Termination w.r.t. Q of the following Term Rewriting System could be proven:

Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
U11(tt) → tt
U21(tt, V2) → U22(isList(activate(V2)))
U22(tt) → tt
U31(tt) → tt
U41(tt, V2) → U42(isNeList(activate(V2)))
U42(tt) → tt
U51(tt, V2) → U52(isList(activate(V2)))
U52(tt) → tt
U61(tt) → tt
U71(tt, P) → U72(isPal(activate(P)))
U72(tt) → tt
U81(tt) → tt
isList(V) → U11(isNeList(activate(V)))
isList(n__nil) → tt
isList(n____(V1, V2)) → U21(isList(activate(V1)), activate(V2))
isNeList(V) → U31(isQid(activate(V)))
isNeList(n____(V1, V2)) → U41(isList(activate(V1)), activate(V2))
isNeList(n____(V1, V2)) → U51(isNeList(activate(V1)), activate(V2))
isNePal(V) → U61(isQid(activate(V)))
isNePal(n____(I, __(P, I))) → U71(isQid(activate(I)), activate(P))
isPal(V) → U81(isNePal(activate(V)))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
an__a
en__e
in__i
on__o
un__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X

Q is empty.


QTRS
  ↳ RRRPoloQTRSProof

Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
U11(tt) → tt
U21(tt, V2) → U22(isList(activate(V2)))
U22(tt) → tt
U31(tt) → tt
U41(tt, V2) → U42(isNeList(activate(V2)))
U42(tt) → tt
U51(tt, V2) → U52(isList(activate(V2)))
U52(tt) → tt
U61(tt) → tt
U71(tt, P) → U72(isPal(activate(P)))
U72(tt) → tt
U81(tt) → tt
isList(V) → U11(isNeList(activate(V)))
isList(n__nil) → tt
isList(n____(V1, V2)) → U21(isList(activate(V1)), activate(V2))
isNeList(V) → U31(isQid(activate(V)))
isNeList(n____(V1, V2)) → U41(isList(activate(V1)), activate(V2))
isNeList(n____(V1, V2)) → U51(isNeList(activate(V1)), activate(V2))
isNePal(V) → U61(isQid(activate(V)))
isNePal(n____(I, __(P, I))) → U71(isQid(activate(I)), activate(P))
isPal(V) → U81(isNePal(activate(V)))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
an__a
en__e
in__i
on__o
un__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X

Q is empty.

The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
U11(tt) → tt
U21(tt, V2) → U22(isList(activate(V2)))
U22(tt) → tt
U31(tt) → tt
U41(tt, V2) → U42(isNeList(activate(V2)))
U42(tt) → tt
U51(tt, V2) → U52(isList(activate(V2)))
U52(tt) → tt
U61(tt) → tt
U71(tt, P) → U72(isPal(activate(P)))
U72(tt) → tt
U81(tt) → tt
isList(V) → U11(isNeList(activate(V)))
isList(n__nil) → tt
isList(n____(V1, V2)) → U21(isList(activate(V1)), activate(V2))
isNeList(V) → U31(isQid(activate(V)))
isNeList(n____(V1, V2)) → U41(isList(activate(V1)), activate(V2))
isNeList(n____(V1, V2)) → U51(isNeList(activate(V1)), activate(V2))
isNePal(V) → U61(isQid(activate(V)))
isNePal(n____(I, __(P, I))) → U71(isQid(activate(I)), activate(P))
isPal(V) → U81(isNePal(activate(V)))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
an__a
en__e
in__i
on__o
un__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X

Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:

isQid(n__a) → tt
isQid(n__i) → tt
Used ordering:
Polynomial interpretation [25]:

POL(U11(x1)) = x1   
POL(U21(x1, x2)) = x1 + 2·x2   
POL(U22(x1)) = x1   
POL(U31(x1)) = x1   
POL(U41(x1, x2)) = x1 + 2·x2   
POL(U42(x1)) = x1   
POL(U51(x1, x2)) = 2·x1 + 2·x2   
POL(U52(x1)) = x1   
POL(U61(x1)) = x1   
POL(U71(x1, x2)) = 2·x1 + 2·x2   
POL(U72(x1)) = x1   
POL(U81(x1)) = 2·x1   
POL(__(x1, x2)) = 2·x1 + x2   
POL(a) = 1   
POL(activate(x1)) = x1   
POL(e) = 0   
POL(i) = 1   
POL(isList(x1)) = 2·x1   
POL(isNeList(x1)) = 2·x1   
POL(isNePal(x1)) = x1   
POL(isPal(x1)) = 2·x1   
POL(isQid(x1)) = x1   
POL(n____(x1, x2)) = 2·x1 + x2   
POL(n__a) = 1   
POL(n__e) = 0   
POL(n__i) = 1   
POL(n__nil) = 0   
POL(n__o) = 0   
POL(n__u) = 0   
POL(nil) = 0   
POL(o) = 0   
POL(tt) = 0   
POL(u) = 0   




