),
                       U31(active(X)) -> U31(X),
                      x(X1, mark(X2)) -> x(X1, X2),
                    x(X1, active(X2)) -> x(X1, X2),
                      x(mark(X1), X2) -> x(X1, X2),
                    x(active(X1), X2) -> x(X1, X2),
                U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
              U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
              U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
              U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                    and(X1, mark(X2)) -> and(X1, X2),
                  and(X1, active(X2)) -> and(X1, X2),
                    and(mark(X1), X2) -> and(X1, X2),
                  and(active(X1), X2) -> and(X1, X2),
                       isNat(mark(X)) -> isNat(X),
                     isNat(active(X)) -> isNat(X)}
         SPSC:
          Simple Projection:
           pi(s#) = 0
          Strict:
           {}
          Qed
    SCC:
     Strict:
      {  U11#(X1, mark(X2)) -> U11#(X1, X2),
       U11#(X1, active(X2)) -> U11#(X1, X2),
         U11#(mark(X1), X2) -> U11#(X1, X2),
       U11#(active(X1), X2) -> U11#(X1, X2)}
     Weak:
     {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                       mark(tt()) -> active(tt()),
                       mark(s(X)) -> active(s(mark(X))),
               mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
            mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                        mark(0()) -> active(0()),
                     mark(U31(X)) -> active(U31(mark(X))),
                  mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
            mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                   mark(isNat(X)) -> active(isNat(X)),
             active(U11(tt(), N)) -> mark(N),
            active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
             active(plus(N, 0())) -> mark(U11(isNat(N), N)),
          active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                active(U31(tt())) -> mark(0()),
               active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                active(x(N, 0())) -> mark(U31(isNat(N))),
          active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
             active(and(tt(), X)) -> mark(X),
             active(isNat(s(V1))) -> mark(isNat(V1)),
      active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
               active(isNat(0())) -> mark(tt()),
         active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                U11(X1, mark(X2)) -> U11(X1, X2),
              U11(X1, active(X2)) -> U11(X1, X2),
                U11(mark(X1), X2) -> U11(X1, X2),
              U11(active(X1), X2) -> U11(X1, X2),
                       s(mark(X)) -> s(X),
                     s(active(X)) -> s(X),
               plus(X1, mark(X2)) -> plus(X1, X2),
             plus(X1, active(X2)) -> plus(X1, X2),
               plus(mark(X1), X2) -> plus(X1, X2),
             plus(active(X1), X2) -> plus(X1, X2),
            U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
          U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
            U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
          U21(X1, active(X2), X3) -> U21(X1, X2, X3),
            U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
          U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                     U31(mark(X)) -> U31(X),
                   U31(active(X)) -> U31(X),
                  x(X1, mark(X2)) -> x(X1, X2),
                x(X1, active(X2)) -> x(X1, X2),
                  x(mark(X1), X2) -> x(X1, X2),
                x(active(X1), X2) -> x(X1, X2),
            U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
          U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
            U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
          U41(X1, active(X2), X3) -> U41(X1, X2, X3),
            U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
          U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                and(X1, mark(X2)) -> and(X1, X2),
              and(X1, active(X2)) -> and(X1, X2),
                and(mark(X1), X2) -> and(X1, X2),
              and(active(X1), X2) -> and(X1, X2),
                   isNat(mark(X)) -> isNat(X),
                 isNat(active(X)) -> isNat(X)}
     SPSC:
      Simple Projection:
       pi(U11#) = 1
      Strict:
       {U11#(X1, active(X2)) -> U11#(X1, X2),
          U11#(mark(X1), X2) -> U11#(X1, X2),
        U11#(active(X1), X2) -> U11#(X1, X2)}
      EDG:
       {(U11#(mark(X1), X2) -> U11#(X1, X2), U11#(active(X1), X2) -> U11#(X1, X2))
        (U11#(mark(X1), X2) -> U11#(X1, X2), U11#(mark(X1), X2) -> U11#(X1, X2))
        (U11#(mark(X1), X2) -> U11#(X1, X2), U11#(X1, active(X2)) -> U11#(X1, X2))
        (U11#(active(X1), X2) -> U11#(X1, X2), U11#(X1, active(X2)) -> U11#(X1, X2))
        (U11#(active(X1), X2) -> U11#(X1, X2), U11#(mark(X1), X2) -> U11#(X1, X2))
        (U11#(active(X1), X2) -> U11#(X1, X2), U11#(active(X1), X2) -> U11#(X1, X2))
        (U11#(X1, active(X2)) -> U11#(X1, X2), U11#(X1, active(X2)) -> U11#(X1, X2))
        (U11#(X1, active(X2)) -> U11#(X1, X2), U11#(mark(X1), X2) -> U11#(X1, X2))
        (U11#(X1, active(X2)) -> U11#(X1, X2), U11#(active(X1), X2) -> U11#(X1, X2))}
       SCCS:
        Scc:
         {U11#(X1, active(X2)) -> U11#(X1, X2),
            U11#(mark(X1), X2) -> U11#(X1, X2),
          U11#(active(X1), X2) -> U11#(X1, X2)}
        SCC:
         Strict:
          {U11#(X1, active(X2)) -> U11#(X1, X2),
             U11#(mark(X1), X2) -> U11#(X1, X2),
           U11#(active(X1), X2) -> U11#(X1, X2)}
         Weak:
         {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                           mark(tt()) -> active(tt()),
                           mark(s(X)) -> active(s(mark(X))),
                   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                            mark(0()) -> active(0()),
                         mark(U31(X)) -> active(U31(mark(X))),
                      mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                    mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                       mark(isNat(X)) -> active(isNat(X)),
                 active(U11(tt(), N)) -> mark(N),
                active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                 active(plus(N, 0())) -> mark(U11(isNat(N), N)),
              active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                    active(U31(tt())) -> mark(0()),
                   active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                    active(x(N, 0())) -> mark(U31(isNat(N))),
              active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                 active(and(tt(), X)) -> mark(X),
                 active(isNat(s(V1))) -> mark(isNat(V1)),
