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(x1))
b(b(x1)) → c(d(x1))
c(c(x1)) → d(d(d(x1)))
d(c(x1)) → b(f(x1))
d(d(d(x1))) → a(c(x1))
f(f(x1)) → f(b(x1))
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(x1)) → b(c(x1))
b(b(x1)) → c(d(x1))
c(c(x1)) → d(d(d(x1)))
d(c(x1)) → b(f(x1))
d(d(d(x1))) → a(c(x1))
f(f(x1)) → f(b(x1))
Q is empty.
We use [27] with the following order to prove termination.
Knuth-Bendix order [24] with precedence:
f1 > b1 > c1
d1 > b1 > c1
and weight map:
c_1=1600
f_1=1312
b_1=1312
d_1=1024
a_1=1464
dummyConstant=1