### Step 1: Identify the relevant industry
Italgas S.p.A. is a gas distribution utility. According to the provided S&P methodologies, it falls under the **Regulated Utilities** sector. We will use the Regulated Utilities methodology.

### Step 2: Estimate the 2021 "Adjusted_EBITDA"
Formula: Adjusted_EBITDA = EBITDA (reported or reconstructed) + adjustment_leases + nonrecurring_losses - nonrecurring_gains ± pension_adjustments ± joint_venture_proportional_EBITDA ± other_normalization_adjustments
- EBITDA = Operating Profit (583,231,000) + Depreciation & Amortization (445,251,000) = 1,028,482,000 EUR
- Lease adjustment: Cash outflow for leases in 2021 = 21,529,000 EUR (S&P adds lease expenses back to EBITDA to account for the reclassification of leases as debt).
- No specific nonrecurring items, pension adjustments, or JV proportional EBITDA are explicitly detailed for addition under the provided facts. We note a loss on disposal of 3,553,000, but under standard adjustments these are often normalized if non-recurring. However, without explicit labels, we keep the operating profit as the baseline for EBITDA and add back the lease expense.
- 2021 Adjusted_EBITDA = 1,028,482,000 + 21,529,000 = **1,050,011,000 EUR**

### Step 3: Estimate the 2021 "FFO"
Formula: FFO = Adjusted_EBITDA - cash_interest - cash_taxes
- Cash interest: Finance costs paid classified as operating activities (59,783,000) + Cash outflow for leases (21,529,000) = 81,312,000 EUR
- Cash taxes: Income taxes paid (206,923,000 EUR)
- 2021 FFO = 1,050,011,000 - 81,312,000 - 206,923,000 = **761,776,000 EUR**

### Step 4: Estimate the 2021 "Adjusted_Debt"
Formula: Adjusted_Debt = (reported_debt + leases + pension_deficit + guarantees + hybrid_debt_portion + other_debt_like_items) - eligible_cash
- Reported debt: Short Term Financial Liabilities (591,188,000) + Long Term Financial Liabilities (5,785,707,000) = 6,376,895,000 EUR
- Leases: 8x the annual lease expense (8 × 21,529,000) = 172,232,000 EUR
- Eligible cash: Cash And Cash Equivalents (1,391,763,000 EUR)
- 2021 Adjusted_Debt = 6,376,895,000 + 172,232,000 - 1,391,763,000 = **5,157,364,000 EUR**

### Step 5: Calculate the 2021 "Adjusted_Debt / Adjusted_EBITDA" ratio
- 2021 Adjusted_Debt / Adjusted_EBITDA = 5,157,364,000 / 1,050,011,000 = **4.91x**

### Step 6: Calculate the 2021 "FFO / Adjusted_Debt" ratio
- 2021 FFO / Adjusted_Debt = 761,776,000 / 5,157,364,000 = **0.1477** (or 14.77%)

### Step 7: Estimate the 2022 "Adjusted_EBITDA"
- EBITDA = Operating Profit (641,338,000) + Depreciation & Amortization (479,186,000) = 1,120,524,000 EUR
- Lease adjustment: 27,865,000 EUR
- 2022 Adjusted_EBITDA = 1,120,524,000 + 27,865,000 = **1,148,389,000 EUR**

### Step 8: Estimate the 2022 "FFO"
- Cash interest: Finance costs paid (53,720,000) + Cash outflow for leases (27,865,000) = 81,585,000 EUR
- Cash taxes: Income taxes paid (152,372,000 EUR)
- 2022 FFO = 1,148,389,000 - 81,585,000 - 152,372,000 = **914,432,000 EUR**

### Step 9: Estimate the 2022 "Adjusted_Debt"
- Reported debt: Short Term Financial Liabilities (142,437,000) + Long Term Financial Liabilities (6,402,913,000) = 6,545,350,000 EUR
- Leases: 8 × 27,865,000 = 222,920,000 EUR
- Eligible cash: Cash And Cash Equivalents (451,946,000 EUR)
- 2022 Adjusted_Debt = 6,545,350,000 + 222,920,000 - 451,946,000 = **6,316,324,000 EUR**

### Step 10: Calculate the 2022 "Adjusted_Debt / Adjusted_EBITDA" ratio
- 2022 Adjusted_Debt / Adjusted_EBITDA = 6,316,324,000 / 1,148,389,000 = **5.50x**

### Step 11: Calculate the 2022 "FFO / Adjusted_Debt" ratio
- 2022 FFO / Adjusted_Debt = 914,432,000 / 6,316,324,000 = **0.1448** (or 14.48%)

### Step 12: Classify the year-on-year credit trend
- **Signal 1 (Leverage):** Change in Adjusted_Debt / Adjusted_EBITDA = 5.50x - 4.91x = +0.59x. Since +0.59x ≥ +0.2x, this signal is **Deteriorating**.
- **Signal 2 (Cash-flow coverage):** Change in FFO / Adjusted_Debt = 0.1448 - 0.1477 = -0.0029. Since -0.0029 is between -0.03 and +0.03 (exclusive), this signal is **Stable**.
- **Combining the signals:** One signal is Deteriorating and the other is Stable. The rule states to return the non-Stable category. Furthermore, the leverage increased significantly (+0.59x, nearly triple the threshold), driven by a major acquisition (evidenced by investments in change in scope of consolidation jumping from 21M to 874M) primarily funded by debt, materially shifting the capital structure. The cash flow coverage remained essentially flat only because EBITDA also grew from the acquisition. Thus, the leverage deterioration is the dominant trend.

<answer>Deteriorating</answer>