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(2⋅X₀+X₁, X₁+1, X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂

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(2⋅X₀+X₁, X₁+1, X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂

Time-Bound by TWN-Loops:

TWN-Loops: t₁ 2⋅X₂+4⋅X₁+20 {O(n)}

TWN-Loops:

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

Termination: true
Formula:

X₀+X₁+1 < 0 ∧ 0 < X₀+X₁+1
∨ X₀+X₁+1 < 0 ∧ 1 < 0 ∧ 0 ≤ X₀+X₁+1 ∧ X₀+X₁+1 ≤ 0
∨ X₀+X₁+1 < 0 ∧ 2+X₁ < 0 ∧ 0 ≤ X₀+X₁+1 ∧ X₀+X₁+1 ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀+X₁+1 < 0 ∧ 0 ≤ X₀+X₁+1 ∧ X₀+X₁+1 ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₁ ≤ 0 ∧ 0 ≤ 2+X₁
∨ 0 < 1 ∧ X₀+X₁+1 ≤ 0 ∧ 0 ≤ X₀+X₁+1 ∧ 0 < X₀+X₁+1
∨ 0 < 1 ∧ 1 < 0 ∧ 0 ≤ X₀+X₁+1 ∧ X₀+X₁+1 ≤ 0
∨ 0 < 1 ∧ 2+X₁ < 0 ∧ 0 ≤ X₀+X₁+1 ∧ X₀+X₁+1 ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 0 ≤ X₀+X₁+1 ∧ X₀+X₁+1 ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₁ ≤ 0 ∧ 0 ≤ 2+X₁
∨ 0 < X₁+1+X₂ ∧ X₀+X₁+1 ≤ 0 ∧ 0 ≤ X₀+X₁+1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀+X₁+1
∨ 0 < X₁+1+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0 ∧ 0 ≤ X₀+X₁+1 ∧ X₀+X₁+1 ≤ 0
∨ 0 < X₁+1+X₂ ∧ 2+X₁ < 0 ∧ 0 ≤ X₀+X₁+1 ∧ X₀+X₁+1 ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₁+1+X₂ ∧ 0 ≤ X₀+X₁+1 ∧ X₀+X₁+1 ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₁ ≤ 0 ∧ 0 ≤ 2+X₁
∨ X₀+X₁+1 ≤ 0 ∧ 0 ≤ X₀+X₁+1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₁+1+X₂ ∧ X₁+1+X₂ ≤ 0 ∧ 0 < X₀+X₁+1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₁+1+X₂ ∧ X₁+1+X₂ ≤ 0 ∧ 1 < 0 ∧ 0 ≤ X₀+X₁+1 ∧ X₀+X₁+1 ≤ 0
∨ 0 ≤ X₁+1+X₂ ∧ X₁+1+X₂ ≤ 0 ∧ 2+X₁ < 0 ∧ 0 ≤ X₀+X₁+1 ∧ X₀+X₁+1 ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₁+1+X₂ ∧ X₁+1+X₂ ≤ 0 ∧ 0 ≤ X₀+X₁+1 ∧ X₀+X₁+1 ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₁ ≤ 0 ∧ 0 ≤ 2+X₁

Stabilization-Threshold for: X₀ ≤ X₂
alphas_abs: 1+X₁+X₂
M: 5
N: 2
Bound: 2⋅X₁+2⋅X₂+8 {O(n)}
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 2+X₁
M: 5
N: 2
Bound: 2⋅X₁+10 {O(n)}

relevant size-bounds w.r.t. t₀:
X₁: X₁ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₂+4⋅X₁+20 {O(n)}

2⋅X₂+4⋅X₁+20 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₂+4⋅X₁+21 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₂+4⋅X₁+20 {O(n)}

Costbounds

Overall costbound: 2⋅X₂+4⋅X₁+21 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₂+4⋅X₁+20 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 20⋅2^(2⋅X₂+4⋅X₁+20)⋅X₁⋅X₂+206⋅2^(2⋅X₂+4⋅X₁+20)⋅X₁+24⋅2^(2⋅X₂+4⋅X₁+20)⋅X₁⋅X₁+2^(2⋅X₂+4⋅X₁+20)⋅4⋅X₂⋅X₂+2^(2⋅X₂+4⋅X₁+20)⋅420+2^(2⋅X₂+4⋅X₁+20)⋅82⋅X₂+2^(2⋅X₂+4⋅X₁+20)⋅X₀ {O(EXP)}
t₁, X₁: 2⋅X₂+5⋅X₁+20 {O(n)}
t₁, X₂: X₂ {O(n)}