I'll work through this step-by-step, analyzing ITALGAS S.P.A.'s financial data to estimate S&P's credit trend from 2021 to 2022.

## Step 1: Identify Relevant Industry

ITALGAS S.P.A. is a gas utility company. Based on the S&P methodology descriptions, this falls under **Regulated Utilities** (specifically "Gas" subsector). The company operates as a regulated gas distribution utility with regulated tariffs and infrastructure assets.

Key characteristics from the data:
- Core business revenue dominated by regulated gas distribution
- Significant intangible assets (likely regulatory asset base / concession rights)
- Stable revenue structure with related party transactions
- Capital-intensive with depreciation and amortization

## Step 2: Estimate 2021 Adjusted_EBITDA

For regulated utilities, we need to reconstruct EBITDA. From the data:

**2021 (period 2021-01-01 to 2022-01-01):**
- Profit Loss From Operating Activities (EBIT): 583,231,000 EUR
- Depreciation Amortisation And Impairment: 445,251,000 EUR

**EBITDA = EBIT + Depreciation/Amortization**
= 583,231,000 + 445,251,000 = **1,028,482,000 EUR**

For regulated utilities, S&P notes they use regulatory accounting and focus on economics/cash flow. The methodology mentions:
- Deconsolidate securitized debt with specialized recovery provisions
- Seasonal working capital adjustments for gas distribution utilities (net inventory against short-term borrowings)

From the data, I don't see explicit securitization. For seasonal working capital adjustment:
- Inventories 2022-01-01: 105,294,000 EUR
- Short Term Financial Liabilities 2022-01-01: 591,188,000 EUR

The methodology says "we adjust inventory and debt balances by netting the value of inventory against outstanding short-term borrowings" when confident of near-term cost recovery. Given the regulated nature, I'll make this adjustment.

However, looking more carefully at the formula structure, the Adjusted_EBITDA formula includes:
- EBITDA (reported or reconstructed)
- adjustment_leases
- nonrecurring_losses - nonrecurring_gains
- pension_adjustments
- joint_venture_proportional_EBITDA
- other_normalization_adjustments

For 2021, I need to identify nonrecurring items. Looking at the data:
- "Other Expense By Nature" has a large related party component: 99,170,000 EUR in 2021 vs 155,131,000 EUR in 2022 — this seems recurring
- "Gains On Change In Fair Value Of Derivatives": 636,000 EUR (2021) — this is likely a nonrecurring gain to exclude

Also need to consider:
- Finance Costs Related Parties 2021: 914,000 EUR — this is below operating line, so not in EBITDA

For regulated utilities, S&P focuses on actual cash flow generation. Let me check for lease-related items. The cash flow statement shows "Cash Outflow For Leases" 2021: 21,529,000 EUR.

Looking at the operating items, I don't see clear nonrecurring losses/gains in the operating section. The "Other Income From Equity Investments" and similar items are below operating profit.

Let me reconstruct more carefully. For regulated utilities, S&P may use regulatory accounts as proxy for earnings stability.

**Base EBITDA 2021: 1,028,482,000 EUR**

Adjustments to consider:
- Leases: Add back operating lease expense if capitalized (but IFRS 16 already in effect, so likely already in D&A)
- Nonrecurring gains: Subtract gains on derivatives 636,000 EUR

Actually, looking at S&P's regulated utilities methodology more carefully: "We do not adjust GAAP earnings or balance-sheet figures to remove the effects of regulatory accounting. While IFRS does not currently provide for any recognition of the effects of rate-setting for financial reporting purposes, our financial analysis focuses on the economics and actual cash flow generation."

For Adjusted_EBITDA, I'll use:
- EBITDA: 1,028,482,000 EUR
- Less: nonrecurring gains (derivatives): -636,000 EUR

**Adjusted_EBITDA 2021 ≈ 1,027,846,000 EUR** or roughly **1,028 million EUR**

Let me round to **1,028 million EUR** for simplicity, or more precisely use 1,027.8 million.

Actually, re-reading: the derivatives gain is in the finance section, not operating. So it's already excluded from operating profit/EBIT. Thus no adjustment needed.

**Adjusted_EBITDA 2021 = 1,028,482,000 EUR ≈ 1,028.5 million EUR**

## Step 3: Estimate 2021 FFO

**FFO = Adjusted_EBITDA - cash_interest - cash_taxes**

From cash flow statement 2021:
- Finance Costs Paid Classified As Operating Activities: 59,783,000 EUR
- Income Taxes Paid Classified As Operating Activities: 206,923,000 EUR

Wait — I need to be careful. The formula says "cash_interest" and "cash_taxes". 

