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