Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G, H
Locations: l0, l1, l2
Transitions:
t₁: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₁-1, X₀, X₁, X₀-2, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, G, X₂, X₃, X₄, H) :|: X₁ ≤ 0 ∧ G ≤ 0
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, H) :|: 1 ≤ X₁ ∧ X₀ ≤ 0

Preprocessing

Eliminate variables {H,X₂,X₃,X₄,X₅} that do not contribute to the problem

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: G
Locations: l0, l1, l2
Transitions:
t₉: l0(X₀, X₁) → l1(X₀, X₁)
t₁₀: l1(X₀, X₁) → l1(X₀-1, X₁-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁₁: l1(X₀, X₁) → l2(X₀, G) :|: X₁ ≤ 0 ∧ G ≤ 0
t₁₂: l1(X₀, X₁) → l2(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 0

Time-Bound by TWN-Loops:

TWN-Loops: t₁₀ 2⋅X₀+2⋅X₁+6 {O(n)}

TWN-Loops:

entry: t₉: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀-1,X₁-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

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

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

relevant size-bounds w.r.t. t₉:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₉: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+6 {O(n)}

2⋅X₀+2⋅X₁+6 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+9 {O(n)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₀+2⋅X₁+6 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+9 {O(n)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₀+2⋅X₁+6 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}

Sizebounds

t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: 2⋅X₀ {O(n)}
t₁₂, X₀: 2⋅X₀ {O(n)}
t₁₂, X₁: 2⋅X₁ {O(n)}