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