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Say that I have the following table:

{{4.95455, 10.8, 0., 0.02}, {3.43939, 7.46667, 0., 0.03}, {2.68182,5.8, 0., 0.04}, 
{2.22727, 4.8, 0., 0.05},{0.3,08,0.1,0.2},{0.5,1,0.2,0.4},{0.564555, -10.3617, 0.99, 0.94}}

Now I want to remove every row in which: a) the first two elements of each row are above 1, and b) the second element of each row is lower than the first element of each row. I tried to search for a solution but the ones that I find are always about lists and/or removing elements that match particular values (and not conditions). Following these conditions, I would get:

{{0.3,08,0.1,0.2},{0.5,1,0.2,0.4}}
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Select[Min[#[[;; 2]]] <= 1 && #[[2]] >= #[[1]] &]@list
 {{0.3, 8, 0.1, 0.2}, {0.5, 1, 0.2, 0.4}}

or

DeleteCases[{a_, b_, __} /; Min[{a, b}] > 1 || b < a]@list
 {{0.3, 8, 0.1, 0.2}, {0.5, 1, 0.2, 0.4}}
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