Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₁, X₁-X₂, X₂+1) :|: 1 ≤ X₀

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₁, X₁-X₂, X₂+1) :|: 1 ≤ X₀

Time-Bound by TWN-Loops:

TWN-Loops: t₁ 12⋅X₀+12⋅X₁+6⋅X₂+12 {O(n)}

TWN-Loops:

entry: t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀+X₁,X₁-X₂,X₂+1) :|: 1 ≤ X₀
order: [X₂; X₁; X₀]
closed-form:
X₂: X₂ + [[n != 0]] * n^1
X₁: X₁ + [[n != 0]] * -X₂ * n^1 + [[n != 0, n != 1]] * -1/2 * n^2 + [[n != 0, n != 1]] * 1/2 * n^1
X₀: X₀ + [[n != 0]] * X₁ * n^1 + [[n != 0, n != 1]] * -1/2⋅X₂ * n^2 + [[n != 0, n != 1]] * 1/2⋅X₂ * n^1 + [[n != 0, n != 1, n != 2]] * -1/6 * n^3 + [[n != 0, n != 1, n != 2]] * 1/2 * n^2 + [[n != 0, n != 1, n != 2]] * -1/3 * n^1

Termination: true
Formula:

1 < 0
∨ 3⋅X₂ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 < 6⋅X₁+3⋅X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 3⋅X₂ ≤ 3 ∧ 3 ≤ 3⋅X₂
∨ 6 < 6⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 3⋅X₂ ≤ 3 ∧ 3 ≤ 3⋅X₂ ∧ 2 ≤ 6⋅X₁+3⋅X₂ ∧ 6⋅X₁+3⋅X₂ ≤ 2
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 3⋅X₂ ≤ 3 ∧ 3 ≤ 3⋅X₂ ∧ 2 ≤ 6⋅X₁+3⋅X₂ ∧ 6⋅X₁+3⋅X₂ ≤ 2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6

Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 3+6⋅X₀+6⋅X₁+3⋅X₂
M: 0
N: 3
Bound: 12⋅X₀+12⋅X₁+6⋅X₂+10 {O(n)}

relevant size-bounds w.r.t. t₀:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 12⋅X₀+12⋅X₁+6⋅X₂+12 {O(n)}

12⋅X₀+12⋅X₁+6⋅X₂+12 {O(n)}

All Bounds

Timebounds

Overall timebound:12⋅X₀+12⋅X₁+6⋅X₂+13 {O(n)}
t₀: 1 {O(1)}
t₁: 12⋅X₀+12⋅X₁+6⋅X₂+12 {O(n)}

Costbounds

Overall costbound: 12⋅X₀+12⋅X₁+6⋅X₂+13 {O(n)}
t₀: 1 {O(1)}
t₁: 12⋅X₀+12⋅X₁+6⋅X₂+12 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 1584⋅X₀⋅X₂⋅X₂+1584⋅X₁⋅X₂⋅X₂+1728⋅X₀⋅X₀⋅X₀+1728⋅X₁⋅X₁⋅X₁+288⋅X₂⋅X₂⋅X₂+2880⋅X₀⋅X₀⋅X₂+2880⋅X₁⋅X₁⋅X₂+5184⋅X₀⋅X₀⋅X₁+5184⋅X₀⋅X₁⋅X₁+5760⋅X₀⋅X₁⋅X₂+10968⋅X₀⋅X₁+1680⋅X₂⋅X₂+5472⋅X₀⋅X₀+5496⋅X₁⋅X₁+6096⋅X₀⋅X₂+6108⋅X₁⋅X₂+3224⋅X₂+5773⋅X₀+5798⋅X₁+2028 {O(n^3)}
t₁, X₁: 144⋅X₀⋅X₀+144⋅X₁⋅X₁+168⋅X₀⋅X₂+168⋅X₁⋅X₂+288⋅X₀⋅X₁+48⋅X₂⋅X₂+176⋅X₂+300⋅X₀+301⋅X₁+156 {O(n^2)}
t₁, X₂: 12⋅X₀+12⋅X₁+7⋅X₂+12 {O(n)}