Term Rewriting System R:
[x]
f(h(x)) -> f(i(x))
g(i(x)) -> g(h(x))
h(a) -> b
i(a) -> b

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

F(h(x)) -> F(i(x))
F(h(x)) -> I(x)
G(i(x)) -> G(h(x))
G(i(x)) -> H(x)

Furthermore, R contains two SCCs. 


   R
     ↳DPs
       →DP Problem 1
         ↳Narrowing Transformation
       →DP Problem 2
         ↳Nar


Dependency Pair:

F(h(x)) -> F(i(x))


Rules:


f(h(x)) -> f(i(x))
g(i(x)) -> g(h(x))
h(a) -> b
i(a) -> b


Strategy:

innermost




On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

F(h(x)) -> F(i(x))
one new Dependency Pair is created:

F(h(a)) -> F(b)

The transformation is resulting in no new DP problems. 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
       →DP Problem 2
         ↳Narrowing Transformation


Dependency Pair:

G(i(x)) -> G(h(x))


Rules:


f(h(x)) -> f(i(x))
g(i(x)) -> g(h(x))
h(a) -> b
i(a) -> b


Strategy:

innermost




On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

G(i(x)) -> G(h(x))
one new Dependency Pair is created:

G(i(a)) -> G(b)

The transformation is resulting in no new DP problems.


Innermost Termination of R successfully shown.
Duration:
0:00 minutes