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:

b(a(a(x1))) → a(b(c(x1)))
c(a(x1)) → a(c(x1))
b(c(a(x1))) → a(b(c(x1)))
c(b(x1)) → b(a(x1))
a(c(b(x1))) → c(b(a(x1)))

Q is empty.


↳ QTRS
  ↳ RRRPoloQTRSProof

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

b(a(a(x1))) → a(b(c(x1)))
c(a(x1)) → a(c(x1))
b(c(a(x1))) → a(b(c(x1)))
c(b(x1)) → b(a(x1))
a(c(b(x1))) → c(b(a(x1)))

Q is empty.

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

b(a(a(x1))) → a(b(c(x1)))
c(a(x1)) → a(c(x1))
b(c(a(x1))) → a(b(c(x1)))
c(b(x1)) → b(a(x1))
a(c(b(x1))) → c(b(a(x1)))

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(a(x1))) → a(b(c(x1)))
c(a(x1)) → a(c(x1))
b(c(a(x1))) → a(b(c(x1)))
a(c(b(x1))) → c(b(a(x1)))
Used ordering:
Polynomial interpretation [25]:

POL(a(x1)) = 1 + 2·x1   
POL(b(x1)) = 2 + 2·x1   
POL(c(x1)) = 2·x1   




↳ QTRS
  ↳ RRRPoloQTRSProof
    ↳ QTRS
      ↳ RRRPoloQTRSProof

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

c(b(x1)) → b(a(x1))

Q is empty.

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

c(b(x1)) → b(a(x1))

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

c(b(x1)) → b(a(x1))
Used ordering:
Polynomial interpretation [25]:

POL(a(x1)) = x1   
POL(b(x1)) = 1 + 2·x1   
POL(c(x1)) = 2 + 2·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.