          active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                   active(isNat(0())) -> mark(tt()),
             active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                    U11(X1, mark(X2)) -> U11(X1, X2),
                  U11(X1, active(X2)) -> U11(X1, X2),
                    U11(mark(X1), X2) -> U11(X1, X2),
                  U11(active(X1), X2) -> U11(X1, X2),
                           s(mark(X)) -> s(X),
                         s(active(X)) -> s(X),
                   plus(X1, mark(X2)) -> plus(X1, X2),
                 plus(X1, active(X2)) -> plus(X1, X2),
                   plus(mark(X1), X2) -> plus(X1, X2),
                 plus(active(X1), X2) -> plus(X1, X2),
                U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
              U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
              U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
              U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                         U31(mark(X)) -> U31(X),
                       U31(active(X)) -> U31(X),
                      x(X1, mark(X2)) -> x(X1, X2),
                    x(X1, active(X2)) -> x(X1, X2),
                      x(mark(X1), X2) -> x(X1, X2),
                    x(active(X1), X2) -> x(X1, X2),
                U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
              U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
              U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
              U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                    and(X1, mark(X2)) -> and(X1, X2),
                  and(X1, active(X2)) -> and(X1, X2),
                    and(mark(X1), X2) -> and(X1, X2),
                  and(active(X1), X2) -> and(X1, X2),
                       isNat(mark(X)) -> isNat(X),
                     isNat(active(X)) -> isNat(X)}
         SPSC:
          Simple Projection:
           pi(U11#) = 0
          Strict:
           {U11#(X1, active(X2)) -> U11#(X1, X2),
              U11#(mark(X1), X2) -> U11#(X1, X2)}
          EDG:
           {(U11#(mark(X1), X2) -> U11#(X1, X2), U11#(mark(X1), X2) -> U11#(X1, X2))
            (U11#(mark(X1), X2) -> U11#(X1, X2), U11#(X1, active(X2)) -> U11#(X1, X2))
            (U11#(X1, active(X2)) -> U11#(X1, X2), U11#(X1, active(X2)) -> U11#(X1, X2))
            (U11#(X1, active(X2)) -> U11#(X1, X2), U11#(mark(X1), X2) -> U11#(X1, X2))}
           SCCS:
            Scc:
             {U11#(X1, active(X2)) -> U11#(X1, X2),
                U11#(mark(X1), X2) -> U11#(X1, X2)}
            SCC:
             Strict:
              {U11#(X1, active(X2)) -> U11#(X1, X2),
                 U11#(mark(X1), X2) -> U11#(X1, X2)}
             Weak:
             {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                               mark(tt()) -> active(tt()),
                               mark(s(X)) -> active(s(mark(X))),
                       mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                    mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                mark(0()) -> active(0()),
                             mark(U31(X)) -> active(U31(mark(X))),
                          mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                    mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                        mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                           mark(isNat(X)) -> active(isNat(X)),
                     active(U11(tt(), N)) -> mark(N),
                    active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                     active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                  active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                        active(U31(tt())) -> mark(0()),
                       active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                        active(x(N, 0())) -> mark(U31(isNat(N))),
                  active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                     active(and(tt(), X)) -> mark(X),
                     active(isNat(s(V1))) -> mark(isNat(V1)),
              active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                       active(isNat(0())) -> mark(tt()),
                 active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                        U11(X1, mark(X2)) -> U11(X1, X2),
                      U11(X1, active(X2)) -> U11(X1, X2),
                        U11(mark(X1), X2) -> U11(X1, X2),
                      U11(active(X1), X2) -> U11(X1, X2),
                               s(mark(X)) -> s(X),
                             s(active(X)) -> s(X),
                       plus(X1, mark(X2)) -> plus(X1, X2),
                     plus(X1, active(X2)) -> plus(X1, X2),
                       plus(mark(X1), X2) -> plus(X1, X2),
                     plus(active(X1), X2) -> plus(X1, X2),
                    U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                  U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                    U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                  U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                    U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                  U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                             U31(mark(X)) -> U31(X),
                           U31(active(X)) -> U31(X),
                          x(X1, mark(X2)) -> x(X1, X2),
                        x(X1, active(X2)) -> x(X1, X2),
                          x(mark(X1), X2) -> x(X1, X2),
                        x(active(X1), X2) -> x(X1, X2),
                    U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                  U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                    U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                  U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                    U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                  U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                        and(X1, mark(X2)) -> and(X1, X2),
                      and(X1, active(X2)) -> and(X1, X2),
                        and(mark(X1), X2) -> and(X1, X2),
                      and(active(X1), X2) -> and(X1, X2),
                           isNat(mark(X)) -> isNat(X),
                         isNat(active(X)) -> isNat(X)}
             SPSC:
              Simple Projection:
               pi(U11#) = 0
              Strict:
               {U11#(X1, active(X2)) -> U11#(X1, X2)}
              EDG:
               {(U11#(X1, active(X2)) -> U11#(X1, X2), U11#(X1, active(X2)) -> U11#(X1, X2))}
               SCCS:
                Scc:
                 {U11#(X1, active(X2)) -> U11#(X1, X2)}
                SCC:
                 Strict:
                  {U11#(X1, active(X2)) -> U11#(X1, X2)}
                 Weak:
