diff --git a/src/bipartite_graph.jl b/src/bipartite_graph.jl
index 1168d1ad24..a72ea7ef31 100644
--- a/src/bipartite_graph.jl
+++ b/src/bipartite_graph.jl
@@ -733,6 +733,8 @@ end
 
 Graphs.has_edge(g::DiCMOBiGraph{true}, a, b) = a in inneighbors(g, b)
 Graphs.has_edge(g::DiCMOBiGraph{false}, a, b) = b in outneighbors(g, a)
+# This definition is required for `induced_subgraph` to work
+(::Type{<:DiCMOBiGraph})(n::Integer) = SimpleDiGraph(n)
 
 # Condensation Graphs
 abstract type AbstractCondensationGraph <: AbstractGraph{Int} end
diff --git a/src/structural_transformation/bipartite_tearing/modia_tearing.jl b/src/structural_transformation/bipartite_tearing/modia_tearing.jl
index e8304752e8..f8be5ccd7b 100644
--- a/src/structural_transformation/bipartite_tearing/modia_tearing.jl
+++ b/src/structural_transformation/bipartite_tearing/modia_tearing.jl
@@ -83,7 +83,7 @@ function tear_graph_modia(structure::SystemStructure, isder::F = nothing,
         max(length(var_eq_matching),
             maximum(x -> x isa Int ? x : 0, var_eq_matching)))
     full_var_eq_matching = copy(var_eq_matching)
-    var_sccs::Vector{Union{Vector{Int}, Int}} = find_var_sccs(graph, var_eq_matching)
+    var_sccs = find_var_sccs(graph, var_eq_matching)
     vargraph = DiCMOBiGraph{true}(graph)
     ict = IncrementalCycleTracker(vargraph; dir = :in)
 
@@ -111,5 +111,5 @@ function tear_graph_modia(structure::SystemStructure, isder::F = nothing,
         empty!(ieqs)
         empty!(filtered_vars)
     end
-    return var_eq_matching, full_var_eq_matching
+    return var_eq_matching, full_var_eq_matching, var_sccs
 end
diff --git a/src/structural_transformation/partial_state_selection.jl b/src/structural_transformation/partial_state_selection.jl
index bae8816b50..aef149dd93 100644
--- a/src/structural_transformation/partial_state_selection.jl
+++ b/src/structural_transformation/partial_state_selection.jl
@@ -299,59 +299,60 @@ function dummy_derivative_graph!(structure::SystemStructure, var_eq_matching, ja
        (n_dummys = length(dummy_derivatives))
         @warn "The number of dummy derivatives ($n_dummys) does not match the number of differentiated equations ($n_diff_eqs)."
     end
-    dummy_derivatives_set = BitSet(dummy_derivatives)
 
-    is_not_present_non_rec = let graph = graph
-        v -> isempty(𝑑neighbors(graph, v))
+    ret = tearing_with_dummy_derivatives(structure, BitSet(dummy_derivatives))
+    if log
+        ret
+    else
+        ret[1]
     end
+end
 
-    is_not_present = let var_to_diff = var_to_diff
-        v -> while true
-            # if a higher derivative is present, then it's present
-            is_not_present_non_rec(v) || return false
-            v = var_to_diff[v]
-            v === nothing && return true
-        end
+function is_present(structure, v)::Bool
+    @unpack var_to_diff, graph = structure
+    while true
+        # if a higher derivative is present, then it's present
+        isempty(𝑑neighbors(graph, v)) || return true
+        v = var_to_diff[v]
+        v === nothing && return false
     end
+end
 
-    # Derivatives that are either in the dummy derivatives set or ended up not
-    # participating in the system at all are not considered differential
-    is_some_diff = let dummy_derivatives_set = dummy_derivatives_set
-        v -> !(v in dummy_derivatives_set) && !is_not_present(v)
-    end
+# Derivatives that are either in the dummy derivatives set or ended up not
+# participating in the system at all are not considered differential
+function is_some_diff(structure, dummy_derivatives, v)::Bool
+    !(v in dummy_derivatives) && is_present(structure, v)
+end
 
-    # We don't want tearing to give us `y_t ~ D(y)`, so we skip equations with
-    # actually differentiated variables.
-    isdiffed = let diff_to_var = diff_to_var
-        v -> diff_to_var[v] !== nothing && is_some_diff(v)
-    end
+# We don't want tearing to give us `y_t ~ D(y)`, so we skip equations with
+# actually differentiated variables.
+function isdiffed((structure, dummy_derivatives), v)::Bool
+    @unpack var_to_diff, graph = structure
+    diff_to_var = invview(var_to_diff)
+    diff_to_var[v] !== nothing && is_some_diff(structure, dummy_derivatives, v)
+end
 
+function tearing_with_dummy_derivatives(structure, dummy_derivatives)
+    @unpack var_to_diff = structure
     # We can eliminate variables that are not a selected state (differential
     # variables). Selected states are differentiated variables that are not
     # dummy derivatives.
-    can_eliminate = let var_to_diff = var_to_diff
-        v -> begin
-            dv = var_to_diff[v]
-            dv === nothing && return true
-            is_some_diff(dv) || return true
-            return false
+    can_eliminate = falses(length(var_to_diff))
+    for (v, dv) in enumerate(var_to_diff)
+        dv = var_to_diff[v]
+        if dv === nothing || !is_some_diff(structure, dummy_derivatives, dv)
+            can_eliminate[v] = true
         end
     end
-
-    var_eq_matching, full_var_eq_matching = tear_graph_modia(structure, isdiffed,
+    var_eq_matching, full_var_eq_matching, var_sccs = tear_graph_modia(structure,
+        Base.Fix1(isdiffed, (structure, dummy_derivatives)),
         Union{Unassigned, SelectedState};
-        varfilter = can_eliminate)
+        varfilter = Base.Fix1(getindex, can_eliminate))
     for v in eachindex(var_eq_matching)
-        is_not_present(v) && continue
+        is_present(structure, v) || continue
         dv = var_to_diff[v]
-        (dv === nothing || !is_some_diff(dv)) && continue
+        (dv === nothing || !is_some_diff(structure, dummy_derivatives, dv)) && continue
         var_eq_matching[v] = SelectedState()
     end
-
-    if log
-        candidates = can_eliminate.(1:ndsts(graph))
-        return var_eq_matching, full_var_eq_matching, candidates
-    else
-        return var_eq_matching
-    end
+    return var_eq_matching, full_var_eq_matching, var_sccs, can_eliminate
 end