Term Rewriting System R:
[x, y, z]
.(.(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), 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)


Rule:


.(.(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'')


Rule:


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


Strategy:

innermost



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