From the cash flow statement:
- "Finance Costs Paid Classified As Operating Activities": 59,783,000 EUR
- "Income Taxes Paid Classified As Operating Activities": 206,923,000 EUR

But also:
- "Finance Income Received Classified As Operating Activities": 3,630,000 EUR

For FFO, S&P typically uses: EBITDA - cash interest paid + cash interest received - cash taxes paid. Or more commonly: EBITDA - net cash interest - cash taxes.

Actually, standard FFO = Funds From Operations = EBITDA - cash interest - cash taxes (sometimes + dividends received from operating).

Let me use: FFO = Adjusted_EBITDA - cash_interest_paid - cash_taxes_paid

= 1,028,482,000 - 59,783,000 - 206,923,000 = **761,776,000 EUR**

Or if we use net interest (interest paid - interest received):
= 1,028,482,000 - (59,783,000 - 3,630,000) - 206,923,000 = 1,028,482,000 - 56,153,000 - 206,923,000 = **765,406,000 EUR**

Also, "Dividends Received Classified As Operating Activities": 1,254,000 EUR — S&P sometimes includes this in FFO.

Standard S&P FFO = Net income + D&A + deferred taxes + other non-cash items - working capital changes... 

Actually, let me use the direct formula given: FFO = Adjusted_EBITDA - cash_interest - cash_taxes

Using gross interest paid: 761,776,000 EUR
Using net interest paid: 765,406,000 EUR

I'll use **765 million EUR** as a reasonable estimate (using net interest, and adding dividends received would give ~767 million).

Let me be more precise: **765,406,000 + 1,254,000 = 766,660,000 ≈ 767 million EUR** if including dividends.

Actually, S&P's standard FFO for utilities typically excludes dividends from investments. Let me stick with **765 million EUR** or more precisely **761.8 million** using gross interest.

For conservatism and following the formula literally (cash_interest likely means paid, not net): **761,776,000 EUR ≈ 762 million EUR**

## Step 4: Estimate 2021 Adjusted_Debt

**Adjusted_Debt = (reported_debt + leases + pension_deficit + guarantees + hybrid_debt_portion + other_debt_like_items) - eligible_cash**

From balance sheet 2022-01-01 (start of 2021 year-end, i.e., 2021 position):
- Short Term Financial Liabilities: 591,188,000 EUR
- Long Term Financial Liabilities: 5,785,707,000 EUR
- Other Current Financial Liabilities: 290,000 EUR
- Other Noncurrent Financial Liabilities: 6,283,000 EUR

Total reported debt = 591,188,000 + 5,785,707,000 + 290,000 + 6,283,000 = **6,383,468,000 EUR**

For regulated utilities, S&P mentions:
- Deconsolidate securitized debt with specialized recovery provisions — none apparent
- Net inventory against short-term borrowings for seasonal working capital — but this affects liquidity, not debt measurement directly in the formula

Leases: From cash flow "Cash Outflow For Leases" 2021: 21,529,000 EUR. Under IFRS 16, leases are likely already in debt.

Pension deficit: "Noncurrent Provisions For Employee Benefits" 2022-01-01: 95,648,000 EUR. This is likely net pension liability. Need to check if this is a deficit.

Looking at reserves: "Reserve Of Remeasurements Of Defined Benefit Plans Member" 2022-01-01: -15,140,000 EUR (negative = deficit). But this is in equity, not liability.

The liability "Noncurrent Provisions For Employee Benefits" 2022-01-01: 95,648,000 EUR — this includes pension obligations.

For S&P, pension deficit = liability - plan assets. We don't have plan assets split out. The "Reserve Of Remeasurements" suggests some net deficit recognized in equity.

Given data limitations, I'll assume the provision is approximately the pension liability, and if plan assets are not separately identified, we may not have a clear deficit. Let me assume no additional pension deficit adjustment beyond what's in debt, or use the remeasurement reserve as indicator.

Actually, S&P typically adds pension deficit (funded status) to debt. Without clear plan asset data, I'll use the noncurrent provision as proxy or assume minimal adjustment.

Hybrid debt: Not apparent.

Guarantees: Not apparent from data.

Other debt-like items: "Trade And Other Current Payables" — these are operating, not debt-like.

For regulated utilities with seasonal working capital, S&P nets inventory against short-term borrowings:
- Inventories 2022-01-01: 105,294,000 EUR
- Short term borrowings to adjust: 105,294,000 EUR of the 591,188,000 EUR

This reduces effective seasonal debt by 105,294,000 EUR.

Eligible cash: "Cash And Cash Equivalents" 2022-01-01: 1,391,763,000 EUR

But S&P typically uses "available cash" — sometimes not all cash is eligible. For utilities, they may consider cash as generally available.

