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)) → b(c(c(c(x1))))
b(c(x1)) → d(d(d(d(x1))))
a(x1) → d(c(d(x1)))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
c(d(d(x1))) → a(x1)
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(x1)) → b(c(c(c(x1))))
b(c(x1)) → d(d(d(d(x1))))
a(x1) → d(c(d(x1)))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
c(d(d(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 > d1
and weight map:
c_1=896
b_1=1472
d_1=592
a_1=2080
dummyConstant=1