Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₄: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₀-2, X₂) :|: 1 ≤ X₀ ∧ 1 ≤ X₁+X₀ ∧ 1 ≤ X₁
t₁: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: 1 ≤ X₀ ∧ X₁+X₀ ≤ 0 ∧ 1 ≤ X₁
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₃: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: X₁ ≤ 0
Preprocessing
Cut unsatisfiable transition t₁: l1→l2
Eliminate variables {D,X₂} that do not contribute to the problem
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₁₃: l0(X₀, X₁) → l1(X₀, X₁)
t₁₄: l1(X₀, X₁) → l1(X₀-1, X₀-2) :|: 1 ≤ X₀ ∧ 1 ≤ X₁+X₀ ∧ 1 ≤ X₁
t₁₅: l1(X₀, X₁) → l2(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₁₆: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ 0
Time-Bound by TWN-Loops:
TWN-Loops: t₁₄ 8⋅X₀+8 {O(n)}
TWN-Loops:
entry: t₁₃: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀-1,X₀-2) :|: 1 ≤ X₀ ∧ 1 ≤ X₁+X₀ ∧ 1 ≤ X₁
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: [[n == 0]] * X₁ + [[n != 0]] * X₀-2 + [[n != 0, n != 1]] * -1 * n^1 + [[n != 0, n != 1]]
Termination: true
Formula:
2 < 0 ∧ 1 < 0
∨ 1 < 0 ∧ 2 < 0 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 2 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 2 < 2⋅X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 < 0
∨ 1 < 0 ∧ 2 < 2⋅X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 2 < 2⋅X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2 ∧ 1 < 0
∨ 1 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 < 0 ∧ 1 < 0
∨ 2 < X₀ ∧ 2 < 0 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 < X₀ ∧ 2 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 < 2⋅X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 < 0
∨ 2 < X₀ ∧ 2 < 2⋅X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 < X₀ ∧ 2 < 2⋅X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2 ∧ 1 < 0
∨ 2 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 1 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 2⋅X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 2⋅X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 2⋅X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2 ∧ 1 < 0
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
Stabilization-Threshold for: 1 ≤ X₁
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: 1 ≤ X₁+X₀
alphas_abs: 2⋅X₀
M: 0
N: 1
Bound: 4⋅X₀+2 {O(n)}
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
relevant size-bounds w.r.t. t₁₃:
X₀: X₀ {O(n)}
Runtime-bound of t₁₃: 1 {O(1)}
Results in: 8⋅X₀+8 {O(n)}
8⋅X₀+8 {O(n)}
All Bounds
Timebounds
Overall timebound:8⋅X₀+11 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 8⋅X₀+8 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
Costbounds
Overall costbound: 8⋅X₀+11 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 8⋅X₀+8 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
Sizebounds
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: 2⋅X₀ {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₆, X₀: 2⋅X₀ {O(n)}
t₁₆, X₁: 2⋅X₀+X₁ {O(n)}