↳ QTRS
  ↳ RRRPoloQTRSProof
QTRS
      ↳ RRRPoloQTRSProof

Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
U11(tt) → tt
U21(tt, V2) → U22(isList(activate(V2)))
U22(tt) → tt
U31(tt) → tt
U41(tt, V2) → U42(isNeList(activate(V2)))
U42(tt) → tt
U51(tt, V2) → U52(isList(activate(V2)))
U52(tt) → tt
U61(tt) → tt
U71(tt, P) → U72(isPal(activate(P)))
U72(tt) → tt
U81(tt) → tt
isList(V) → U11(isNeList(activate(V)))
isList(n__nil) → tt
isList(n____(V1, V2)) → U21(isList(activate(V1)), activate(V2))
isNeList(V) → U31(isQid(activate(V)))
isNeList(n____(V1, V2)) → U41(isList(activate(V1)), activate(V2))
isNeList(n____(V1, V2)) → U51(isNeList(activate(V1)), activate(V2))
isNePal(V) → U61(isQid(activate(V)))
isNePal(n____(I, __(P, I))) → U71(isQid(activate(I)), activate(P))
isPal(V) → U81(isNePal(activate(V)))
isPal(n__nil) → tt
isQid(n__e) → tt
isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
an__a
en__e
in__i
on__o
un__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X

Q is empty.

The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
U11(tt) → tt
U21(tt, V2) → U22(isList(activate(V2)))
U22(tt) → tt
U31(tt) → tt
U41(tt, V2) → U42(isNeList(activate(V2)))
U42(tt) → tt
U51(tt, V2) → U52(isList(activate(V2)))
U52(tt) → tt
U61(tt) → tt
U71(tt, P) → U72(isPal(activate(P)))
U72(tt) → tt
U81(tt) → tt
isList(V) → U11(isNeList(activate(V)))
isList(n__nil) → tt
isList(n____(V1, V2)) → U21(isList(activate(V1)), activate(V2))
isNeList(V) → U31(isQid(activate(V)))
isNeList(n____(V1, V2)) → U41(isList(activate(V1)), activate(V2))
isNeList(n____(V1, V2)) → U51(isNeList(activate(V1)), activate(V2))
isNePal(V) → U61(isQid(activate(V)))
isNePal(n____(I, __(P, I))) → U71(isQid(activate(I)), activate(P))
isPal(V) → U81(isNePal(activate(V)))
isPal(n__nil) → tt
isQid(n__e) → tt
isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
an__a
en__e
in__i
on__o
un__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X

Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:

__(X, nil) → X
__(nil, X) → X
U41(tt, V2) → U42(isNeList(activate(V2)))
U42(tt) → tt
U51(tt, V2) → U52(isList(activate(V2)))
U52(tt) → tt
U71(tt, P) → U72(isPal(activate(P)))
U72(tt) → tt
isList(V) → U11(isNeList(activate(V)))
isList(n____(V1, V2)) → U21(isList(activate(V1)), activate(V2))
isNeList(n____(V1, V2)) → U51(isNeList(activate(V1)), activate(V2))
isNePal(n____(I, __(P, I))) → U71(isQid(activate(I)), activate(P))
isPal(V) → U81(isNePal(activate(V)))
isQid(n__e) → tt
Used ordering:
Polynomial interpretation [25]:

POL(U11(x1)) = x1   
POL(U21(x1, x2)) = x1 + 2·x2   
POL(U22(x1)) = x1   
POL(U31(x1)) = x1   
POL(U41(x1, x2)) = 2 + x1 + 2·x2   
POL(U42(x1)) = 2 + x1   
POL(U51(x1, x2)) = 2 + x1 + 2·x2   
POL(U52(x1)) = 1 + x1   
POL(U61(x1)) = x1   
POL(U71(x1, x2)) = 2·x1 + 2·x2   
POL(U72(x1)) = 1 + x1   
POL(U81(x1)) = x1   
POL(__(x1, x2)) = 2 + x1 + x2   
POL(a) = 0   
POL(activate(x1)) = x1   
POL(e) = 2   
POL(i) = 0   
POL(isList(x1)) = 2 + 2·x1   
POL(isNeList(x1)) = 2·x1   
POL(isNePal(x1)) = 2·x1   
POL(isPal(x1)) = 2 + 2·x1   
POL(isQid(x1)) = 2·x1   
POL(n____(x1, x2)) = 2 + x1 + x2   
POL(n__a) = 0   
POL(n__e) = 2   
POL(n__i) = 0   
POL(n__nil) = 0   
POL(n__o) = 1   
POL(n__u) = 1   
POL(nil) = 0   
POL(o) = 1   
POL(tt) = 2   
POL(u) = 1   




