diff --git a/pkg/reconciler/pipeline/dag/dag.go b/pkg/reconciler/pipeline/dag/dag.go
index 16f39fc4fce..d632aec0d98 100644
--- a/pkg/reconciler/pipeline/dag/dag.go
+++ b/pkg/reconciler/pipeline/dag/dag.go
@@ -128,7 +128,7 @@ func linkPipelineTasks(prev *Node, next *Node) error {
 	// Check if we are adding cycles.
 	visited := map[string]bool{prev.Task.HashKey(): true, next.Task.HashKey(): true}
 	path := []string{next.Task.HashKey(), prev.Task.HashKey()}
-	if err := visit(next.Task.HashKey(), prev.Prev, path, visited); err != nil {
+	if err := visit(prev.Prev, path, visited); err != nil {
 		return fmt.Errorf("cycle detected: %w", err)
 	}
 	next.Prev = append(next.Prev, prev)
@@ -136,18 +136,13 @@ func linkPipelineTasks(prev *Node, next *Node) error {
 	return nil
 }
 
-func visit(currentName string, nodes []*Node, path []string, visited map[string]bool) error {
-	var sb strings.Builder
+func visit(nodes []*Node, path []string, visited map[string]bool) error {
 	for _, n := range nodes {
 		path = append(path, n.Task.HashKey())
 		if _, ok := visited[n.Task.HashKey()]; ok {
 			return errors.New(getVisitedPath(path))
 		}
-		sb.WriteString(currentName)
-		sb.WriteByte('.')
-		sb.WriteString(n.Task.HashKey())
-		visited[sb.String()] = true
-		if err := visit(n.Task.HashKey(), n.Prev, path, visited); err != nil {
+		if err := visit(n.Prev, path, visited); err != nil {
 			return err
 		}
 	}