                 {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                                   mark(tt()) -> active(tt()),
                                   mark(s(X)) -> active(s(mark(X))),
                           mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                        mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                                    mark(0()) -> active(0()),
                                 mark(U31(X)) -> active(U31(mark(X))),
                              mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                        mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                            mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                               mark(isNat(X)) -> active(isNat(X)),
                         active(U11(tt(), N)) -> mark(N),
                        active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                         active(plus(N, 0())) -> mark(U11(isNat(N), N)),
                      active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                            active(U31(tt())) -> mark(0()),
                           active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                            active(x(N, 0())) -> mark(U31(isNat(N))),
                      active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                         active(and(tt(), X)) -> mark(X),
                         active(isNat(s(V1))) -> mark(isNat(V1)),
                  active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                           active(isNat(0())) -> mark(tt()),
                     active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                            U11(X1, mark(X2)) -> U11(X1, X2),
                          U11(X1, active(X2)) -> U11(X1, X2),
                            U11(mark(X1), X2) -> U11(X1, X2),
                          U11(active(X1), X2) -> U11(X1, X2),
                                   s(mark(X)) -> s(X),
                                 s(active(X)) -> s(X),
                           plus(X1, mark(X2)) -> plus(X1, X2),
                         plus(X1, active(X2)) -> plus(X1, X2),
                           plus(mark(X1), X2) -> plus(X1, X2),
                         plus(active(X1), X2) -> plus(X1, X2),
                        U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
                      U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                        U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
                      U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                        U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
                      U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                                 U31(mark(X)) -> U31(X),
                               U31(active(X)) -> U31(X),
                              x(X1, mark(X2)) -> x(X1, X2),
                            x(X1, active(X2)) -> x(X1, X2),
                              x(mark(X1), X2) -> x(X1, X2),
                            x(active(X1), X2) -> x(X1, X2),
                        U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
                      U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                        U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
                      U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                        U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
                      U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                            and(X1, mark(X2)) -> and(X1, X2),
                          and(X1, active(X2)) -> and(X1, X2),
                            and(mark(X1), X2) -> and(X1, X2),
                          and(active(X1), X2) -> and(X1, X2),
                               isNat(mark(X)) -> isNat(X),
                             isNat(active(X)) -> isNat(X)}
                 SPSC:
                  Simple Projection:
                   pi(U11#) = 1
                  Strict:
                   {}
                  Qed
    SCC:
     Strict:
      {          mark#(U11(X1, X2)) -> mark#(X1),
                 mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)),
                        mark#(s(X)) -> mark#(X),
                        mark#(s(X)) -> active#(s(mark(X))),
                mark#(plus(X1, X2)) -> mark#(X1),
                mark#(plus(X1, X2)) -> mark#(X2),
                mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))),
             mark#(U21(X1, X2, X3)) -> mark#(X1),
             mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)),
                      mark#(U31(X)) -> mark#(X),
                      mark#(U31(X)) -> active#(U31(mark(X))),
                   mark#(x(X1, X2)) -> mark#(X1),
                   mark#(x(X1, X2)) -> mark#(X2),
                   mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))),
             mark#(U41(X1, X2, X3)) -> mark#(X1),
             mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)),
                 mark#(and(X1, X2)) -> mark#(X1),
                 mark#(and(X1, X2)) -> active#(and(mark(X1), X2)),
                    mark#(isNat(X)) -> active#(isNat(X)),
              active#(U11(tt(), N)) -> mark#(N),
             active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)),
              active#(plus(N, 0())) -> mark#(U11(isNat(N), N)),
           active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))),
                active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)),
                 active#(x(N, 0())) -> mark#(U31(isNat(N))),
           active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)),
              active#(and(tt(), X)) -> mark#(X),
              active#(isNat(s(V1))) -> mark#(isNat(V1)),
       active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))),
          active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2)))}
     Weak:
     {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                       mark(tt()) -> active(tt()),
                       mark(s(X)) -> active(s(mark(X))),
               mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
            mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                        mark(0()) -> active(0()),
                     mark(U31(X)) -> active(U31(mark(X))),
                  mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
            mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                   mark(isNat(X)) -> active(isNat(X)),
             active(U11(tt(), N)) -> mark(N),
            active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
             active(plus(N, 0())) -> mark(U11(isNat(N), N)),
          active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                active(U31(tt())) -> mark(0()),
