Termination w.r.t. Q of the following Term Rewriting System could not be shown:
Q restricted rewrite system:
The TRS R consists of the following rules:
a(x1) → g(d(x1))
b(b(b(x1))) → c(d(c(x1)))
b(b(x1)) → a(g(g(x1)))
c(d(x1)) → g(g(x1))
g(g(g(x1))) → b(b(x1))
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
a(x1) → g(d(x1))
b(b(b(x1))) → c(d(c(x1)))
b(b(x1)) → a(g(g(x1)))
c(d(x1)) → g(g(x1))
g(g(g(x1))) → b(b(x1))
Q is empty.
Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
G(g(g(x1))) → B(x1)
B(b(x1)) → G(g(x1))
C(d(x1)) → G(x1)
B(b(b(x1))) → C(x1)
A(x1) → G(d(x1))
G(g(g(x1))) → B(b(x1))
B(b(b(x1))) → C(d(c(x1)))
C(d(x1)) → G(g(x1))
B(b(x1)) → G(x1)
B(b(x1)) → A(g(g(x1)))
The TRS R consists of the following rules:
a(x1) → g(d(x1))
b(b(b(x1))) → c(d(c(x1)))
b(b(x1)) → a(g(g(x1)))
c(d(x1)) → g(g(x1))
g(g(g(x1))) → b(b(x1))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
G(g(g(x1))) → B(x1)
B(b(x1)) → G(g(x1))
C(d(x1)) → G(x1)
B(b(b(x1))) → C(x1)
A(x1) → G(d(x1))
G(g(g(x1))) → B(b(x1))
B(b(b(x1))) → C(d(c(x1)))
C(d(x1)) → G(g(x1))
B(b(x1)) → G(x1)
B(b(x1)) → A(g(g(x1)))
The TRS R consists of the following rules:
a(x1) → g(d(x1))
b(b(b(x1))) → c(d(c(x1)))
b(b(x1)) → a(g(g(x1)))
c(d(x1)) → g(g(x1))
g(g(g(x1))) → b(b(x1))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
G(g(g(x1))) → B(x1)
B(b(x1)) → G(g(x1))
C(d(x1)) → G(x1)
B(b(b(x1))) → C(x1)
G(g(g(x1))) → B(b(x1))
B(b(b(x1))) → C(d(c(x1)))
B(b(x1)) → G(x1)
C(d(x1)) → G(g(x1))
The TRS R consists of the following rules:
a(x1) → g(d(x1))
b(b(b(x1))) → c(d(c(x1)))
b(b(x1)) → a(g(g(x1)))
c(d(x1)) → g(g(x1))
g(g(g(x1))) → b(b(x1))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.