Initial Problem

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

Preprocessing

Problem after Preprocessing

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

Time-Bound by TWN-Loops:

TWN-Loops: t₁ 4⋅X₀+4⋅X₁+7 {O(n)}

TWN-Loops:

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

Termination: true
Formula:

1 < 0
∨ 2⋅X₁ < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₁ ≤ 1 ∧ 1 ≤ 2⋅X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₁ ≤ 1 ∧ 1 ≤ 2⋅X₁ ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2

Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 1+2⋅X₀+2⋅X₁
M: 0
N: 2
Bound: 4⋅X₀+4⋅X₁+5 {O(n)}

relevant size-bounds w.r.t. t₀:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+7 {O(n)}

4⋅X₀+4⋅X₁+7 {O(n)}

All Bounds

Timebounds

Overall timebound:4⋅X₀+4⋅X₁+8 {O(n)}
t₀: 1 {O(1)}
t₁: 4⋅X₀+4⋅X₁+7 {O(n)}

Costbounds

Overall costbound: 4⋅X₀+4⋅X₁+8 {O(n)}
t₀: 1 {O(1)}
t₁: 4⋅X₀+4⋅X₁+7 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: 16⋅X₀⋅X₀+24⋅X₁⋅X₁+40⋅X₀⋅X₁+61⋅X₀+76⋅X₁+56 {O(n^2)}
t₁, X₁: 4⋅X₀+5⋅X₁+7 {O(n)}