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

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

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

Furthermore, R contains one SCC. 


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




The following remains to be proven:
Dependency Pairs:

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


Rules:


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


Strategy:

innermost



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