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

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

IMPLIES(not(x), or(y, z)) -> IMPLIES(y, or(x, z))
IMPLIES(x, or(y, z)) -> IMPLIES(x, z)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

IMPLIES(x, or(y, z)) -> IMPLIES(x, z)
IMPLIES(not(x), or(y, z)) -> IMPLIES(y, or(x, z))


Rules:


implies(not(x), y) -> or(x, y)
implies(not(x), or(y, z)) -> implies(y, or(x, z))
implies(x, or(y, z)) -> or(y, implies(x, z))




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