Termination w.r.t. Q proof of /tmp/tmpBWAOOx/PALINDROME_nokinds-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) → 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, n____(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
nil → n__nil
__(X1, X2) → n____(X1, X2)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(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, n____(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
nil → n__nil
__(X1, X2) → n____(X1, X2)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(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, n____(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
nil → n__nil
__(X1, X2) → n____(X1, X2)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(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
U21(tt, V2) → U22(isList(activate(V2)))
U22(tt) → tt
U41(tt, V2) → U42(isNeList(activate(V2)))
U42(tt) → tt
U51(tt, V2) → U52(isList(activate(V2)))
U71(tt, P) → U72(isPal(activate(P)))
U72(tt) → tt

Used ordering:
Polynomial interpretation [25]:

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

↳ 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
U31(tt) → tt
U52(tt) → tt
U61(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, n____(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
nil → n__nil
__(X1, X2) → n____(X1, X2)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(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
U31(tt) → tt
U52(tt) → tt
U61(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, n____(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
nil → n__nil
__(X1, X2) → n____(X1, X2)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(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:

U81(tt) → tt
isPal(V) → U81(isNePal(activate(V)))
isPal(n__nil) → tt
isQid(n__a) → tt

Used ordering:
Polynomial interpretation [25]:

POL(U11(x₁)) = x₁
POL(U21(x₁, x₂)) = 2·x₁ + 2·x₂
POL(U31(x₁)) = 2·x₁
POL(U41(x₁, x₂)) = 2·x₁ + 2·x₂
POL(U51(x₁, x₂)) = x₁ + 2·x₂
POL(U52(x₁)) = 2·x₁
POL(U61(x₁)) = x₁
POL(U71(x₁, x₂)) = x₁ + 2·x₂
POL(U81(x₁)) = 1 + x₁
POL(__(x₁, x₂)) = 2·x₁ + x₂
POL(a) = 1
POL(activate(x₁)) = x₁
POL(e) = 0
POL(i) = 0
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) = 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

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

__(__(X, Y), Z) → __(X, __(Y, Z))
U11(tt) → tt
U31(tt) → tt
U52(tt) → tt
U61(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, n____(P, I))) → U71(isQid(activate(I)), activate(P))
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(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
U31(tt) → tt
U52(tt) → tt
U61(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, n____(P, I))) → U71(isQid(activate(I)), activate(P))
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(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, Y), Z) → __(X, __(Y, Z))
isList(V) → U11(isNeList(activate(V)))
isList(n__nil) → tt
isList(n____(V1, V2)) → U21(isList(activate(V1)), activate(V2))
isNeList(n____(V1, V2)) → U41(isList(activate(V1)), activate(V2))
isNeList(n____(V1, V2)) → U51(isNeList(activate(V1)), activate(V2))
isNePal(n____(I, n____(P, I))) → U71(isQid(activate(I)), activate(P))

Used ordering:
Polynomial interpretation [25]:

POL(U11(x₁)) = 2·x₁
POL(U21(x₁, x₂)) = 2 + 2·x₁ + x₂
POL(U31(x₁)) = x₁
POL(U41(x₁, x₂)) = x₁ + x₂
POL(U51(x₁, x₂)) = 1 + 2·x₁ + x₂
POL(U52(x₁)) = 2·x₁
POL(U61(x₁)) = x₁
POL(U71(x₁, x₂)) = x₁ + 2·x₂
POL(__(x₁, x₂)) = 2 + 2·x₁ + x₂
POL(a) = 0
POL(activate(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(isList(x₁)) = 1 + 2·x₁
POL(isNeList(x₁)) = x₁
POL(isNePal(x₁)) = x₁
POL(isQid(x₁)) = x₁
POL(n____(x₁, x₂)) = 2 + 2·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

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

U11(tt) → tt
U31(tt) → tt
U52(tt) → tt
U61(tt) → tt
isNeList(V) → U31(isQid(activate(V)))
isNePal(V) → U61(isQid(activate(V)))
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(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:

U11(tt) → tt
U31(tt) → tt
U52(tt) → tt
U61(tt) → tt
isNeList(V) → U31(isQid(activate(V)))
isNePal(V) → U61(isQid(activate(V)))
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(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
U52(tt) → tt
isQid(n__i) → tt
isQid(n__u) → tt
nil → n__nil
e → n__e
o → n__o
activate(n__nil) → nil
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__u) → u
activate(X) → X

Used ordering:
Polynomial interpretation [25]:

POL(U11(x₁)) = 1 + 2·x₁
POL(U31(x₁)) = x₁
POL(U52(x₁)) = 1 + 2·x₁
POL(U61(x₁)) = x₁
POL(__(x₁, x₂)) = 2 + x₁ + x₂
POL(a) = 2
POL(activate(x₁)) = 2 + 2·x₁
POL(e) = 1
POL(i) = 2
POL(isNeList(x₁)) = 2 + 2·x₁
POL(isNePal(x₁)) = 2 + 2·x₁
POL(isQid(x₁)) = x₁
POL(n____(x₁, x₂)) = 2 + x₁ + x₂
POL(n__a) = 2
POL(n__e) = 0
POL(n__i) = 2
POL(n__nil) = 0
POL(n__o) = 0
POL(n__u) = 1
POL(nil) = 1
POL(o) = 2
POL(tt) = 0
POL(u) = 1

