Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₂: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁
t₁: l1(X₀, X₁) → l1(X₁, X₁) :|: 1 ≤ X₀ ∧ X₁+1 ≤ X₀
Preprocessing
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₂: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁
t₁: l1(X₀, X₁) → l1(X₁, X₁) :|: 1 ≤ X₀ ∧ X₁+1 ≤ X₀
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁: l1(X₀, X₁) → l1(X₁, X₁) :|: 1 ≤ X₀ ∧ X₁+1 ≤ X₀
Found invariant 1 ≤ 0 for location l1
Time-Bound by TWN-Loops:
TWN-Loops: t₀ 4⋅X₀+8⋅X₁+14 {O(n)}
TWN-Loops:
entry: t₁: l1(X₀, X₁) → l1(X₁, X₁) :|: 1 ≤ X₀ ∧ X₁+1 ≤ X₀
results in twn-loop: twn: (X₀,X₁) -> (X₀-1,X₁) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁
entry: t₂: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀-1,X₁) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
Termination: true
Formula:
0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ X₀ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₀ < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
Stabilization-Threshold for: X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 1+X₀
M: 0
N: 1
Bound: 2⋅X₀+4 {O(n)}
relevant size-bounds w.r.t. t₁:
X₀: X₁ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 6⋅X₁+8 {O(n)}
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
Termination: true
Formula:
0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ X₀ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₀ < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
Stabilization-Threshold for: X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+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. t₂:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂: 1 {O(1)}
Results in: 2⋅X₁+4⋅X₀+6 {O(n)}
4⋅X₀+8⋅X₁+14 {O(n)}
All Bounds
Timebounds
Overall timebound:4⋅X₀+8⋅X₁+16 {O(n)}
t₂: 1 {O(1)}
t₀: 4⋅X₀+8⋅X₁+14 {O(n)}
t₁: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₀+8⋅X₁+16 {O(n)}
t₂: 1 {O(1)}
t₀: 4⋅X₀+8⋅X₁+14 {O(n)}
t₁: 1 {O(1)}
Sizebounds
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₀, X₀: X₀+X₁ {O(n)}
t₀, X₁: 2⋅X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}