Termination w.r.t. Q proof of /tmp/tmpSqj6Lo/2.60.trs

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:

f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))

Q is empty.

↳ QTRS

  ↳ RRRPoloQTRSProof

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

f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))

Q is empty.

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

f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))

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

f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))

Used ordering:
Polynomial interpretation [25]:

POL(a) = 0
POL(f(x₁)) = 2·x₁
POL(g(x₁, x₂)) = 2·x₁ + 2·x₂
POL(h(x₁, x₂)) = 2 + x₁ + x₂

↳ QTRS

  ↳ RRRPoloQTRSProof

    ↳ QTRS

      ↳ RisEmptyProof

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

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