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