               active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                active(x(N, 0())) -> mark(U31(isNat(N))),
          active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
             active(and(tt(), X)) -> mark(X),
             active(isNat(s(V1))) -> mark(isNat(V1)),
      active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
               active(isNat(0())) -> mark(tt()),
         active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                U11(X1, mark(X2)) -> U11(X1, X2),
              U11(X1, active(X2)) -> U11(X1, X2),
                U11(mark(X1), X2) -> U11(X1, X2),
              U11(active(X1), X2) -> U11(X1, X2),
                       s(mark(X)) -> s(X),
                     s(active(X)) -> s(X),
               plus(X1, mark(X2)) -> plus(X1, X2),
             plus(X1, active(X2)) -> plus(X1, X2),
               plus(mark(X1), X2) -> plus(X1, X2),
             plus(active(X1), X2) -> plus(X1, X2),
            U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
          U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
            U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
          U21(X1, active(X2), X3) -> U21(X1, X2, X3),
            U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
          U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                     U31(mark(X)) -> U31(X),
                   U31(active(X)) -> U31(X),
                  x(X1, mark(X2)) -> x(X1, X2),
                x(X1, active(X2)) -> x(X1, X2),
                  x(mark(X1), X2) -> x(X1, X2),
                x(active(X1), X2) -> x(X1, X2),
            U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
          U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
            U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
          U41(X1, active(X2), X3) -> U41(X1, X2, X3),
            U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
          U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                and(X1, mark(X2)) -> and(X1, X2),
              and(X1, active(X2)) -> and(X1, X2),
                and(mark(X1), X2) -> and(X1, X2),
              and(active(X1), X2) -> and(X1, X2),
                   isNat(mark(X)) -> isNat(X),
                 isNat(active(X)) -> isNat(X)}
     POLY:
      Argument Filtering:
       pi(isNat) = [], pi(and) = [], pi(U41) = [], pi(x) = [], pi(U31) = [], pi(0) = [], pi(U21) = [], pi(plus) = [], pi(s) = [], pi(tt) = [], pi(U11) = [], pi(active#) = 0, pi(active) = [], pi(mark#) = [], pi(mark) = []
      Usable Rules:
       {}
      Interpretation:
       [mark#] = 1,
       [U41] = 1,
       [U21] = 1,
       [and] = 1,
       [x] = 1,
       [plus] = 1,
       [U11] = 1,
       [isNat] = 1,
       [U31] = 0,
       [s] = 0
      Strict:
       {          mark#(U11(X1, X2)) -> mark#(X1),
                  mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)),
                         mark#(s(X)) -> mark#(X),
                 mark#(plus(X1, X2)) -> mark#(X1),
                 mark#(plus(X1, X2)) -> mark#(X2),
                 mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))),
              mark#(U21(X1, X2, X3)) -> mark#(X1),
              mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)),
                       mark#(U31(X)) -> mark#(X),
                    mark#(x(X1, X2)) -> mark#(X1),
                    mark#(x(X1, X2)) -> mark#(X2),
                    mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))),
              mark#(U41(X1, X2, X3)) -> mark#(X1),
              mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)),
                  mark#(and(X1, X2)) -> mark#(X1),
                  mark#(and(X1, X2)) -> active#(and(mark(X1), X2)),
                     mark#(isNat(X)) -> active#(isNat(X)),
               active#(U11(tt(), N)) -> mark#(N),
              active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)),
               active#(plus(N, 0())) -> mark#(U11(isNat(N), N)),
            active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))),
                 active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)),
                  active#(x(N, 0())) -> mark#(U31(isNat(N))),
            active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)),
               active#(and(tt(), X)) -> mark#(X),
               active#(isNat(s(V1))) -> mark#(isNat(V1)),
        active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))),
           active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2)))}
      Weak:
       {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                         mark(tt()) -> active(tt()),
                         mark(s(X)) -> active(s(mark(X))),
                 mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
              mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                          mark(0()) -> active(0()),
                       mark(U31(X)) -> active(U31(mark(X))),
                    mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
              mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                  mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                     mark(isNat(X)) -> active(isNat(X)),
               active(U11(tt(), N)) -> mark(N),
              active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
               active(plus(N, 0())) -> mark(U11(isNat(N), N)),
            active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                  active(U31(tt())) -> mark(0()),
                 active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                  active(x(N, 0())) -> mark(U31(isNat(N))),
            active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
               active(and(tt(), X)) -> mark(X),
               active(isNat(s(V1))) -> mark(isNat(V1)),
        active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                 active(isNat(0())) -> mark(tt()),
           active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                  U11(X1, mark(X2)) -> U11(X1, X2),
                U11(X1, active(X2)) -> U11(X1, X2),
                  U11(mark(X1), X2) -> U11(X1, X2),
                U11(active(X1), X2) -> U11(X1, X2),
                         s(mark(X)) -> s(X),
                       s(active(X)) -> s(X),
                 plus(X1, mark(X2)) -> plus(X1, X2),
               plus(X1, active(X2)) -> plus(X1, X2),
                 plus(mark(X1), X2) -> plus(X1, X2),
               plus(active(X1), X2) -> plus(X1, X2),
              U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
            U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
              U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
            U21(X1, active(X2), X3) -> U21(X1, X2, X3),
              U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
            U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                       U31(mark(X)) -> U31(X),
