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

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)
:'(+(x, y), z) -> :'(x, z)
:'(+(x, y), z) -> :'(y, z)
:'(z, +(x, f(y))) -> :'(g(z, y), +(x, a))

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


Rules:


:(:(x, y), z) -> :(x, :(y, z))
:(+(x, y), z) -> +(:(x, z), :(y, z))
:(z, +(x, f(y))) -> :(g(z, y), +(x, a))




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