Term Rewriting System R:
[X, Y]
f(0, 1, X) -> f(g(X, X), X, X)
g(X, Y) -> X
g(X, Y) -> Y
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(0, 1, X) -> F(g(X, X), X, X)
F(0, 1, X) -> G(X, X)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Usable Rules (Innermost)
Dependency Pair:
F(0, 1, X) -> F(g(X, X), X, X)
Rules:
f(0, 1, X) -> f(g(X, X), X, X)
g(X, Y) -> X
g(X, Y) -> Y
Strategy:
innermost
As we are in the innermost case, we can delete all 1 non-usable-rules.
R
↳DPs
→DP Problem 1
↳UsableRules
→DP Problem 2
↳Narrowing Transformation
Dependency Pair:
F(0, 1, X) -> F(g(X, X), X, X)
Rules:
g(X, Y) -> Y
g(X, Y) -> X
Strategy:
innermost
On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule
F(0, 1, X) -> F(g(X, X), X, X)
one new Dependency Pair
is created:
F(0, 1, X'') -> F(X'', X'', X'')
The transformation is resulting in no new DP problems.
Innermost Termination of R successfully shown.
Duration:
0:00 minutes