                     U31(active(X)) -> U31(X),
                    x(X1, mark(X2)) -> x(X1, X2),
                  x(X1, active(X2)) -> x(X1, X2),
                    x(mark(X1), X2) -> x(X1, X2),
                  x(active(X1), X2) -> x(X1, X2),
              U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
            U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
              U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
            U41(X1, active(X2), X3) -> U41(X1, X2, X3),
              U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
            U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                  and(X1, mark(X2)) -> and(X1, X2),
                and(X1, active(X2)) -> and(X1, X2),
                  and(mark(X1), X2) -> and(X1, X2),
                and(active(X1), X2) -> and(X1, X2),
                     isNat(mark(X)) -> isNat(X),
                   isNat(active(X)) -> isNat(X)}
      EDG:
       {
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(isNat(X)) -> active#(isNat(X)))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(and(X1, X2)) -> mark#(X1))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(x(X1, X2)) -> mark#(X2))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(x(X1, X2)) -> mark#(X1))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U31(X)) -> mark#(X))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(plus(X1, X2)) -> mark#(X2))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(plus(X1, X2)) -> mark#(X1))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(s(X)) -> mark#(X))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (active#(x(N, 0())) -> mark#(U31(isNat(N))), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(isNat(X)) -> active#(isNat(X)))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> mark#(X1))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X2))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X1))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(U31(X)) -> mark#(X))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X2))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X1))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(s(X)) -> mark#(X))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (mark#(x(X1, X2)) -> mark#(X2), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(U31(X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
        (mark#(U31(X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (mark#(U31(X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
        (mark#(U31(X)) -> mark#(X), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (mark#(U31(X)) -> mark#(X), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (mark#(U31(X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (mark#(U31(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
        (mark#(U31(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
        (mark#(U31(X)) -> mark#(X), mark#(U31(X)) -> mark#(X))
        (mark#(U31(X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (mark#(U31(X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (mark#(U31(X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (mark#(U31(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
        (mark#(U31(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
        (mark#(U31(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
        (mark#(U31(X)) -> mark#(X), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (mark#(U31(X)) -> mark#(X), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(isNat(s(V1))) -> mark#(isNat(V1)))
        (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(and(tt(), X)) -> mark#(X))
        (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
        (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(x(N, 0())) -> mark#(U31(isNat(N))))
        (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
        (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
        (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
        (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
        (mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)), active#(U11(tt(), N)) -> mark#(N))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(isNat(X)) -> active#(isNat(X)))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(and(X1, X2)) -> mark#(X1))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(x(X1, X2)) -> mark#(X2))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(x(X1, X2)) -> mark#(X1))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(U31(X)) -> mark#(X))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(plus(X1, X2)) -> mark#(X2))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(plus(X1, X2)) -> mark#(X1))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(s(X)) -> mark#(X))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (active#(plus(N, 0())) -> mark#(U11(isNat(N), N)), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(U31(X)) -> mark#(X))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
        (mark#(U11(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
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        (mark#(U11(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(U31(X)) -> mark#(X))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(s(X)) -> mark#(X))
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        (mark#(U21(X1, X2, X3)) -> mark#(X1), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
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        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(U31(X)) -> mark#(X))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(s(X)) -> mark#(X))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (mark#(U41(X1, X2, X3)) -> mark#(X1), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(isNat(s(V1))) -> mark#(isNat(V1)))
        (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(and(tt(), X)) -> mark#(X))
        (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
        (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, 0())) -> mark#(U31(isNat(N))))
        (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
        (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
        (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
        (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
        (mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))), active#(U11(tt(), N)) -> mark#(N))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(isNat(X)) -> active#(isNat(X)))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(and(X1, X2)) -> mark#(X1))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(x(X1, X2)) -> mark#(X2))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(x(X1, X2)) -> mark#(X1))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U31(X)) -> mark#(X))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(plus(X1, X2)) -> mark#(X2))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(plus(X1, X2)) -> mark#(X1))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(s(X)) -> mark#(X))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(isNat(s(V1))) -> mark#(isNat(V1)))
