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

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

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


Rules:


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


Strategy:

innermost



Innermost Termination of R could not be shown.
Duration:
0:01 minutes