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))
b(x1) → a(x1)
c(c(x1)) → d(f(x1))
d(d(x1)) → f(f(f(x1)))
d(x1) → b(x1)
f(f(x1)) → g(a(x1))
g(g(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(x1))
b(b(x1)) → c(d(x1))
b(x1) → a(x1)
c(c(x1)) → d(f(x1))
d(d(x1)) → f(f(f(x1)))
d(x1) → b(x1)
f(f(x1)) → g(a(x1))
g(g(x1)) → 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:
f_1=4045058649637888
c_1=5097748191012096
g_1=2696705674011328
a_1=5393411348022592
d_1=6145782749292032
b_1=5655461046052224
dummyConstant=1