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

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

-'(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -'(-(x, y), -(x, y))
-'(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -'(x, y)

Furthermore, R contains one SCC. 


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


Dependency Pairs:

-'(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -'(x, y)
-'(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -'(-(x, y), -(x, y))


Rule:


-(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -(-(x, y), -(x, y))


Strategy:

innermost




The following dependency pairs can be strictly oriented:

-'(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -'(x, y)
-'(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -'(-(x, y), -(x, y))


The following usable rule for innermost can be oriented:

-(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -(-(x, y), -(x, y))


Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System:
-'(x1, x2) -> x1
-(x1, x2) -> x1
neg(x1) -> neg(x1)


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


Dependency Pair:


Rule:


-(-(neg(x), neg(x)), -(neg(y), neg(y))) -> -(-(x, y), -(x, y))


Strategy:

innermost




Using the Dependency Graph resulted in no new DP problems.

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