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:
a(x1) → b(b(x1))
a(b(b(x1))) → b(b(c(c(c(a(x1))))))
b(b(x1)) → c(c(c(x1)))
c(c(c(b(b(x1))))) → a(x1)
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(x1) → b(b(x1))
a(b(b(x1))) → b(b(c(c(c(a(x1))))))
b(b(x1)) → c(c(c(x1)))
c(c(c(b(b(x1))))) → a(x1)
Q is empty.
We use [27] with the following order to prove termination.
Knuth-Bendix order [24] with precedence:
c1 > a1 > b1
c1 > dummyConstant
and weight map:
c_1=0
b_1=1
a_1=2
dummyConstant=1