Initial Problem

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

Preprocessing

Eliminate variables {D,X₁} that do not contribute to the problem

Found invariant X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₀, X₂) → l1(X₀, X₂)
t₉: l1(X₀, X₂) → l1(X₀+X₂, X₂-1) :|: 1 ≤ X₀
t₈: l1(X₀, X₂) → l2(X₀, X₂) :|: X₀ ≤ 0

Found invariant X₀ ≤ 0 for location l2

Time-Bound by TWN-Loops:

TWN-Loops: t₉ 4⋅X₀+4⋅X₂+7 {O(n)}

TWN-Loops:

entry: t₇: l0(X₀, X₂) → l1(X₀, X₂)
results in twn-loop: twn: (X₀,X₂) -> (X₀+X₂,X₂-1) :|: 1 ≤ X₀
order: [X₂; X₀]
closed-form:
X₂: X₂ + [[n != 0]] * -1 * n^1
X₀: X₀ + [[n != 0]] * X₂ * n^1 + [[n != 0, n != 1]] * -1/2 * n^2 + [[n != 0, n != 1]] * 1/2 * n^1

Termination: true
Formula:

1 < 0
∨ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2

Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 1+2⋅X₀+2⋅X₂
M: 0
N: 2
Bound: 4⋅X₀+4⋅X₂+5 {O(n)}

relevant size-bounds w.r.t. t₇:
X₀: X₀ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₇: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₂+7 {O(n)}

4⋅X₀+4⋅X₂+7 {O(n)}

All Bounds

Timebounds

Overall timebound:4⋅X₀+4⋅X₂+9 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 4⋅X₀+4⋅X₂+7 {O(n)}

Costbounds

Overall costbound: 4⋅X₀+4⋅X₂+9 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 4⋅X₀+4⋅X₂+7 {O(n)}

Sizebounds

t₇, X₀: X₀ {O(n)}
t₇, X₂: X₂ {O(n)}
t₈, X₀: 16⋅X₀⋅X₀+24⋅X₂⋅X₂+40⋅X₀⋅X₂+62⋅X₀+76⋅X₂+56 {O(n^2)}
t₈, X₂: 4⋅X₀+6⋅X₂+7 {O(n)}
t₉, X₀: 16⋅X₀⋅X₀+24⋅X₂⋅X₂+40⋅X₀⋅X₂+61⋅X₀+76⋅X₂+56 {O(n^2)}
t₉, X₂: 4⋅X₀+5⋅X₂+7 {O(n)}