Term Rewriting System R:
[X]
f(X, g(X)) -> f(1, g(X))
g(1) -> g(0)
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(X, g(X)) -> F(1, g(X))
G(1) -> G(0)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Instantiation Transformation
Dependency Pair:
F(X, g(X)) -> F(1, g(X))
Rules:
f(X, g(X)) -> f(1, g(X))
g(1) -> g(0)
On this DP problem, an Instantiation SCC transformation can be performed.
As a result of transforming the rule
F(X, g(X)) -> F(1, g(X))
one new Dependency Pair
is created:
F(1, g(1)) -> F(1, g(1))
The transformation is resulting in one new DP problem:
R
↳DPs
→DP Problem 1
↳Inst
→DP Problem 2
↳Remaining Obligation(s)
The following remains to be proven:
Dependency Pair:
F(1, g(1)) -> F(1, g(1))
Rules:
f(X, g(X)) -> f(1, g(X))
g(1) -> g(0)
Termination of R could not be shown.
Duration:
0:00 minutes