Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₁+X₂, -X₂-1, X₂) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁
Preprocessing
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₁+X₂, -X₂-1, X₂) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁
Time-Bound by TWN-Loops:
TWN-Loops: t₁ 2⋅X₂+4⋅X₀+4⋅X₁+8 {O(n)}
TWN-Loops:
entry: t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀+X₁+X₂,-X₂-1,X₂) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁
order: [X₂; X₁; X₀]
closed-form:
X₂: X₂
X₁: [[n == 0]] * X₁ + [[n != 0]] * -X₂-1
X₀: X₀ + [[n != 0]] * X₂ * n^1 + [[n != 0]] * X₁ + [[n != 0, n != 1]] * -X₂-1 * n^1 + [[n != 0, n != 1]] * X₂+1
Termination: true
Formula:
1 < 0
∨ 1 < 0 ∧ 0 < X₀+X₁+X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁+X₂+1 ∧ X₀+X₁+X₂+1 ≤ 0
∨ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < X₀+X₁ ∧ 0 < X₀+X₁+X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁+X₂+1 ∧ X₀+X₁+X₂+1 ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < 0
∨ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀+X₁+X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁+X₂+1 ∧ X₀+X₁+X₂+1 ≤ 0
Stabilization-Threshold for: 0 ≤ X₀+X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀+X₁+X₂+1
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2⋅X₂+4 {O(n)}
relevant size-bounds w.r.t. t₀:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₂+4⋅X₀+4⋅X₁+8 {O(n)}
2⋅X₂+4⋅X₀+4⋅X₁+8 {O(n)}
All Bounds
Timebounds
Overall timebound:2⋅X₂+4⋅X₀+4⋅X₁+9 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₂+4⋅X₀+4⋅X₁+8 {O(n)}
Costbounds
Overall costbound: 2⋅X₂+4⋅X₀+4⋅X₁+9 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₂+4⋅X₀+4⋅X₁+8 {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 16⋅X₀⋅X₂+18⋅X₁⋅X₂+4⋅X₀⋅X₁+4⋅X₁⋅X₁+8⋅X₂⋅X₂+17⋅X₁+40⋅X₂+9⋅X₀+18 {O(n^2)}
t₁, X₁: 2⋅X₂+2 {O(n)}
t₁, X₂: X₂ {O(n)}