**Adjusted_Debt 2021 calculation:**
= (6,383,468,000 + 0 leases already included + 0 pension deficit unclear + 0 guarantees + 0 hybrid + 0 other) - 1,391,763,000 eligible cash

= 6,383,468,000 - 1,391,763,000 = **4,991,705,000 EUR**

Or with seasonal adjustment netting inventory against ST debt:
Effective ST debt = 591,188,000 - 105,294,000 = 485,894,000
Total debt = 485,894,000 + 5,785,707,000 + 290,000 + 6,283,000 = 6,278,174,000
Adjusted_Debt = 6,278,174,000 - 1,391,763,000 = **4,886,411,000 EUR**

I'll use approximately **4,990 million EUR** without seasonal adjustment, or **4,890 million EUR** with it. Let me use **4,940 million EUR** as midpoint, or more precisely **4,991.7 million** without seasonal adjustment.

Actually, re-reading: the netting is for "leverage measures" distortion, so it should be applied. But the formula says "reported_debt" — this is gross. Let me use gross debt minus cash: **4,992 million EUR**.

## Step 5: Calculate 2021 Adjusted_Debt / Adjusted_EBITDA

= 4,991,705,000 / 1,028,482,000 = **4.85x**

Or with FFO-based debt: 4,886,411,000 / 1,028,482,000 = **4.75x**

I'll use **4.85x** as primary estimate.

## Step 6: Calculate 2021 FFO / Adjusted_Debt

= 761,776,000 / 4,991,705,000 = **0.153** or **15.3%**

Or with 766,660,000 / 4,991,705,000 = **0.154** or **15.4%**

## Step 7: Estimate 2022 Adjusted_EBITDA

**2022 (period 2022-01-01 to 2023-01-01):**
- Profit Loss From Operating Activities (EBIT): 641,338,000 EUR
- Depreciation Amortisation And Impairment: 479,186,000 EUR

**EBITDA = 641,338,000 + 479,186,000 = 1,120,524,000 EUR**

**Adjusted_EBITDA 2022 = 1,120,524,000 EUR ≈ 1,120.5 million EUR**

## Step 8: Estimate 2022 FFO

From cash flow statement 2022:
- Finance Costs Paid Classified As Operating Activities: 53,720,000 EUR
- Finance Income Received Classified As Operating Activities: 4,043,000 EUR
- Income Taxes Paid Classified As Operating Activities: 152,372,000 EUR
- Dividends Received Classified As Operating Activities: 1,372,000 EUR

Using formula: FFO = Adjusted_EBITDA - cash_interest - cash_taxes
= 1,120,524,000 - 53,720,000 - 152,372,000 = **914,432,000 EUR**

Or with net interest: 1,120,524,000 - (53,720,000 - 4,043,000) - 152,372,000 = 1,120,524,000 - 49,677,000 - 152,372,000 = **918,475,000 EUR**

With dividends: **919,847,000 EUR ≈ 920 million EUR**

I'll use **914 million EUR** (gross interest) or **918 million EUR** (net interest). Let's use **914.4 million EUR** for consistency with 2021 methodology.

## Step 9: Estimate 2022 Adjusted_Debt

From balance sheet 2023-01-01 (end of 2022):
- Short Term Financial Liabilities: 142,437,000 EUR
- Long Term Financial Liabilities: 6,402,913,000 EUR
- Other Current Financial Liabilities: 290,000 EUR
- Other Noncurrent Financial Liabilities: 34,000 EUR

Total reported debt = 142,437,000 + 6,402,913,000 + 290,000 + 34,000 = **6,545,674,000 EUR**

Eligible cash: "Cash And Cash Equivalents" 2023-01-01: 451,946,000 EUR

Seasonal adjustment: Inventories 2023-01-01: 120,486,000 EUR

With seasonal adjustment: ST debt effective = 142,437,000 - 120,486,000 = 21,951,000
Total debt = 21,951,000 + 6,402,913,000 + 290,000 + 34,000 = 6,425,188,000

Adjusted_Debt without seasonal = 6,545,674,000 - 451,946,000 = **6,093,728,000 EUR**
Adjusted_Debt with seasonal = 6,425,188,000 - 451,946,000 = **5,973,242,000 EUR**

I'll use **6,094 million EUR** without seasonal adjustment for consistency.

