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:
f(X, n__g(X), Y) → f(activate(Y), activate(Y), activate(Y))
g(b) → c
b → c
g(X) → n__g(X)
activate(n__g(X)) → g(X)
activate(X) → X
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(X, n__g(X), Y) → f(activate(Y), activate(Y), activate(Y))
g(b) → c
b → c
g(X) → n__g(X)
activate(n__g(X)) → g(X)
activate(X) → X
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:
F(X, n__g(X), Y) → ACTIVATE(Y)
F(X, n__g(X), Y) → F(activate(Y), activate(Y), activate(Y))
ACTIVATE(n__g(X)) → G(X)
The TRS R consists of the following rules:
f(X, n__g(X), Y) → f(activate(Y), activate(Y), activate(Y))
g(b) → c
b → c
g(X) → n__g(X)
activate(n__g(X)) → g(X)
activate(X) → X
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:
F(X, n__g(X), Y) → ACTIVATE(Y)
F(X, n__g(X), Y) → F(activate(Y), activate(Y), activate(Y))
ACTIVATE(n__g(X)) → G(X)
The TRS R consists of the following rules:
f(X, n__g(X), Y) → f(activate(Y), activate(Y), activate(Y))
g(b) → c
b → c
g(X) → n__g(X)
activate(n__g(X)) → g(X)
activate(X) → X
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:
F(X, n__g(X), Y) → F(activate(Y), activate(Y), activate(Y))
The TRS R consists of the following rules:
f(X, n__g(X), Y) → f(activate(Y), activate(Y), activate(Y))
g(b) → c
b → c
g(X) → n__g(X)
activate(n__g(X)) → g(X)
activate(X) → X
Q is empty.
We have to consider all minimal (P,Q,R)-chains.