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.