Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁) → l1(X₀, X₁)
t₂: l1(X₀, X₁) → l1(X₀, X₁-X₀) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀
t₀: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0
t₁: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ X₀

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁) → l1(X₀, X₁)
t₂: l1(X₀, X₁) → l1(X₀, X₁-X₀) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀
t₀: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0
t₁: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ X₀

Time-Bound by TWN-Loops:

TWN-Loops: t₂ 2⋅X₀+2⋅X₁+5 {O(n)}

TWN-Loops:

entry: t₃: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀,X₁-X₀) :|: X₀+1 ≤ X₁ ∧ 1 ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -X₀ * n^1

Termination: true
Formula:

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

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

relevant size-bounds w.r.t. t₃:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₃: 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+8 {O(n)}
t₃: 1 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅X₀+2⋅X₁+5 {O(n)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+8 {O(n)}
t₃: 1 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅X₀+2⋅X₁+5 {O(n)}

Sizebounds

t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: 2⋅X₀ {O(n)}
t₁, X₁: 2⋅X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}