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

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

+'(-(x, y), z) -> -'(+(x, z), y)
+'(-(x, y), z) -> +'(x, z)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Polynomial Ordering


Dependency Pair:

+'(-(x, y), z) -> +'(x, z)


Rules:


+(-(x, y), z) -> -(+(x, z), y)
-(+(x, y), y) -> x


Strategy:

innermost




The following dependency pair can be strictly oriented:

+'(-(x, y), z) -> +'(x, z)


There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:
  POL(-(x1, x2))=  1 + x1  
  POL(+'(x1, x2))=  x1  

resulting in one new DP problem. 



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


Dependency Pair:


Rules:


+(-(x, y), z) -> -(+(x, z), y)
-(+(x, y), y) -> x


Strategy:

innermost




Using the Dependency Graph resulted in no new DP problems.

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