↳ QTRS
  ↳ RRRPoloQTRSProof
    ↳ QTRS
      ↳ RRRPoloQTRSProof
QTRS
          ↳ RRRPoloQTRSProof

Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
U11(tt) → tt
U21(tt, V2) → U22(isList(activate(V2)))
U22(tt) → tt
U31(tt) → tt
U61(tt) → tt
U81(tt) → tt
isList(n__nil) → tt
isNeList(V) → U31(isQid(activate(V)))
isNeList(n____(V1, V2)) → U41(isList(activate(V1)), activate(V2))
isNePal(V) → U61(isQid(activate(V)))
isPal(n__nil) → tt
isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
an__a
en__e
in__i
on__o
un__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X

Q is empty.

The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
U11(tt) → tt
U21(tt, V2) → U22(isList(activate(V2)))
U22(tt) → tt
U31(tt) → tt
U61(tt) → tt
U81(tt) → tt
isList(n__nil) → tt
isNeList(V) → U31(isQid(activate(V)))
isNeList(n____(V1, V2)) → U41(isList(activate(V1)), activate(V2))
isNePal(V) → U61(isQid(activate(V)))
isPal(n__nil) → tt
isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
an__a
en__e
in__i
on__o
un__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X

Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:

U11(tt) → tt
U31(tt) → tt
U61(tt) → tt
U81(tt) → tt
isList(n__nil) → tt
isNeList(n____(V1, V2)) → U41(isList(activate(V1)), activate(V2))
isNePal(V) → U61(isQid(activate(V)))
isPal(n__nil) → tt
Used ordering:
Polynomial interpretation [25]:

POL(U11(x1)) = 2 + 2·x1   
POL(U21(x1, x2)) = x1 + 2·x2   
POL(U22(x1)) = 2·x1   
POL(U31(x1)) = 2 + 2·x1   
POL(U41(x1, x2)) = 1 + x1 + x2   
POL(U61(x1)) = 1 + 2·x1   
POL(U81(x1)) = 1 + x1   
POL(__(x1, x2)) = 2·x1 + x2   
POL(a) = 0   
POL(activate(x1)) = x1   
POL(e) = 0   
POL(i) = 0   
POL(isList(x1)) = x1   
POL(isNeList(x1)) = 2 + 2·x1   
POL(isNePal(x1)) = 2 + 2·x1   
POL(isPal(x1)) = 1 + 2·x1   
POL(isQid(x1)) = x1   
POL(n____(x1, x2)) = 2·x1 + x2   
POL(n__a) = 0   
POL(n__e) = 0   
POL(n__i) = 0   
POL(n__nil) = 2   
POL(n__o) = 0   
POL(n__u) = 0   
POL(nil) = 2   
POL(o) = 0   
POL(tt) = 0   
POL(u) = 0   




↳ QTRS
  ↳ RRRPoloQTRSProof
    ↳ QTRS
      ↳ RRRPoloQTRSProof
        ↳ QTRS
          ↳ RRRPoloQTRSProof
QTRS
              ↳ RRRPoloQTRSProof

Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
U21(tt, V2) → U22(isList(activate(V2)))
U22(tt) → tt
isNeList(V) → U31(isQid(activate(V)))
isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
an__a
en__e
in__i
on__o
un__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X

Q is empty.

The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
U21(tt, V2) → U22(isList(activate(V2)))
U22(tt) → tt
isNeList(V) → U31(isQid(activate(V)))
isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
an__a
en__e
in__i
on__o
un__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X

Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:

U21(tt, V2) → U22(isList(activate(V2)))
Used ordering:
Polynomial interpretation [25]:

POL(U21(x1, x2)) = 2 + 2·x1 + 2·x2   
POL(U22(x1)) = 2·x1   
POL(U31(x1)) = 2·x1   
POL(__(x1, x2)) = x1 + x2   
POL(a) = 0   
POL(activate(x1)) = x1   
POL(e) = 0   
POL(i) = 0   
POL(isList(x1)) = x1   
POL(isNeList(x1)) = 2·x1   
POL(isQid(x1)) = x1   
POL(n____(x1, x2)) = x1 + x2   
POL(n__a) = 0   
POL(n__e) = 0   
POL(n__i) = 0   
POL(n__nil) = 0   
POL(n__o) = 0   
POL(n__u) = 0   
POL(nil) = 0   
POL(o) = 0   
POL(tt) = 0   
POL(u) = 0   




↳ QTRS
  ↳ RRRPoloQTRSProof
    ↳ QTRS
      ↳ RRRPoloQTRSProof
        ↳ QTRS
          ↳ RRRPoloQTRSProof
            ↳ QTRS
              ↳ RRRPoloQTRSProof
QTRS
                  ↳ RRRPoloQTRSProof

Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
U22(tt) → tt
isNeList(V) → U31(isQid(activate(V)))
isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
an__a
en__e
in__i
on__o
un__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X

Q is empty.

