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:

g(b) → f(b)
f(a) → g(a)
b → a

Q is empty.


↳ QTRS
  ↳ RRRPoloQTRSProof

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

g(b) → f(b)
f(a) → g(a)
b → a

Q is empty.

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

g(b) → f(b)
f(a) → g(a)
b → 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:

b → a
Used ordering:
Polynomial interpretation [25]:

POL(a) = 1   
POL(b) = 2   
POL(f(x1)) = 2·x1   
POL(g(x1)) = 2·x1   




↳ QTRS
  ↳ RRRPoloQTRSProof
    ↳ QTRS
      ↳ RRRPoloQTRSProof

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

g(b) → f(b)
f(a) → g(a)

Q is empty.

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

g(b) → f(b)
f(a) → g(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:

g(b) → f(b)
f(a) → g(a)
Used ordering:
Polynomial interpretation [25]:

POL(a) = 2   
POL(b) = 0   
POL(f(x1)) = 2·x1   
POL(g(x1)) = 1 + x1   




↳ 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.