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Informally but clearly describe counter machines that accept the following languages. In each case, use as few counters as possible,but not more than two counters.

  1. $\left\{0^{n}1^{m} \mid n\geq m\geq 1\right\}.$
  2. $\left\{0^{n}1^{m} \mid m\geq n\geq 1\right\}.$
  3. $\left\{a^{i}b^{j}c^{k} \mid i=j \text{or} i=k\right\}.$
  4. $\left\{a^{i}b^{j}c^{k} \mid  i=j \  \text{or} \ i=k \ \text{or}\ j=k\right\}.$  
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