Compensate loss of transitivity

We only have transitivity between givens or between implicits. To cope with that

 - We tank first all implicits, giving a best implicit search result.
 - Then we rank all givens startign with the implicit result. If there is
   a given that is better than the best implicit, the best given will be chosen.
   Otherwise we will stick with the best implicit.

compiler/src/dotty/tools/dotc/typer/Implicits.scala

@@ -1381,8 +1381,6 @@ trait Implicits:
       def disambiguate(alt1: SearchResult, alt2: SearchSuccess) = alt1 match
         case alt1: SearchSuccess =>
           var diff = compareAlternatives(alt1, alt2, disambiguate = true)
-          assert(diff <= 0 || isWarnPriorityChangeVersion(Feature.sourceVersion))
-            // diff > 0 candidates should already have been eliminated in `rank`
           if diff == 0 && alt1.ref =:= alt2.ref then
             diff = 1 // See i12951 for a test where this happens
           else if diff == 0 && alt2.isExtension then
@@ -1622,7 +1620,21 @@ trait Implicits:
             validateOrdering(ord)
             throw ex
 
-      val result = rank(sort(eligible), NoMatchingImplicitsFailure, Nil)
+      val sorted = sort(eligible)
+      val result = sorted match
+        case first :: rest =>
+          val firstIsImplicit = first.ref.symbol.is(Implicit)
+          if rest.exists(_.ref.symbol.is(Implicit) != firstIsImplicit) then
+            // Mixture of implicits and givens
+            // Rank implicits first, then, if there is a given that it better than the best implicit(s)
+            // switch over to givens.
+            val (sortedImplicits, sortedGivens) = sorted.partition(_.ref.symbol.is(Implicit))
+            val implicitResult = rank(sortedImplicits, NoMatchingImplicitsFailure, Nil)
+            rank(sortedGivens, implicitResult, Nil)
+          else
+            rank(sorted, NoMatchingImplicitsFailure, Nil)
+        case _ =>
+          NoMatchingImplicitsFailure
 
       // Issue all priority change warnings that can affect the result
       val shownWarnings = priorityChangeWarnings.toList.collect:

tests/pos/given-owner-disambiguate.scala

@@ -0,0 +1,13 @@
+class General
+class Specific extends General
+
+class LowPriority:
+  given a:General()
+
+object NormalPriority extends LowPriority:
+  given b:Specific()
+
+def run =
+  import NormalPriority.given
+  val x = summon[General]
+  val _: Specific = x // <- b was picked