Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(2⋅X₀, X₂, X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁+1
Preprocessing
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(2⋅X₀, X₂, X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁+1
Time-Bound by TWN-Loops:
TWN-Loops: t₁ 2⋅X₂+10 {O(n)}
TWN-Loops:
entry: t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
results in twn-loop: twn: (X₀,X₁,X₂) -> (2⋅X₀,X₂,X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁+1
order: [X₀; X₂; X₁]
closed-form:
X₀: X₀ * 2^n
X₂: X₂
X₁: [[n == 0]] * X₁ + [[n != 0]] * X₂
Termination: true
Formula:
X₀ < 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₂+1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ 0 < X₂+1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₂+1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₂+1 ∧ X₂+1 ≤ 0 ∧ 0 < X₀
∨ 0 ≤ X₂+1 ∧ X₂+1 ≤ 0 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 ≤ X₂+1 ∧ X₂+1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: X₀ ≤ X₁+1
alphas_abs: X₂+1
M: 0
N: 1
Bound: 2⋅X₂+4 {O(n)}
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 1
M: 0
N: 1
Bound: 4 {O(1)}
relevant size-bounds w.r.t. t₀:
X₂: X₂ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₂+10 {O(n)}
2⋅X₂+10 {O(n)}
All Bounds
Timebounds
Overall timebound:2⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₂+10 {O(n)}
Costbounds
Overall costbound: 2⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₂+10 {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 2^(2⋅X₂+10)⋅X₀ {O(EXP)}
t₁, X₁: 2⋅X₂ {O(n)}
t₁, X₂: X₂ {O(n)}