Term Rewriting System R:
[x, y, z]
cons(x, cons(y, z)) -> big
inf(x) -> cons(x, inf(s(x)))

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

INF(x) -> CONS(x, inf(s(x)))
INF(x) -> INF(s(x))

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Instantiation Transformation


Dependency Pair:

INF(x) -> INF(s(x))


Rules:


cons(x, cons(y, z)) -> big
inf(x) -> cons(x, inf(s(x)))





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

INF(x) -> INF(s(x))
one new Dependency Pair is created:

INF(s(x'')) -> INF(s(s(x'')))

The transformation is resulting in one new DP problem: 



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




The following remains to be proven:
Dependency Pair:

INF(s(x'')) -> INF(s(s(x'')))


Rules:


cons(x, cons(y, z)) -> big
inf(x) -> cons(x, inf(s(x)))




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