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(a(x1)) → d(c(x1))
a(b(x1)) → c(c(c(x1)))
b(b(x1)) → a(c(c(x1)))
c(c(x1)) → b(x1)
c(d(x1)) → a(a(x1))
d(d(x1)) → b(a(c(x1)))
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(x1)) → d(c(x1))
a(b(x1)) → c(c(c(x1)))
b(b(x1)) → a(c(c(x1)))
c(c(x1)) → b(x1)
c(d(x1)) → a(a(x1))
d(d(x1)) → b(a(c(x1)))
Q is empty.
We use [27] with the following order to prove termination.
Knuth-Bendix order [24] with precedence:
c1 > a1 > d1
and weight map:
c_1=46980
d_1=108540
b_1=92160
a_1=77760
dummyConstant=1