repeated application of structural_simplify leads to error

[hexaeder]

Describe the bug 🐞

Repeated aplication of structural_simplify can lead to errors. I've observed at least two:

• unbalanced system error and
• (far less important) out of bounds error on equations in a case where structural simplify reduced the system to 0 equations

Expected behavior

Either error because it should not be called on a completed system or be a no-op.

Minimal Reproducible Example 👇

using Pkg
pkg"activate --temp"
pkg"add ModelingToolkit, ModelingToolkitStandardLibrary"

using ModelingToolkit
using ModelingToolkitStandardLibrary.Electrical
using ModelingToolkitStandardLibrary.Blocks: Constant
using ModelingToolkit: t_nounits as t

R = 1.0
C = 1.0
V = 1.0
systems = @named begin
    resistor = Resistor(R = R)
    capacitor = Capacitor(C = C, v = 0.0)
    source = Voltage()
    constant = Constant(k = V)
    ground = Ground()
end

rc_eqs = [connect(constant.output, source.V)
          connect(source.p, resistor.p)
          connect(resistor.n, capacitor.p)
          connect(capacitor.n, source.n, ground.g)]

@named rc_model = ODESystem(rc_eqs, t; systems)
sys = structural_simplify(rc_model)
structural_simplify(sys)

Error & Stacktrace ⚠️

julia> structural_simplify(sys)
ERROR: ExtraVariablesSystemException: The system is unbalanced. There are 2 highest order derivative variables and 1 equations.
More variables than equations, here are the potential extra variable(s):
 capacitor₊v(t)
 capacitor₊i(t)
Note that the process of determining extra variables is a best-effort heuristic. The true extra variables are dependent on the model and may not be in this list.
Stacktrace:
  [1] error_reporting(state::TearingState{…}, bad_idxs::Vector{…}, n_highest_vars::Int64, iseqs::Bool, orig_inputs::Set{…})
    @ ModelingToolkit.StructuralTransformations ~/.julia/packages/ModelingToolkit/yfT8s/src/structural_transformation/utils.jl:50
  [2] check_consistency(state::TearingState{ODESystem}, orig_inputs::Set{Any})
    @ ModelingToolkit.StructuralTransformations ~/.julia/packages/ModelingToolkit/yfT8s/src/structural_transformation/utils.jl:85
  [3] _structural_simplify!(state::TearingState{…}, io::Nothing; simplify::Bool, check_consistency::Bool, fully_determined::Bool, warn_initialize_determined::Bool, dummy_derivative::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/yfT8s/src/systems/systemstructure.jl:692
  [4] _structural_simplify!
    @ ~/.julia/packages/ModelingToolkit/yfT8s/src/systems/systemstructure.jl:675 [inlined]
  [5] structural_simplify!(state::TearingState{…}, io::Nothing; simplify::Bool, check_consistency::Bool, fully_determined::Bool, warn_initialize_determined::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/yfT8s/src/systems/systemstructure.jl:635
  [6] __structural_simplify(sys::ODESystem, io::Nothing; simplify::Bool, kwargs::@Kwargs{…})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/yfT8s/src/systems/systems.jl:85
  [7] __structural_simplify
    @ ~/.julia/packages/ModelingToolkit/yfT8s/src/systems/systems.jl:66 [inlined]
  [8] structural_simplify(sys::ODESystem, io::Nothing; simplify::Bool, split::Bool, allow_symbolic::Bool, allow_parameter::Bool, conservative::Bool, fully_determined::Bool, kwargs::@Kwargs{})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/yfT8s/src/systems/systems.jl:24
  [9] structural_simplify
    @ ~/.julia/packages/ModelingToolkit/yfT8s/src/systems/systems.jl:20 [inlined]
 [10] structural_simplify(sys::ODESystem)
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/yfT8s/src/systems/systems.jl:20
 [11] top-level scope
    @ REPL[40]:1
 [12] top-level scope
    @ none:1
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

(jl_S36F9c) pkg> st
Status `/tmp/jl_S36F9c/Project.toml`
  [961ee093] ModelingToolkit v9.36.0
  [16a59e39] ModelingToolkitStandardLibrary v2.11.0

• Output of versioninfo()

julia> versioninfo()
Julia Version 1.11.0-rc3
Commit 616e45539db (2024-08-26 15:46 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 16 × AMD Ryzen 9 8945HS w/ Radeon 780M Graphics
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 16 default, 0 interactive, 8 GC (on 16 virtual cores)
Environment:
  JULIA_NUM_THREADS = auto

[ChrisRackauckas]

Either error because it should not be called on a completed system or be a no-op.

It shoulderror, and throw a nice error. Right now it throws a bad error 😅 but we should throw a nice contextual error if you try to repeat or call on a complete system.