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:
f(X, g(X), Y) → f(Y, Y, Y)
g(b) → c
b → c
The set Q consists of the following terms:
b
f(x0, g(x0), x1)
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(X, g(X), Y) → f(Y, Y, Y)
g(b) → c
b → c
The set Q consists of the following terms:
b
f(x0, g(x0), x1)
Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
F(X, g(X), Y) → F(Y, Y, Y)
The TRS R consists of the following rules:
f(X, g(X), Y) → f(Y, Y, Y)
g(b) → c
b → c
The set Q consists of the following terms:
b
f(x0, g(x0), x1)
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:
F(X, g(X), Y) → F(Y, Y, Y)
The TRS R consists of the following rules:
f(X, g(X), Y) → f(Y, Y, Y)
g(b) → c
b → c
The set Q consists of the following terms:
b
f(x0, g(x0), x1)
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 0 SCCs with 1 less node.