Term Rewriting System R:
[x, y]
f(g(x, y), f(y, y)) -> f(g(y, x), y)
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(g(x, y), f(y, y)) -> F(g(y, x), y)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Instantiation Transformation
Dependency Pair:
F(g(x, y), f(y, y)) -> F(g(y, x), y)
Rule:
f(g(x, y), f(y, y)) -> f(g(y, x), y)
Strategy:
innermost
On this DP problem, an Instantiation SCC transformation can be performed.
As a result of transforming the rule
F(g(x, y), f(y, y)) -> F(g(y, x), y)
one new Dependency Pair
is created:
F(g(f(y'', y''), y''), f(y'', y'')) -> F(g(y'', f(y'', y'')), y'')
The transformation is resulting in no new DP problems.
Innermost Termination of R successfully shown.
Duration:
0:00 minutes