Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₄: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀, X₀) :|: X₀ ≤ 0 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₁: l1(X₀, X₁) → l1(X₀, X₀) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₀+1 ≤ X₁
t₂: l1(X₀, X₁) → l1(X₀, 0) :|: 1 ≤ X₀ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₃: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₁ ≤ X₀
Preprocessing
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₄: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀, X₀) :|: X₀ ≤ 0 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₁: l1(X₀, X₁) → l1(X₀, X₀) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₀+1 ≤ X₁
t₂: l1(X₀, X₁) → l1(X₀, 0) :|: 1 ≤ X₀ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₃: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₁ ≤ X₀
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₀: l1(X₀, X₁) → l1(X₀, X₀) :|: X₀ ≤ 0 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁: l1(X₀, X₁) → l1(X₀, X₀) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₀+1 ≤ X₁
Found invariant 1 ≤ 0 for location l1
Time-Bound by TWN-Loops:
TWN-Loops: t₃ 10⋅X₀+6⋅X₁+22 {O(n)}
TWN-Loops:
entry: t₁: l1(X₀, X₁) → l1(X₀, X₀) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₀+1 ≤ X₁
results in twn-loop: twn: (X₀,X₁) -> (X₀,X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₁ ≤ X₀
entry: t₄: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀,X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₁ ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ 1 < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < 1 ∧ 0 < 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < 1 ∧ 0 < 1+X₁ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 0 < 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 < 0
∨ 0 < 1 ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ X₁ < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₁ < X₀ ∧ 1 < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ X₁ < X₀ ∧ 0 < 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ < X₀ ∧ 0 < 1+X₁ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 0 < 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 < 0
∨ X₁ < X₀ ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 < 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 < 1+X₁ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 < 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 0 ≤ 1+X₁
alphas_abs: 1+X₁
M: 0
N: 1
Bound: 2⋅X₁+4 {O(n)}
Stabilization-Threshold for: 1 ≤ X₁
alphas_abs: 1+X₁
M: 0
N: 1
Bound: 2⋅X₁+4 {O(n)}
relevant size-bounds w.r.t. t₁:
X₀: X₀ {O(n)}
X₁: X₀ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 8⋅X₀+12 {O(n)}
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
0 < 1 ∧ 1 < 0
∨ 0 < 1 ∧ 1 < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < 1 ∧ 0 < 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < 1 ∧ 0 < 1+X₁ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 0 < 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 < 0
∨ 0 < 1 ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ X₁ < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₁ < X₀ ∧ 1 < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ X₁ < X₀ ∧ 0 < 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ < X₀ ∧ 0 < 1+X₁ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 0 < 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 < 0
∨ X₁ < X₀ ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 < 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 < 1+X₁ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 < 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 0 ≤ 1+X₁
alphas_abs: 1+X₁
M: 0
N: 1
Bound: 2⋅X₁+4 {O(n)}
Stabilization-Threshold for: 1 ≤ X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₄:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₄: 1 {O(1)}
Results in: 2⋅X₀+6⋅X₁+10 {O(n)}
10⋅X₀+6⋅X₁+22 {O(n)}
knowledge_propagation leads to new time bound 10⋅X₀+6⋅X₁+24 {O(n)} for transition t₂: l1(X₀, X₁) → l1(X₀, 0) :|: 1 ≤ X₀ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
All Bounds
Timebounds
Overall timebound:12⋅X₁+20⋅X₀+49 {O(n)}
t₄: 1 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 10⋅X₀+6⋅X₁+24 {O(n)}
t₃: 10⋅X₀+6⋅X₁+22 {O(n)}
Costbounds
Overall costbound: 12⋅X₁+20⋅X₀+49 {O(n)}
t₄: 1 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 10⋅X₀+6⋅X₁+24 {O(n)}
t₃: 10⋅X₀+6⋅X₁+22 {O(n)}
Sizebounds
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₀ {O(n)}
t₂, X₀: 4⋅X₀ {O(n)}
t₂, X₁: 0 {O(1)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: X₀+X₁ {O(n)}