        (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(and(tt(), X)) -> mark#(X))
        (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
        (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(x(N, 0())) -> mark#(U31(isNat(N))))
        (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
        (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
        (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
        (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
        (mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)), active#(U11(tt(), N)) -> mark#(N))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(isNat(X)) -> active#(isNat(X)))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(and(X1, X2)) -> mark#(X1))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(x(X1, X2)) -> mark#(X2))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(x(X1, X2)) -> mark#(X1))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U31(X)) -> mark#(X))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> mark#(X2))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> mark#(X1))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(s(X)) -> mark#(X))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)), mark#(U11(X1, X2)) -> mark#(X1))
        (active#(U11(tt(), N)) -> mark#(N), mark#(isNat(X)) -> active#(isNat(X)))
        (active#(U11(tt(), N)) -> mark#(N), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (active#(U11(tt(), N)) -> mark#(N), mark#(and(X1, X2)) -> mark#(X1))
        (active#(U11(tt(), N)) -> mark#(N), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (active#(U11(tt(), N)) -> mark#(N), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (active#(U11(tt(), N)) -> mark#(N), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (active#(U11(tt(), N)) -> mark#(N), mark#(x(X1, X2)) -> mark#(X2))
        (active#(U11(tt(), N)) -> mark#(N), mark#(x(X1, X2)) -> mark#(X1))
        (active#(U11(tt(), N)) -> mark#(N), mark#(U31(X)) -> mark#(X))
        (active#(U11(tt(), N)) -> mark#(N), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (active#(U11(tt(), N)) -> mark#(N), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (active#(U11(tt(), N)) -> mark#(N), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (active#(U11(tt(), N)) -> mark#(N), mark#(plus(X1, X2)) -> mark#(X2))
        (active#(U11(tt(), N)) -> mark#(N), mark#(plus(X1, X2)) -> mark#(X1))
        (active#(U11(tt(), N)) -> mark#(N), mark#(s(X)) -> mark#(X))
        (active#(U11(tt(), N)) -> mark#(N), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (active#(U11(tt(), N)) -> mark#(N), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (mark#(isNat(X)) -> active#(isNat(X)), active#(isNat(s(V1))) -> mark#(isNat(V1)))
        (mark#(isNat(X)) -> active#(isNat(X)), active#(and(tt(), X)) -> mark#(X))
        (mark#(isNat(X)) -> active#(isNat(X)), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
        (mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, 0())) -> mark#(U31(isNat(N))))
        (mark#(isNat(X)) -> active#(isNat(X)), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
        (mark#(isNat(X)) -> active#(isNat(X)), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
        (mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
        (mark#(isNat(X)) -> active#(isNat(X)), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
        (mark#(isNat(X)) -> active#(isNat(X)), active#(U11(tt(), N)) -> mark#(N))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U11(X1, X2)) -> mark#(X1))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(s(X)) -> mark#(X))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(plus(X1, X2)) -> mark#(X1))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(plus(X1, X2)) -> mark#(X2))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U31(X)) -> mark#(X))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(x(X1, X2)) -> mark#(X1))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(x(X1, X2)) -> mark#(X2))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(and(X1, X2)) -> mark#(X1))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (active#(isNat(s(V1))) -> mark#(isNat(V1)), mark#(isNat(X)) -> active#(isNat(X)))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U11(X1, X2)) -> mark#(X1))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(s(X)) -> mark#(X))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> mark#(X1))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> mark#(X2))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U31(X)) -> mark#(X))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(x(X1, X2)) -> mark#(X1))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(x(X1, X2)) -> mark#(X2))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(and(X1, X2)) -> mark#(X1))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)), mark#(isNat(X)) -> active#(isNat(X)))
        (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(U11(tt(), N)) -> mark#(N))
        (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
        (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
        (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
        (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
        (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(x(N, 0())) -> mark#(U31(isNat(N))))
        (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
        (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(and(tt(), X)) -> mark#(X))
        (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(s(V1))) -> mark#(isNat(V1)))
        (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U11(X1, X2)) -> mark#(X1))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(s(X)) -> mark#(X))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(plus(X1, X2)) -> mark#(X1))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(plus(X1, X2)) -> mark#(X2))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U31(X)) -> mark#(X))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(x(X1, X2)) -> mark#(X1))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(x(X1, X2)) -> mark#(X2))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(and(X1, X2)) -> mark#(X1))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))), mark#(isNat(X)) -> active#(isNat(X)))
        (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U11(tt(), N)) -> mark#(N))
        (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
        (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
        (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
        (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
