Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₂: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁+1 ≤ 0
t₃: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, 0, 0, 0, 0, 0) :|: 0 ≤ X₁
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+X₁, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₀
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, 0, 0, 0, 0, 0) :|: X₀+1 ≤ 0

Preprocessing

Eliminate variables {X₂,X₃,X₄,X₅,X₆} that do not contribute to the problem

Found invariant 1+X₁ ≤ 0 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) :|: X₁+1 ≤ 0
t₉: l0(X₀, X₁) → l2(X₀, X₁) :|: 0 ≤ X₁
t₁₀: l1(X₀, X₁) → l1(X₀+X₁, X₁) :|: 0 ≤ X₀ ∧ 1+X₁ ≤ 0
t₁₁: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀+1 ≤ 0 ∧ 1+X₁ ≤ 0

Found invariant 1+X₁ ≤ 0 for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₁₀ 2⋅X₀+4 {O(n)}

TWN-Loops:

entry: t₈: l0(X₀, X₁) → l1(X₀, X₁) :|: X₁+1 ≤ 0
results in twn-loop: twn:Inv: [1+X₁ ≤ 0] , (X₀,X₁) -> (X₀+X₁,X₁) :|: 0 ≤ X₀
order: [X₁; X₀]
closed-form:
X₁: X₁
X₀: X₀ + [[n != 0]] * X₁ * n^1

Termination: true
Formula:

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

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

relevant size-bounds w.r.t. t₈:
X₀: X₀ {O(n)}
Runtime-bound of t₈: 1 {O(1)}
Results in: 2⋅X₀+4 {O(n)}

2⋅X₀+4 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₀+7 {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₀+4 {O(n)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+7 {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₀+4 {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+X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: 2⋅X₀+2⋅X₁ {O(n)}
t₁₁, X₁: 2⋅X₁ {O(n)}