Term Rewriting System R:
[x, y]
f(g(x), y, y) -> g(f(x, x, y))

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

F(g(x), y, y) -> F(x, x, y)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Argument Filtering and Ordering


Dependency Pair:

F(g(x), y, y) -> F(x, x, y)


Rule:


f(g(x), y, y) -> g(f(x, x, y))





The following dependency pair can be strictly oriented:

F(g(x), y, y) -> F(x, x, y)


The following rule can be oriented:

f(g(x), y, y) -> g(f(x, x, y))


Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:
f > g

resulting in one new DP problem.
Used Argument Filtering System:
F(x1, x2, x3) -> F(x1, x2, x3)
g(x1) -> g(x1)
f(x1, x2, x3) -> f(x1, x2, x3)


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


Dependency Pair:


Rule:


f(g(x), y, y) -> g(f(x, x, y))





Using the Dependency Graph resulted in no new DP problems.

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