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+1-2⋅X₀) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁
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+1-2⋅X₀) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁
TWN: t₁: l1→l1
cycle: [t₁: l1→l1]
loop: (X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁,(X₀,X₁) -> (X₀,X₁+1-2⋅X₀)
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * 1-2⋅X₀ * n^1
Termination: true
Formula:
2⋅X₀ < 1 ∧ 1 < 2⋅X₀
∨ 2⋅X₀ < 1 ∧ X₁ < X₀ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1
∨ 2⋅X₀ < 1 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1 < X₀+X₁ ∧ 2⋅X₀ ≤ 1 ∧ 1 ≤ 2⋅X₀ ∧ 1 < 2⋅X₀
∨ 1 < X₀+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1
∨ 1 < X₀+X₁ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 2⋅X₀ ≤ 1 ∧ 1 ≤ 2⋅X₀ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 2⋅X₀
∨ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ X₁ < X₀ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1
∨ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
Stabilization-Threshold for: 1 ≤ X₀+X₁
alphas_abs: 1+X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
TWN - Lifting for t₁: l1→l1 of 4⋅X₀+4⋅X₁+8 {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+4⋅X₁+8 {O(n)}
All Bounds
Timebounds
Overall timebound:4⋅X₀+4⋅X₁+9 {O(n)}
t₀: 1 {O(1)}
t₁: 4⋅X₀+4⋅X₁+8 {O(n)}
Costbounds
Overall costbound: 4⋅X₀+4⋅X₁+9 {O(n)}
t₀: 1 {O(1)}
t₁: 4⋅X₀+4⋅X₁+8 {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 6⋅X₀ {O(n)}