Term Rewriting System R:
[]
f(0) -> cons(0)
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

F(s(0)) -> F(p(s(0)))
F(s(0)) -> P(s(0))

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Polynomial Ordering


Dependency Pair:

F(s(0)) -> F(p(s(0)))


Rules:


f(0) -> cons(0)
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0





The following dependency pair can be strictly oriented:

F(s(0)) -> F(p(s(0)))


Additionally, the following usable rule w.r.t. to the implicit AFS can be oriented:

p(s(0)) -> 0


Used ordering: Polynomial ordering with Polynomial interpretation:
  POL(0)=  0  
  POL(s(x1))=  1  
  POL(F(x1))=  x1  
  POL(p(x1))=  0  

resulting in one new DP problem.



   R
DPs
       →DP Problem 1
Polo
           →DP Problem 2
Dependency Graph


Dependency Pair:


Rules:


f(0) -> cons(0)
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0





Using the Dependency Graph resulted in no new DP problems.

Termination of R successfully shown.
Duration:
0:00 minutes