Term Rewriting System R:
[x, y]
rev(a) -> a
rev(b) -> b
rev(++(x, y)) -> ++(rev(y), rev(x))
rev(++(x, x)) -> rev(x)

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC. 


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


Dependency Pairs:

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


Rules:


rev(a) -> a
rev(b) -> b
rev(++(x, y)) -> ++(rev(y), rev(x))
rev(++(x, x)) -> rev(x)





The following dependency pairs can be strictly oriented:

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


The following rules can be oriented:

rev(a) -> a
rev(b) -> b
rev(++(x, y)) -> ++(rev(y), rev(x))
rev(++(x, x)) -> rev(x)


Used ordering: Polynomial ordering with Polynomial interpretation:
  POL(rev(x1))=  x1  
  POL(REV(x1))=  1 + x1  
  POL(b)=  0  
  POL(++(x1, x2))=  1 + x1 + x2  
  POL(a)=  0  

resulting in one new DP problem.
Used Argument Filtering System:
REV(x1) -> REV(x1)
++(x1, x2) -> ++(x1, x2)
rev(x1) -> rev(x1)


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


Dependency Pair:


Rules:


rev(a) -> a
rev(b) -> b
rev(++(x, y)) -> ++(rev(y), rev(x))
rev(++(x, x)) -> rev(x)





Using the Dependency Graph resulted in no new DP problems.

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