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

Innermost Termination of R to be shown.

Dependency Pair Analysis

R contains the following Dependency Pairs:

IMPLIES(false, y) -> NOT(false)
IMPLIES(x, false) -> NOT(x)
IMPLIES(not(x), not(y)) -> IMPLIES(y, and(x, y))
IMPLIES(not(x), not(y)) -> AND(x, y)

R contains no SCCs.

Innermost Termination of R successfully shown.
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