Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀+X₁, X₁-1) :|: 1 ≤ X₀ ∧ X₁+1 ≤ 0
Preprocessing
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀+X₁, X₁-1) :|: 1 ≤ X₀ ∧ X₁+1 ≤ 0
Time-Bound by TWN-Loops:
TWN-Loops: t₁ 4⋅X₀+6⋅X₁+11 {O(n)}
TWN-Loops:
entry: t₀: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀+X₁,X₁-1) :|: 1 ≤ X₀ ∧ X₁+1 ≤ 0
order: [X₁; X₀]
closed-form:
X₁: X₁ + [[n != 0]] * -1 * 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:
0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ 0 < 2⋅X₁+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 2 < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2
∨ X₁+1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₁+1 < 0 ∧ 0 < 2⋅X₁+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁+1 < 0 ∧ 2 < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0
∨ X₁+1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₁+1 ≤ 0 ∧ 0 ≤ X₁+1 ∧ 1 < 0
∨ X₁+1 ≤ 0 ∧ 0 ≤ X₁+1 ∧ 0 < 2⋅X₁+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁+1 ≤ 0 ∧ 0 ≤ X₁+1 ∧ 2 < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0
∨ X₁+1 ≤ 0 ∧ 0 ≤ X₁+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2
Stabilization-Threshold for: X₁+1 ≤ 0
alphas_abs: X₁+1
M: 0
N: 1
Bound: 2⋅X₁+4 {O(n)}
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 1+2⋅X₀+2⋅X₁
M: 0
N: 2
Bound: 4⋅X₀+4⋅X₁+5 {O(n)}
relevant size-bounds w.r.t. t₀:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 4⋅X₀+6⋅X₁+11 {O(n)}
4⋅X₀+6⋅X₁+11 {O(n)}
All Bounds
Timebounds
Overall timebound:4⋅X₀+6⋅X₁+12 {O(n)}
t₀: 1 {O(1)}
t₁: 4⋅X₀+6⋅X₁+11 {O(n)}
Costbounds
Overall costbound: 4⋅X₀+6⋅X₁+12 {O(n)}
t₀: 1 {O(1)}
t₁: 4⋅X₀+6⋅X₁+11 {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: 5⋅X₀+8⋅X₁+11 {O(n)}
t₁, X₁: 4⋅X₀+7⋅X₁+11 {O(n)}