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(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(X₁, X₁-1) :|: 1 ≤ X₀

Time-Bound by TWN-Loops:

TWN-Loops: t₁ 2⋅X₁+4 {O(n)}

TWN-Loops:

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

Termination: true
Formula:

1 < 0
∨ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0

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

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

2⋅X₁+4 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₁+5 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₁+4 {O(n)}

Costbounds

Overall costbound: 2⋅X₁+5 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₁+4 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: 4⋅X₁+4 {O(n)}
t₁, X₁: 3⋅X₁+4 {O(n)}