Test a complicated alias example

Author: YingboMa

test/reduction.jl

@@ -302,3 +302,25 @@ ss = alias_elimination(sys)
 @test length(equations(ss)) == length(states(ss)) == 1
 ss = structural_simplify(sys)
 @test length(equations(ss)) == length(states(ss)) == 2
+
+@variables t
+vars = @variables x(t) y(t) k(t) z(t) zₜ(t) ddx(t)
+D = Differential(t)
+eqs = [D(D(x)) ~ ddx
+       ddx ~ y
+       D(x) ~ z
+       D(z) ~ zₜ
+       D(zₜ) ~ sin(t)
+       D(x) ~ D(k)
+       D(D(D(x))) ~ sin(t)]
+@named sys = ODESystem(eqs, t, vars, [])
+state = TearingState(sys);
+ag, mm, complete_ag, complete_mm = ModelingToolkit.alias_eliminate_graph!(state)
+fullvars = state.fullvars
+aliases = []
+for (v, (c, a)) in complete_ag
+    push!(aliases, fullvars[v] => c == 0 ? 0 : c * fullvars[a])
+end
+ref_aliases = [D(k) => D(x); z => D(x); D(z) => D(D(x)); zₜ => D(D(x)); ddx => D(D(x));
+               y => D(D(x)); D(zₜ) => D(D(D(x)))]
+@test Set(aliases) == Set(ref_aliases)