Termination Proof using AProVE

Term Rewriting System R:
[x, y]
not(x) -> if(x, false, true)
and(x, y) -> if(x, y, false)
or(x, y) -> if(x, true, y)
implies(x, y) -> if(x, y, true)
=(x, x) -> true
=(x, y) -> if(x, y, not(y))
=(x, y) -> if(x, y, if(y, false, true))
if(true, x, y) -> x
if(false, x, y) -> y
if(x, x, if(x, false, true)) -> true

Termination of R to be shown.

     ↳Dependency Pair Analysis

R contains the following Dependency Pairs:

NOT(x) -> IF(x, false, true)
AND(x, y) -> IF(x, y, false)
OR(x, y) -> IF(x, true, y)
IMPLIES(x, y) -> IF(x, y, true)
='(x, y) -> IF(x, y, not(y))
='(x, y) -> NOT(y)
='(x, y) -> IF(x, y, if(y, false, true))
='(x, y) -> IF(y, false, true)

R contains no SCCs.

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