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

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Forward Instantiation Transformation


Dependency Pair:

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


Rules:


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


Strategy:

innermost




On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule

*'(*(x, y), z) -> *'(y, z)
one new Dependency Pair is created:

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

The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳FwdInst
           →DP Problem 2
             ↳Remaining Obligation(s)




The following remains to be proven:
Dependency Pair:

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


Rules:


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


Strategy:

innermost



Innermost Termination of R could not be shown.
Duration:
0:00 minutes