        (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(x(N, 0())) -> mark#(U31(isNat(N))))
        (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
        (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(and(tt(), X)) -> mark#(X))
        (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(s(V1))) -> mark#(isNat(V1)))
        (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(U31(X)) -> mark#(X))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (mark#(and(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(U31(X)) -> mark#(X))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (mark#(x(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X1))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> mark#(X2))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(U31(X)) -> mark#(X))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X1))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> mark#(X2))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> mark#(X1))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (mark#(plus(X1, X2)) -> mark#(X1), mark#(isNat(X)) -> active#(isNat(X)))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U11(X1, X2)) -> mark#(X1))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(s(X)) -> mark#(X))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(plus(X1, X2)) -> mark#(X1))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(plus(X1, X2)) -> mark#(X2))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U31(X)) -> mark#(X))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(x(X1, X2)) -> mark#(X1))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(x(X1, X2)) -> mark#(X2))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(and(X1, X2)) -> mark#(X1))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)), mark#(isNat(X)) -> active#(isNat(X)))
        (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U11(tt(), N)) -> mark#(N))
        (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)))
        (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(plus(N, 0())) -> mark#(U11(isNat(N), N)))
        (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))))
        (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)))
        (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(x(N, 0())) -> mark#(U31(isNat(N))))
        (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)))
        (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(and(tt(), X)) -> mark#(X))
        (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(s(V1))) -> mark#(isNat(V1)))
        (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (mark#(and(X1, X2)) -> active#(and(mark(X1), X2)), active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))))
        (active#(and(tt(), X)) -> mark#(X), mark#(U11(X1, X2)) -> mark#(X1))
        (active#(and(tt(), X)) -> mark#(X), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (active#(and(tt(), X)) -> mark#(X), mark#(s(X)) -> mark#(X))
        (active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
        (active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
        (active#(and(tt(), X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (active#(and(tt(), X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (active#(and(tt(), X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (active#(and(tt(), X)) -> mark#(X), mark#(U31(X)) -> mark#(X))
        (active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
        (active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
        (active#(and(tt(), X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (active#(and(tt(), X)) -> mark#(X), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (active#(and(tt(), X)) -> mark#(X), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (active#(and(tt(), X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
        (active#(and(tt(), X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (active#(and(tt(), X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
        (mark#(s(X)) -> mark#(X), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(s(X)) -> mark#(X), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (mark#(s(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
        (mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X1))
        (mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> mark#(X2))
        (mark#(s(X)) -> mark#(X), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (mark#(s(X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (mark#(s(X)) -> mark#(X), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (mark#(s(X)) -> mark#(X), mark#(U31(X)) -> mark#(X))
        (mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X1))
        (mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> mark#(X2))
        (mark#(s(X)) -> mark#(X), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (mark#(s(X)) -> mark#(X), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (mark#(s(X)) -> mark#(X), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (mark#(s(X)) -> mark#(X), mark#(and(X1, X2)) -> mark#(X1))
        (mark#(s(X)) -> mark#(X), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (mark#(s(X)) -> mark#(X), mark#(isNat(X)) -> active#(isNat(X)))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(U11(X1, X2)) -> mark#(X1))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(s(X)) -> mark#(X))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X1))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> mark#(X2))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(U31(X)) -> mark#(X))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X1))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> mark#(X2))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> mark#(X1))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (mark#(plus(X1, X2)) -> mark#(X2), mark#(isNat(X)) -> active#(isNat(X)))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U11(X1, X2)) -> mark#(X1))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(s(X)) -> mark#(X))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> mark#(X1))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> mark#(X2))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U21(X1, X2, X3)) -> mark#(X1))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U31(X)) -> mark#(X))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> mark#(X1))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> mark#(X2))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U41(X1, X2, X3)) -> mark#(X1))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(and(X1, X2)) -> mark#(X1))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(and(X1, X2)) -> active#(and(mark(X1), X2)))
        (active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))), mark#(isNat(X)) -> active#(isNat(X)))
       }
       SCCS:
        Scc:
         {          mark#(U11(X1, X2)) -> mark#(X1),
                    mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)),
