Term Rewriting System R:
[x, y]
or(x, x) -> x
and(x, x) -> x
not(not(x)) -> x
not(and(x, y)) -> or(not(x), not(y))
not(or(x, y)) -> and(not(x), not(y))

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

NOT(and(x, y)) -> OR(not(x), not(y))
NOT(and(x, y)) -> NOT(x)
NOT(and(x, y)) -> NOT(y)
NOT(or(x, y)) -> AND(not(x), not(y))
NOT(or(x, y)) -> NOT(x)
NOT(or(x, y)) -> NOT(y)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

NOT(or(x, y)) -> NOT(y)
NOT(or(x, y)) -> NOT(x)
NOT(and(x, y)) -> NOT(y)
NOT(and(x, y)) -> NOT(x)


Rules:


or(x, x) -> x
and(x, x) -> x
not(not(x)) -> x
not(and(x, y)) -> or(not(x), not(y))
not(or(x, y)) -> and(not(x), not(y))




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