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(c(a(x1))) → a(b(x1))
b(b(b(x1))) → c(a(c(x1)))
c(d(x1)) → d(c(x1))
c(d(b(x1))) → d(c(c(x1)))
d(c(x1)) → b(b(b(x1)))
c(b(x1)) → d(a(x1))
d(b(c(x1))) → a(a(x1))
d(a(x1)) → b(x1)
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
b(c(a(x1))) → a(b(x1))
b(b(b(x1))) → c(a(c(x1)))
c(d(x1)) → d(c(x1))
c(d(b(x1))) → d(c(c(x1)))
d(c(x1)) → b(b(b(x1)))
c(b(x1)) → d(a(x1))
d(b(c(x1))) → a(a(x1))
d(a(x1)) → b(x1)
Q is empty.
We use [27] with the following order to prove termination.
Knuth-Bendix order [24] with precedence:
a1 > c1 > d1 > b1
a1 > dummyConstant
and weight map:
c_1=3
b_1=3
d_1=6
a_1=0
dummyConstant=1