                           mark#(s(X)) -> mark#(X),
                   mark#(plus(X1, X2)) -> mark#(X1),
                   mark#(plus(X1, X2)) -> mark#(X2),
                   mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))),
                mark#(U21(X1, X2, X3)) -> mark#(X1),
                mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)),
                         mark#(U31(X)) -> mark#(X),
                      mark#(x(X1, X2)) -> mark#(X1),
                      mark#(x(X1, X2)) -> mark#(X2),
                      mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))),
                mark#(U41(X1, X2, X3)) -> mark#(X1),
                mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)),
                    mark#(and(X1, X2)) -> mark#(X1),
                    mark#(and(X1, X2)) -> active#(and(mark(X1), X2)),
                       mark#(isNat(X)) -> active#(isNat(X)),
                 active#(U11(tt(), N)) -> mark#(N),
                active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)),
                 active#(plus(N, 0())) -> mark#(U11(isNat(N), N)),
              active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))),
                   active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)),
                    active#(x(N, 0())) -> mark#(U31(isNat(N))),
              active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)),
                 active#(and(tt(), X)) -> mark#(X),
                 active#(isNat(s(V1))) -> mark#(isNat(V1)),
          active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))),
             active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2)))}
        SCC:
         Strict:
          {          mark#(U11(X1, X2)) -> mark#(X1),
                     mark#(U11(X1, X2)) -> active#(U11(mark(X1), X2)),
                            mark#(s(X)) -> mark#(X),
                    mark#(plus(X1, X2)) -> mark#(X1),
                    mark#(plus(X1, X2)) -> mark#(X2),
                    mark#(plus(X1, X2)) -> active#(plus(mark(X1), mark(X2))),
                 mark#(U21(X1, X2, X3)) -> mark#(X1),
                 mark#(U21(X1, X2, X3)) -> active#(U21(mark(X1), X2, X3)),
                          mark#(U31(X)) -> mark#(X),
                       mark#(x(X1, X2)) -> mark#(X1),
                       mark#(x(X1, X2)) -> mark#(X2),
                       mark#(x(X1, X2)) -> active#(x(mark(X1), mark(X2))),
                 mark#(U41(X1, X2, X3)) -> mark#(X1),
                 mark#(U41(X1, X2, X3)) -> active#(U41(mark(X1), X2, X3)),
                     mark#(and(X1, X2)) -> mark#(X1),
                     mark#(and(X1, X2)) -> active#(and(mark(X1), X2)),
                        mark#(isNat(X)) -> active#(isNat(X)),
                  active#(U11(tt(), N)) -> mark#(N),
                 active#(plus(N, s(M))) -> mark#(U21(and(isNat(M), isNat(N)), M, N)),
                  active#(plus(N, 0())) -> mark#(U11(isNat(N), N)),
               active#(U21(tt(), M, N)) -> mark#(s(plus(N, M))),
                    active#(x(N, s(M))) -> mark#(U41(and(isNat(M), isNat(N)), M, N)),
                     active#(x(N, 0())) -> mark#(U31(isNat(N))),
               active#(U41(tt(), M, N)) -> mark#(plus(x(N, M), N)),
                  active#(and(tt(), X)) -> mark#(X),
                  active#(isNat(s(V1))) -> mark#(isNat(V1)),
           active#(isNat(plus(V1, V2))) -> mark#(and(isNat(V1), isNat(V2))),
              active#(isNat(x(V1, V2))) -> mark#(and(isNat(V1), isNat(V2)))}
         Weak:
         {          mark(U11(X1, X2)) -> active(U11(mark(X1), X2)),
                           mark(tt()) -> active(tt()),
                           mark(s(X)) -> active(s(mark(X))),
                   mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))),
                mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)),
                            mark(0()) -> active(0()),
                         mark(U31(X)) -> active(U31(mark(X))),
                      mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))),
                mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)),
                    mark(and(X1, X2)) -> active(and(mark(X1), X2)),
                       mark(isNat(X)) -> active(isNat(X)),
                 active(U11(tt(), N)) -> mark(N),
                active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)),
                 active(plus(N, 0())) -> mark(U11(isNat(N), N)),
              active(U21(tt(), M, N)) -> mark(s(plus(N, M))),
                    active(U31(tt())) -> mark(0()),
                   active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)),
                    active(x(N, 0())) -> mark(U31(isNat(N))),
              active(U41(tt(), M, N)) -> mark(plus(x(N, M), N)),
                 active(and(tt(), X)) -> mark(X),
                 active(isNat(s(V1))) -> mark(isNat(V1)),
          active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                   active(isNat(0())) -> mark(tt()),
             active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))),
                    U11(X1, mark(X2)) -> U11(X1, X2),
                  U11(X1, active(X2)) -> U11(X1, X2),
                    U11(mark(X1), X2) -> U11(X1, X2),
                  U11(active(X1), X2) -> U11(X1, X2),
                           s(mark(X)) -> s(X),
                         s(active(X)) -> s(X),
                   plus(X1, mark(X2)) -> plus(X1, X2),
                 plus(X1, active(X2)) -> plus(X1, X2),
                   plus(mark(X1), X2) -> plus(X1, X2),
                 plus(active(X1), X2) -> plus(X1, X2),
                U21(X1, X2, mark(X3)) -> U21(X1, X2, X3),
              U21(X1, X2, active(X3)) -> U21(X1, X2, X3),
                U21(X1, mark(X2), X3) -> U21(X1, X2, X3),
              U21(X1, active(X2), X3) -> U21(X1, X2, X3),
                U21(mark(X1), X2, X3) -> U21(X1, X2, X3),
              U21(active(X1), X2, X3) -> U21(X1, X2, X3),
                         U31(mark(X)) -> U31(X),
                       U31(active(X)) -> U31(X),
                      x(X1, mark(X2)) -> x(X1, X2),
                    x(X1, active(X2)) -> x(X1, X2),
                      x(mark(X1), X2) -> x(X1, X2),
                    x(active(X1), X2) -> x(X1, X2),
                U41(X1, X2, mark(X3)) -> U41(X1, X2, X3),
              U41(X1, X2, active(X3)) -> U41(X1, X2, X3),
                U41(X1, mark(X2), X3) -> U41(X1, X2, X3),
              U41(X1, active(X2), X3) -> U41(X1, X2, X3),
                U41(mark(X1), X2, X3) -> U41(X1, X2, X3),
              U41(active(X1), X2, X3) -> U41(X1, X2, X3),
                    and(X1, mark(X2)) -> and(X1, X2),
                  and(X1, active(X2)) -> and(X1, X2),
                    and(mark(X1), X2) -> and(X1, X2),
                  and(active(X1), X2) -> and(X1, X2),
                       isNat(mark(X)) -> isNat(X),
                     isNat(active(X)) -> isNat(X)}
         Fail