Initial Problem

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

Preprocessing

Problem after Preprocessing

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

Time-Bound by TWN-Loops:

TWN-Loops: t₀ 2⋅X₀+2⋅X₁+5 {O(n)}

TWN-Loops:

entry: t₁: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀,X₁+X₂,X₂) :|: X₁ ≤ X₀ ∧ 1 ≤ X₂
order: [X₀; X₂; X₁]
closed-form:
X₀: X₀
X₂: X₂
X₁: X₁ + [[n != 0]] * X₂ * n^1

Termination: true
Formula:

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

Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₁:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+5 {O(n)}

2⋅X₀+2⋅X₁+5 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+6 {O(n)}
t₁: 1 {O(1)}
t₀: 2⋅X₀+2⋅X₁+5 {O(n)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+6 {O(n)}
t₁: 1 {O(1)}
t₀: 2⋅X₀+2⋅X₁+5 {O(n)}

Sizebounds

t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: 4⋅X₀⋅X₂+4⋅X₁⋅X₂+12⋅X₂+X₁ {O(n^2)}
t₀, X₂: X₂ {O(n)}