The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
U22(tt) → tt
isNeList(V) → U31(isQid(activate(V)))
isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
an__a
en__e
in__i
on__o
un__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X

Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:

U22(tt) → tt
isNeList(V) → U31(isQid(activate(V)))
Used ordering:
Polynomial interpretation [25]:

POL(U22(x1)) = 1 + x1   
POL(U31(x1)) = x1   
POL(__(x1, x2)) = x1 + x2   
POL(a) = 0   
POL(activate(x1)) = x1   
POL(e) = 0   
POL(i) = 2   
POL(isNeList(x1)) = 1 + x1   
POL(isQid(x1)) = x1   
POL(n____(x1, x2)) = x1 + x2   
POL(n__a) = 0   
POL(n__e) = 0   
POL(n__i) = 2   
POL(n__nil) = 0   
POL(n__o) = 0   
POL(n__u) = 0   
POL(nil) = 0   
POL(o) = 0   
POL(tt) = 0   
POL(u) = 0   




↳ QTRS
  ↳ RRRPoloQTRSProof
    ↳ QTRS
      ↳ RRRPoloQTRSProof
        ↳ QTRS
          ↳ RRRPoloQTRSProof
            ↳ QTRS
              ↳ RRRPoloQTRSProof
                ↳ QTRS
                  ↳ RRRPoloQTRSProof
QTRS
                      ↳ RRRPoloQTRSProof

Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
an__a
en__e
in__i
on__o
un__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X

Q is empty.

The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
an__a
en__e
in__i
on__o
un__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X

Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:

isQid(n__o) → tt
isQid(n__u) → tt
niln__nil
__(X1, X2) → n____(X1, X2)
en__e
in__i
on__o
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Used ordering:
Polynomial interpretation [25]:

POL(__(x1, x2)) = 1 + x1 + x2   
POL(a) = 2   
POL(activate(x1)) = 2 + x1   
POL(e) = 1   
POL(i) = 2   
POL(isQid(x1)) = 2 + x1   
POL(n____(x1, x2)) = x1 + x2   
POL(n__a) = 2   
POL(n__e) = 0   
POL(n__i) = 0   
POL(n__nil) = 0   
POL(n__o) = 1   
POL(n__u) = 0   
POL(nil) = 1   
POL(o) = 2   
POL(tt) = 1   
POL(u) = 0   




↳ QTRS
  ↳ RRRPoloQTRSProof
    ↳ QTRS
      ↳ RRRPoloQTRSProof
        ↳ QTRS
          ↳ RRRPoloQTRSProof
            ↳ QTRS
              ↳ RRRPoloQTRSProof
                ↳ QTRS
                  ↳ RRRPoloQTRSProof
                    ↳ QTRS
                      ↳ RRRPoloQTRSProof
QTRS
                          ↳ RRRPoloQTRSProof

Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
an__a
un__u
activate(n__i) → i

Q is empty.

The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:

__(__(X, Y), Z) → __(X, __(Y, Z))
an__a
un__u
activate(n__i) → i

Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:

__(__(X, Y), Z) → __(X, __(Y, Z))
an__a
un__u
activate(n__i) → i
Used ordering:
Polynomial interpretation [25]:

POL(__(x1, x2)) = 1 + 2·x1 + x2   
POL(a) = 2   
POL(activate(x1)) = 2 + 2·x1   
POL(i) = 1   
POL(n__a) = 1   
POL(n__i) = 2   
POL(n__u) = 1   
POL(u) = 2   




↳ QTRS
  ↳ RRRPoloQTRSProof
    ↳ QTRS
      ↳ RRRPoloQTRSProof
        ↳ QTRS
          ↳ RRRPoloQTRSProof
            ↳ QTRS
              ↳ RRRPoloQTRSProof
                ↳ QTRS
                  ↳ RRRPoloQTRSProof
                    ↳ QTRS
                      ↳ RRRPoloQTRSProof
                        ↳ QTRS
                          ↳ RRRPoloQTRSProof
QTRS
                              ↳ RisEmptyProof

Q restricted rewrite system:
R is empty.
Q is empty.

The TRS R is empty. Hence, termination is trivially proven.