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, ?Q s (x)?Q s (y) ? Border(x, y) 2) ¬min(x)?¬min(y)?Border(x?1, y?1)?Q s (x)? Q s (y) ? Border(x, y), for all s ? ?, min(x)?¬min(y)

, Processing the contradiction clauses

, min(x)?¬min(y)?Q s (x)?Q s (y) ?

, ¬min(x)?¬min(y)?Border(x?1, y?1)?Q s (x)? Q s (y) ? Border(x, y), for all s ? ?

, R ? (x, y) is never used and therefore can be withdraw for more clarity. 2) Processing the input

, Q s (x) ? min(y) ? W x s

, Q s (y) ? min(x) ? W y s

, ¬min(y) ? W x s (x, y ? 1) ? W x s

?. W-y-s,

, min(x) ? ¬min(y) ? W x s

, Restriction of computation atoms to R(x ? 1, y)

, Q s (x) ? min(y) ? W x s

, Q s (y) ? min(x) ? W y s

, ¬min(y) ? W x s (x, y ? 1) ? W x s

?. W-y-s,

, min(x) ? ¬min(y) ? W x s

, Q s (x) ? min(y) ? W x s

, Q s (y) ? min(x) ? W y s

, min(x) ? min(y) ? R min(x)

, ¬min(y) ? W x s (x, y ? 1) ? W x s

?. W-y-s,

, ¬min(y) ? R min(x) (x, y ? 1) ? R min(x

, R min(x) (x, y) ? ¬min(y) ? W x s

, ¬min(x) ? ¬min(y) ? Border y?1 (x ? 1, y) ? W x s

R. Max,