Term Rewriting System R:
[x]
a(b(x)) -> b(a(x))
a(c(x)) -> x

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

A(b(x)) -> A(x)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Argument Filtering and Ordering


Dependency Pair:

A(b(x)) -> A(x)


Rules:


a(b(x)) -> b(a(x))
a(c(x)) -> x





The following dependency pair can be strictly oriented:

A(b(x)) -> A(x)


The following rules can be oriented:

a(b(x)) -> b(a(x))
a(c(x)) -> x


Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System:
A(x1) -> A(x1)
b(x1) -> b(x1)
a(x1) -> x1
c(x1) -> c(x1)


   R
DPs
       →DP Problem 1
AFS
           →DP Problem 2
Dependency Graph


Dependency Pair:


Rules:


a(b(x)) -> b(a(x))
a(c(x)) -> x





Using the Dependency Graph resulted in no new DP problems.

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