Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₁: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ X₁
t₃: l0(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: X₁ ≤ 0
t₀: l1(X₀, X₁, X₂) → l1(X₀-X₁, 1+X₁, X₂) :|: 1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: X₀ ≤ 0

Preprocessing

Eliminate variables {D,X₂} that do not contribute to the problem

Found invariant 1 ≤ X₁ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₈: l0(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₁
t₉: l0(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ 0
t₁₀: l1(X₀, X₁) → l1(X₀-X₁, 1+X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁₁: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₁

Found invariant 1 ≤ X₁ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₁₀ 4⋅X₀+7 {O(n)}

TWN-Loops:

entry: t₈: l0(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₁
results in twn-loop: twn:Inv: [1 ≤ X₁] , (X₀,X₁) -> (X₀-X₁,1+X₁) :|: 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
M: 2
N: 1
Bound: 4⋅X₀+5 {O(n)}

relevant size-bounds w.r.t. t₈:
X₀: X₀ {O(n)}
Runtime-bound of t₈: 1 {O(1)}
Results in: 4⋅X₀+7 {O(n)}

4⋅X₀+7 {O(n)}

All Bounds

Timebounds

Overall timebound:4⋅X₀+10 {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 4⋅X₀+7 {O(n)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₀+10 {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 4⋅X₀+7 {O(n)}
t₁₁: 1 {O(1)}

Sizebounds

t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₁₀, X₀: 2⋅X₁+5⋅X₀+7 {O(n)}
t₁₀, X₁: 4⋅X₀+X₁+7 {O(n)}
t₁₁, X₀: 2⋅X₁+6⋅X₀+7 {O(n)}
t₁₁, X₁: 2⋅X₁+4⋅X₀+7 {O(n)}