Termination w.r.t. Q proof of /tmp/tmp_Ifk3E/PALINDROME_nosorts-noand

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) → U12(tt)
U12(tt) → tt
isNePal(__(I, __(P, I))) → U11(tt)
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) → U12(tt)
U12(tt) → tt
isNePal(__(I, __(P, I))) → U11(tt)
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) → U12(tt)
U12(tt) → tt
isNePal(__(I, __(P, I))) → U11(tt)
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
activate(X) → X

Used ordering:
Polynomial interpretation [25]:

POL(U11(x₁)) = 2·x₁
POL(U12(x₁)) = x₁
POL(__(x₁, x₂)) = x₁ + x₂
POL(activate(x₁)) = 2 + x₁
POL(isNePal(x₁)) = 2·x₁
POL(nil) = 1
POL(tt) = 0

↳ QTRS

  ↳ RRRPoloQTRSProof

    ↳ QTRS

      ↳ RRRPoloQTRSProof

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

__(__(X, Y), Z) → __(X, __(Y, Z))
U11(tt) → U12(tt)
U12(tt) → tt
isNePal(__(I, __(P, I))) → U11(tt)

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) → U12(tt)
U12(tt) → tt
isNePal(__(I, __(P, I))) → U11(tt)

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) → U12(tt)

Used ordering:
Polynomial interpretation [25]:

POL(U11(x₁)) = 1 + 2·x₁
POL(U12(x₁)) = 2·x₁
POL(__(x₁, x₂)) = 2·x₁ + x₂
POL(isNePal(x₁)) = 1 + 2·x₁
POL(tt) = 0

↳ QTRS

  ↳ RRRPoloQTRSProof

    ↳ QTRS

      ↳ RRRPoloQTRSProof

        ↳ QTRS

          ↳ RRRPoloQTRSProof

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

__(__(X, Y), Z) → __(X, __(Y, Z))
U12(tt) → tt
isNePal(__(I, __(P, I))) → U11(tt)

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))
U12(tt) → tt
isNePal(__(I, __(P, I))) → U11(tt)

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))
U12(tt) → tt
isNePal(__(I, __(P, I))) → U11(tt)

Used ordering:
Polynomial interpretation [25]:

POL(U11(x₁)) = 1 + 2·x₁
POL(U12(x₁)) = 1 + 2·x₁
POL(__(x₁, x₂)) = 2 + 2·x₁ + x₂
POL(isNePal(x₁)) = 2·x₁
POL(tt) = 2

↳ 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.