Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₂: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀-3, X₁, X₂) :|: 4 ≤ X₀
t₀: l2(X₀, X₁, X₂) → l2(X₀-1, X₁-1, X₂-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂
Preprocessing
Cut unreachable locations [l1] from the program graph
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l2
Transitions:
t₂: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₀: l2(X₀, X₁, X₂) → l2(X₀-1, X₁-1, X₂-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂
Time-Bound by TWN-Loops:
TWN-Loops: t₀ 2⋅X₀+2⋅X₁+2⋅X₂+8 {O(n)}
TWN-Loops:
entry: t₂: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀-1,X₁-1,X₂-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁ + [[n != 0]] * -1 * n^1
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
1 < 0
∨ 1 < 0 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1 < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₂ ∧ 1 < 0 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 1 < X₂ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₂ ∧ 1 < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₂ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 < X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 < 0 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
Stabilization-Threshold for: 1 ≤ X₂
alphas_abs: X₂
M: 0
N: 1
Bound: 2⋅X₂+2 {O(n)}
Stabilization-Threshold for: 1 ≤ X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 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)}
X₂: X₂ {O(n)}
Runtime-bound of t₂: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+2⋅X₂+8 {O(n)}
2⋅X₀+2⋅X₁+2⋅X₂+8 {O(n)}
All Bounds
Timebounds
Overall timebound:2⋅X₀+2⋅X₁+2⋅X₂+9 {O(n)}
t₂: 1 {O(1)}
t₀: 2⋅X₀+2⋅X₁+2⋅X₂+8 {O(n)}
Costbounds
Overall costbound: 2⋅X₀+2⋅X₁+2⋅X₂+9 {O(n)}
t₂: 1 {O(1)}
t₀: 2⋅X₀+2⋅X₁+2⋅X₂+8 {O(n)}
Sizebounds
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}