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Gymhgy
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C# (Visual C# Interactive Compiler), 252242 bytes

a=>b=>a==b?a+" 2":((d=a.LastIndexOfAny(z=((j=new[]{a,b}.Count(x=>"- ".Any(x.Contains)))>0?"- ":"aeiouAEIOU").ToArray()))<0?a:a.SubstringRemove(0,d+1))+b.SubstringRemove(j>0|new0,j+new Random().Next()<1>0?Math.Max(0,bd=b.IndexOfAny(z)-j%2+1)<0?0:d:b.LastIndexOfAny(z));dynamic z,d,j;

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C# (Visual C# Interactive Compiler), 252 bytes

a=>b=>a==b?a+" 2":((d=a.LastIndexOfAny(z=((j=new[]{a,b}.Count(x=>"- ".Any(x.Contains)))>0?"- ":"aeiouAEIOU").ToArray()))<0?a:a.Substring(0,d+1))+b.Substring(j>0|new Random().Next()<1?Math.Max(0,b.IndexOfAny(z)-j%2+1):b.LastIndexOfAny(z));dynamic z,d,j;

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C# (Visual C# Interactive Compiler), 242 bytes

a=>b=>a==b?a+" 2":((d=a.LastIndexOfAny(z=((j=new[]{a,b}.Count(x=>"- ".Any(x.Contains)))>0?"- ":"aeiouAEIOU").ToArray()))<0?a:a.Remove(d+1))+b.Remove(0,j+new Random().Next()>0?(d=b.IndexOfAny(z)-j%2+1)<0?0:d:b.LastIndexOfAny(z));dynamic z,d,j;

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Gymhgy
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C# (Visual C# Interactive Compiler), 276252 bytes

a=>b=>a==b?a+" 2":a.Substring(0,(d=a.LastIndexOfAny(z=((j="j=new[]{a,b}.Count(x=>"- ".Any((a+b)x.Contains)))>0?"- ":"aeiouAEIOU").ToArray()))<0?a.Length:a.Substring(0,d+1))+b.Substring(j|newj>0|new Random().Next()<1?Math.Max(0,b.IndexOfAny(z)-new[]{a,b}.Count(x=>"- ".Any(x.Contains))%2+1j%2+1):b.LastIndexOfAny(z));dynamic z,d,j;

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C# (Visual C# Interactive Compiler), 276 bytes

a=>b=>a==b?a+" 2":a.Substring(0,(d=a.LastIndexOfAny(z=((j="- ".Any((a+b).Contains))?"- ":"aeiouAEIOU").ToArray()))<0?a.Length:d+1)+b.Substring(j|new Random().Next()<1?Math.Max(0,b.IndexOfAny(z)-new[]{a,b}.Count(x=>"- ".Any(x.Contains))%2+1):b.LastIndexOfAny(z));dynamic z,d,j;

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C# (Visual C# Interactive Compiler), 252 bytes

a=>b=>a==b?a+" 2":((d=a.LastIndexOfAny(z=((j=new[]{a,b}.Count(x=>"- ".Any(x.Contains)))>0?"- ":"aeiouAEIOU").ToArray()))<0?a:a.Substring(0,d+1))+b.Substring(j>0|new Random().Next()<1?Math.Max(0,b.IndexOfAny(z)-j%2+1):b.LastIndexOfAny(z));dynamic z,d,j;

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Gymhgy
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C# (Visual C# Interactive Compiler), 283276 bytes

a=>b=>a==b?a+" 2":a.Substring(0,(d=a.LastIndexOfAny(z=((j="- ".Any((a+b).Contains))?"- ":"aeiouAEIOU").ToArray()))<0?a.Length:d+1)+b.Substring(j|new Random().Next()<1?Math.Max(0,b.IndexOfAny(z)-new[]{a,b}.Count(x=>"- ".Any(x.Contains))%2+1):b.LastIndexOfAny(z));char[]z;int d;bool;dynamic z,d,j;

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C# (Visual C# Interactive Compiler), 283 bytes

a=>b=>a==b?a+" 2":a.Substring(0,(d=a.LastIndexOfAny(z=((j="- ".Any((a+b).Contains))?"- ":"aeiouAEIOU").ToArray()))<0?a.Length:d+1)+b.Substring(j|new Random().Next()<1?Math.Max(0,b.IndexOfAny(z)-new[]{a,b}.Count(x=>"- ".Any(x.Contains))%2+1):b.LastIndexOfAny(z));char[]z;int d;bool j;

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C# (Visual C# Interactive Compiler), 276 bytes

a=>b=>a==b?a+" 2":a.Substring(0,(d=a.LastIndexOfAny(z=((j="- ".Any((a+b).Contains))?"- ":"aeiouAEIOU").ToArray()))<0?a.Length:d+1)+b.Substring(j|new Random().Next()<1?Math.Max(0,b.IndexOfAny(z)-new[]{a,b}.Count(x=>"- ".Any(x.Contains))%2+1):b.LastIndexOfAny(z));dynamic z,d,j;

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Gymhgy
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Gymhgy
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