↳ QTRS

  ↳ RRRPoloQTRSProof

    ↳ QTRS

      ↳ RRRPoloQTRSProof

        ↳ QTRS

          ↳ RRRPoloQTRSProof

            ↳ QTRS

              ↳ RRRPoloQTRSProof

                ↳ QTRS

                  ↳ RRRPoloQTRSProof

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

U31(tt) → tt
U61(tt) → tt
isNeList(V) → U31(isQid(activate(V)))
isNePal(V) → U61(isQid(activate(V)))
isQid(n__e) → tt
isQid(n__o) → tt
__(X1, X2) → n____(X1, X2)
a → n__a
i → n__i
u → n__u
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__o) → o

Q is empty.

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

U31(tt) → tt
U61(tt) → tt
isNeList(V) → U31(isQid(activate(V)))
isNePal(V) → U61(isQid(activate(V)))
isQid(n__e) → tt
isQid(n__o) → tt
__(X1, X2) → n____(X1, X2)
a → n__a
i → n__i
u → n__u
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__o) → o

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

U31(tt) → tt
isNePal(V) → U61(isQid(activate(V)))
isQid(n__e) → tt
isQid(n__o) → tt
a → n__a
i → n__i
u → n__u

Used ordering:
Polynomial interpretation [25]:

POL(U31(x₁)) = 1 + x₁
POL(U61(x₁)) = x₁
POL(__(x₁, x₂)) = x₁ + x₂
POL(a) = 1
POL(activate(x₁)) = x₁
POL(i) = 2
POL(isNeList(x₁)) = 2 + 2·x₁
POL(isNePal(x₁)) = 2 + 2·x₁
POL(isQid(x₁)) = 1 + x₁
POL(n____(x₁, x₂)) = x₁ + x₂
POL(n__a) = 0
POL(n__e) = 0
POL(n__i) = 1
POL(n__o) = 0
POL(n__u) = 1
POL(o) = 0
POL(tt) = 0
POL(u) = 2

↳ QTRS

  ↳ RRRPoloQTRSProof

    ↳ QTRS

      ↳ RRRPoloQTRSProof

        ↳ QTRS

          ↳ RRRPoloQTRSProof

            ↳ QTRS

              ↳ RRRPoloQTRSProof

                ↳ QTRS

                  ↳ RRRPoloQTRSProof

                    ↳ QTRS

                      ↳ RRRPoloQTRSProof

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

U61(tt) → tt
isNeList(V) → U31(isQid(activate(V)))
__(X1, X2) → n____(X1, X2)
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__o) → o

Q is empty.

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

U61(tt) → tt
isNeList(V) → U31(isQid(activate(V)))
__(X1, X2) → n____(X1, X2)
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__o) → o

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

U61(tt) → tt
isNeList(V) → U31(isQid(activate(V)))
activate(n__o) → o

Used ordering:
Polynomial interpretation [25]:

POL(U31(x₁)) = x₁
POL(U61(x₁)) = 2 + 2·x₁
POL(__(x₁, x₂)) = 2·x₁ + 2·x₂
POL(activate(x₁)) = x₁
POL(isNeList(x₁)) = 2 + 2·x₁
POL(isQid(x₁)) = x₁
POL(n____(x₁, x₂)) = 2·x₁ + 2·x₂
POL(n__o) = 2
POL(o) = 1
POL(tt) = 1

↳ 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:

__(X1, X2) → n____(X1, X2)
activate(n____(X1, X2)) → __(activate(X1), activate(X2))

Q is empty.

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

__(X1, X2) → n____(X1, X2)
activate(n____(X1, X2)) → __(activate(X1), activate(X2))

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

activate(n____(X1, X2)) → __(activate(X1), activate(X2))

Used ordering:
Polynomial interpretation [25]:

POL(__(x₁, x₂)) = 1 + 2·x₁ + 2·x₂
POL(activate(x₁)) = 2·x₁
POL(n____(x₁, x₂)) = 1 + 2·x₁ + 2·x₂

↳ QTRS

  ↳ RRRPoloQTRSProof

    ↳ 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:

__(X1, X2) → n____(X1, X2)

Q is empty.

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

__(X1, X2) → n____(X1, X2)

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

__(X1, X2) → n____(X1, X2)

Used ordering:
Polynomial interpretation [25]:

POL(__(x₁, x₂)) = 2 + 2·x₁ + 2·x₂
POL(n____(x₁, x₂)) = 1 + x₁ + x₂

↳ QTRS

  ↳ RRRPoloQTRSProof

    ↳ 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.