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(a(a(x1)))) → b(b(b(b(b(b(x1))))))
b(b(b(b(x1)))) → c(c(c(c(c(c(x1))))))
c(c(c(c(x1)))) → d(d(d(d(d(d(x1))))))
b(b(x1)) → d(d(d(d(x1))))
c(c(d(d(d(d(x1)))))) → a(a(x1))
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(a(a(a(x1)))) → b(b(b(b(b(b(x1))))))
b(b(b(b(x1)))) → c(c(c(c(c(c(x1))))))
c(c(c(c(x1)))) → d(d(d(d(d(d(x1))))))
b(b(x1)) → d(d(d(d(x1))))
c(c(d(d(d(d(x1)))))) → a(a(x1))
Q is empty.
We use [27] with the following order to prove termination.
Knuth-Bendix order [24] with precedence:trivial
and weight map:
c_1=5536
b_1=8368
d_1=3520
a_1=12568
dummyConstant=1