diff --git a/src/main/scala/leon/solvers/templates/LambdaManager.scala b/src/main/scala/leon/solvers/templates/LambdaManager.scala
index 74bfe2fd467237e6be79c967e25c5cc35f2dfa59..75d163815a17fbf31c56b684d58e3d26efe7feaa 100644
--- a/src/main/scala/leon/solvers/templates/LambdaManager.scala
+++ b/src/main/scala/leon/solvers/templates/LambdaManager.scala
@@ -54,7 +54,7 @@ object LambdaTemplate {
       ids,
       encoder,
       manager,
-      pathVar._2,
+      pathVar,
       arguments,
       condVars,
       exprVars,
@@ -76,7 +76,7 @@ class LambdaTemplate[T] private (
   val ids: (Identifier, T),
   val encoder: TemplateEncoder[T],
   val manager: QuantificationManager[T],
-  val start: T,
+  val pathVar: (Identifier, T),
   val arguments: Seq[(Identifier, T)],
   val condVars: Map[Identifier, T],
   val exprVars: Map[Identifier, T],
@@ -122,7 +122,7 @@ class LambdaTemplate[T] private (
       ids._1 -> substituter(ids._2),
       encoder,
       manager,
-      newStart,
+      pathVar._1 -> newStart,
       arguments,
       condVars,
       exprVars,
diff --git a/src/main/scala/leon/solvers/templates/QuantificationManager.scala b/src/main/scala/leon/solvers/templates/QuantificationManager.scala
index 9bc278f0998a7a4a5cc9321ca3976312861be1f1..c7f715b5eefe573d88eeb94b45293ba7cde646bf 100644
--- a/src/main/scala/leon/solvers/templates/QuantificationManager.scala
+++ b/src/main/scala/leon/solvers/templates/QuantificationManager.scala
@@ -45,7 +45,7 @@ case class Matcher[T](caller: T, tpe: TypeTree, args: Seq[Either[T, Matcher[T]]]
 
 class QuantificationTemplate[T](
   val quantificationManager: QuantificationManager[T],
-  val start: T,
+  val pathVar: (Identifier, T),
   val qs: (Identifier, T),
   val q2s: (Identifier, T),
   val insts: (Identifier, T),
@@ -60,10 +60,12 @@ class QuantificationTemplate[T](
   val matchers: Map[T, Set[Matcher[T]]],
   val lambdas: Seq[LambdaTemplate[T]]) {
 
+  lazy val start = pathVar._2
+
   def substitute(substituter: T => T): QuantificationTemplate[T] = {
     new QuantificationTemplate[T](
       quantificationManager,
-      substituter(start),
+      pathVar._1 -> substituter(start),
       qs,
       q2s,
       insts,
@@ -114,7 +116,7 @@ object QuantificationTemplate {
         substMap = subst + q2s + insts + guards + qs)
 
     new QuantificationTemplate[T](quantificationManager,
-      pathVar._2, qs, q2s, insts, guards._2, quantifiers,
+      pathVar, qs, q2s, insts, guards._2, quantifiers,
       condVars, exprVars, condTree, clauses, blockers, applications, matchers, lambdas)
   }
 }
@@ -328,7 +330,7 @@ class QuantificationManager[T](encoder: TemplateEncoder[T]) extends LambdaManage
   }
 
   private trait MatcherQuantification {
-    val start: T
+    val pathVar: (Identifier, T)
     val quantified: Set[T]
     val matchers: Set[Matcher[T]]
     val allMatchers: Map[T, Set[Matcher[T]]]
@@ -340,6 +342,8 @@ class QuantificationManager[T](encoder: TemplateEncoder[T]) extends LambdaManage
     val applications: Map[T, Set[App[T]]]
     val lambdas: Seq[LambdaTemplate[T]]
 
+    lazy val start = pathVar._2
+
     private lazy val depth = matchers.map(matcherDepth).max
     private lazy val transMatchers: Set[Matcher[T]] = (for {
       (b, ms) <- allMatchers.toSeq
@@ -438,7 +442,7 @@ class QuantificationManager[T](encoder: TemplateEncoder[T]) extends LambdaManage
         }
 
         val baseSubstMap = exprVars.map { case (id, idT) => idT -> encoder.encodeId(id) } ++
-                           freshConds(enabler, condVars, condTree)
+                           freshConds(pathVar._1 -> enabler, condVars, condTree)
         val lambdaSubstMap = lambdas map (lambda => lambda.ids._2 -> encoder.encodeId(lambda.ids._1))
         val substMap = subst.mapValues(Matcher.argValue) ++ baseSubstMap ++ lambdaSubstMap ++ instanceSubst(enablers)
 