## Step 10: Calculate 2022 Adjusted_Debt / Adjusted_EBITDA

= 6,093,728,000 / 1,120,524,000 = **5.44x**

## Step 11: Calculate 2022 FFO / Adjusted_Debt

= 914,432,000 / 6,093,728,000 = **0.150** or **15.0%**

## Step 12: Classify Year-on-Year Credit Trend

**Signal 1: Leverage (Adjusted_Debt / Adjusted_EBITDA)**
- 2021: 4.85x
- 2022: 5.44x
- Change: 5.44 - 4.85 = **+0.59x**

Threshold: ≥ +0.2x is Deteriorating
**Signal 1: Deteriorating** (0.59 > 0.2)

**Signal 2: Cash-flow coverage (FFO / Adjusted_Debt)**
- 2021: 0.153 (15.3%)
- 2022: 0.150 (15.0%)
- Change: 0.150 - 0.153 = **-0.003** or **-0.3 percentage points**

Threshold: ≤ -0.03 is Deteriorating
**Signal 2: Stable** (-0.003 is between -0.03 and +0.03)

**Combining signals:**
- Signal 1: Deteriorating
- Signal 2: Stable

Per instructions: "If one is Stable and the other is Improving or Deteriorating, return the non-Stable category."

Therefore: **Deteriorating**

Let me verify my calculations more carefully, as the leverage increase seems large. Let me recheck debt figures.

Actually, let me recheck 2021 debt. The 2021 year-end is 2022-01-01 position:
- Short Term Financial Liabilities: 591,188,000
- Long Term Financial Liabilities: 5,785,707,000
- Other Current Financial Liabilities: 290,000
- Other Noncurrent Financial Liabilities: 6,283,000

Total: 6,383,468,000

Cash: 1,391,763,000

Net debt: 4,991,705,000

For 2022 year-end (2023-01-01):
- Short Term Financial Liabilities: 142,437,000
- Long Term Financial Liabilities: 6,402,913,000
- Other Current Financial Liabilities: 290,000
- Other Noncurrent Financial Liabilities: 34,000

Total: 6,545,674,000

Cash: 451,946,000

Net debt: 6,093,728,000

The cash dropped significantly from 1,392m to 452m, while debt increased. This is consistent with the cash flow statement showing large investing outflows (1,284m) and financing outflows (negative, meaning inflows of 204m? Actually "Cash Flows From Used In Financing Activities" 2022 is -204,160,000 which is negative, meaning net repayment? Wait, negative means used in, so outflow.

Actually looking at cash flow: "Increase Decrease In Cash And Cash Equivalents" 2022: -939,817,000 (decrease).

This is consistent: cash decreased by ~940m, from 1,392m to 452m.

The leverage increase is driven by both debt increase and cash decrease. This is a real deterioration.

Let me recheck EBITDA to make sure I have the right figures.

2021 EBIT: 583,231,000
2021 D&A: 445,251,000
2021 EBITDA: 1,028,482,000

2022 EBIT: 641,338,000
2022 D&A: 479,186,000
2022 EBITDA: 1,120,524,000

EBITDA growth: 1,120,524 / 1,028,482 = 1.089 or 8.9% growth

Debt growth: 6,093,728 / 4,991,705 = 1.221 or 22.1% growth

So debt grew much faster than EBITDA, leading to leverage deterioration.

Rechecking FFO:
2021: 1,028,482 - 59,783 - 206,923 = 761,776
2022: 1,120,524 - 53,720 - 152,372 = 914,432

FFO actually improved significantly! From 762m to 914m, up 20%.

FFO/Debt:
2021: 761,776 / 4,991,705 = 0.1527
2022: 914,432 / 6,093,728 = 0.1501

So FFO/Debt is nearly flat (15.3% to 15.0%), despite FFO growing, because debt grew even more.

The coverage ratio is nearly stable, but leverage worsened significantly.

Given the instructions: when one signal is Stable and other is Deteriorating, return non-Stable → Deteriorating.

But let me also consider if I should use net interest for FFO. If I use net interest:

2021 FFO: 1,028,482 - (59,783 - 3,630) - 206,923 = 765,406
2022 FFO: 1,120,524 - (53,720 - 4,043) - 152,372 = 918,475

2021 FFO/Debt: 765,406 / 4,991,705 = 0.1533
2022 FFO/Debt: 918,475 / 6,093,728 = 0.1507

Change: -0.0026, still Stable.

What if I include dividends received in operating activities in FFO?

2021: 765,406 + 1,254 = 766,660; /4,991,705 = 0.1536
2022: 918,475 + 1,372 = 919,847; /6,093,728 = 0.1510

Still Stable.

The leverage signal is clearly Deteriorating at +0.59x, well above the 0.2x threshold.

Given the explicit instruction: "If one is Stable and the other is Improving or Deteriorating, return the non-Stable category."

**Final classification: Deteriorating**

The deterioration in leverage is substantial (0.59x increase) and driven by a significant increase in net debt position (debt up, cash down substantially) despite decent EBITDA growth. The FFO coverage is nearly stable but slightly negative, masking that FFO actually improved in absolute terms but was outpaced by debt growth. The material signal is the leverage deterioration, which is well beyond the threshold.

<answer>Deteriorating</answer>