Term Rewriting System R:
[x]
s1(s1(s0(s0(x)))) -> s0(s0(s0(s1(s1(s1(x))))))

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

S1(s1(s0(s0(x)))) -> S1(s1(s1(x)))
S1(s1(s0(s0(x)))) -> S1(s1(x))
S1(s1(s0(s0(x)))) -> S1(x)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Narrowing Transformation


Dependency Pairs:

S1(s1(s0(s0(x)))) -> S1(x)
S1(s1(s0(s0(x)))) -> S1(s1(x))
S1(s1(s0(s0(x)))) -> S1(s1(s1(x)))


Rule:


s1(s1(s0(s0(x)))) -> s0(s0(s0(s1(s1(s1(x))))))





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

S1(s1(s0(s0(x)))) -> S1(s1(s1(x)))
two new Dependency Pairs are created:

S1(s1(s0(s0(s0(s0(x'')))))) -> S1(s0(s0(s0(s1(s1(s1(x'')))))))
S1(s1(s0(s0(s1(s0(s0(x''))))))) -> S1(s1(s0(s0(s0(s1(s1(s1(x''))))))))

The transformation is resulting in one new DP problem:



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




The following remains to be proven:
Dependency Pairs:

S1(s1(s0(s0(s1(s0(s0(x''))))))) -> S1(s1(s0(s0(s0(s1(s1(s1(x''))))))))
S1(s1(s0(s0(x)))) -> S1(s1(x))
S1(s1(s0(s0(x)))) -> S1(x)


Rule:


s1(s1(s0(s0(x)))) -> s0(s0(s0(s1(s1(s1(x))))))




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