@@ -473,7 +477,7 @@ class QuantificationManager[T](encoder: TemplateEncoder[T]) extends LambdaManage
   }
 
   private class Quantification (
-    val start: T,
+    val pathVar: (Identifier, T),
     val qs: (Identifier, T),
     val q2s: (Identifier, T),
     val insts: (Identifier, T),
@@ -520,7 +524,7 @@ class QuantificationManager[T](encoder: TemplateEncoder[T]) extends LambdaManage
   }
 
   private class LambdaAxiom (
-    val start: T,
+    val pathVar: (Identifier, T),
     val blocker: T,
     val guardVar: T,
     val quantified: Set[T],
@@ -599,7 +603,7 @@ class QuantificationManager[T](encoder: TemplateEncoder[T]) extends LambdaManage
       val enablingClause = encoder.mkImplies(guardT, blockerT)
 
       instantiateAxiom(
-        substMap(template.start),
+        template.pathVar._1 -> substMap(template.start),
         blockerT,
         guardT,
         quantifiers,
@@ -621,7 +625,7 @@ class QuantificationManager[T](encoder: TemplateEncoder[T]) extends LambdaManage
   }
 
   def instantiateAxiom(
-    start: T,
+    pathVar: (Identifier, T),
     blocker: T,
     guardVar: T,
     quantifiers: Seq[(Identifier, T)],
@@ -641,7 +645,7 @@ class QuantificationManager[T](encoder: TemplateEncoder[T]) extends LambdaManage
     var instantiation = Instantiation.empty[T]
 
     for (matchers <- matchQuorums) {
-      val axiom = new LambdaAxiom(start, blocker, guardVar, quantified,
+      val axiom = new LambdaAxiom(pathVar, blocker, guardVar, quantified,
         matchers, allMatchers, condVars, exprVars, condTree,
         clauses, blockers, applications, lambdas
       )
@@ -679,7 +683,7 @@ class QuantificationManager[T](encoder: TemplateEncoder[T]) extends LambdaManage
 
       val substituter = encoder.substitute(subst)
       val quantification = new Quantification(
-        substituter(template.start),
+        template.pathVar._1 -> substituter(template.start),
         template.qs._1 -> newQ,
         template.q2s, template.insts, template.guardVar,
         quantified,
diff --git a/src/main/scala/leon/solvers/templates/TemplateManager.scala b/src/main/scala/leon/solvers/templates/TemplateManager.scala
index 618a23c3a285b11bc9d4fb2da4eccecc87a45f16..bb6629ec16988a79eb686259aea4fa32c6111dbb 100644
--- a/src/main/scala/leon/solvers/templates/TemplateManager.scala
+++ b/src/main/scala/leon/solvers/templates/TemplateManager.scala
@@ -62,7 +62,7 @@ trait Template[T] { self =>
   val encoder : TemplateEncoder[T]
   val manager : QuantificationManager[T]
 
-  val start : T
+  val pathVar: (Identifier, T)
   val args : Seq[T]
   val condVars : Map[Identifier, T]
   val exprVars : Map[Identifier, T]
@@ -74,6 +74,8 @@ trait Template[T] { self =>
   val matchers : Map[T, Set[Matcher[T]]]
   val lambdas : Seq[LambdaTemplate[T]]
 
+  lazy val start = pathVar._2
+
   private var substCache : Map[Seq[T],Map[T,T]] = Map.empty
 
   def instantiate(aVar: T, args: Seq[T]): Instantiation[T] = {
@@ -82,7 +84,7 @@ trait Template[T] { self =>
       case Some(subst) => subst
       case None =>
         val subst = exprVars.map { case (id, idT) => idT -> encoder.encodeId(id) } ++
-                    manager.freshConds(aVar, condVars, condTree) ++
+                    manager.freshConds(pathVar._1 -> aVar, condVars, condTree) ++
                     (this.args zip args)
         substCache += args -> subst
         subst
@@ -303,7 +305,7 @@ object FunctionTemplate {
       tfd,
       encoder,
       manager,
-      pathVar._2,
+      pathVar,
       arguments.map(_._2),
       condVars,
       exprVars,
@@ -324,7 +326,7 @@ class FunctionTemplate[T] private(
   val tfd: TypedFunDef,
   val encoder: TemplateEncoder[T],
   val manager: QuantificationManager[T],
-  val start: T,
+  val pathVar: (Identifier, T),
   val args: Seq[T],
   val condVars: Map[Identifier, T],
   val exprVars: Map[Identifier, T],
@@ -358,10 +360,9 @@ class TemplateManager[T](protected[templates] val encoder: TemplateEncoder[T]) e
   def push(): Unit = incrementals.foreach(_.push())
   def pop(): Unit = incrementals.foreach(_.pop())
 
-  def freshConds(path: T, condVars: Map[Identifier, T], tree: Map[Identifier, Set[Identifier]]): Map[T, T] = {
+  def freshConds(path: (Identifier, T), condVars: Map[Identifier, T], tree: Map[Identifier, Set[Identifier]]): Map[T, T] = {
     val subst = condVars.map { case (id, idT) => idT -> encoder.encodeId(id) }
-    val pathVar = tree.keys.filter(id => !condVars.isDefinedAt(id)).head
-    val mapping = condVars.mapValues(subst) + (pathVar -> path)
+    val mapping = condVars.mapValues(subst) + path
 
     for ((parent, children) <- tree; ep = mapping(parent); child <- children) {
       val ec = mapping(child)