Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(2⋅X₀, X₁+1) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁+1
Preprocessing
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(2⋅X₀, X₁+1) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁+1
Time-Bound by TWN-Loops:
TWN-Loops: t₁ 2⋅X₁+14 {O(n)}
TWN-Loops:
entry: t₀: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (2⋅X₀,X₁+1) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁+1
order: [X₀; X₁]
closed-form:
X₀: X₀ * 2^n
X₁: X₁ + [[n != 0]] * n^1
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 < 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ 0 < 1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₁+1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀
∨ 0 < X₁+1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₁+1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₁+1 ∧ X₁+1 ≤ 0 ∧ 0 < X₀
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₁+1 ∧ X₁+1 ≤ 0 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 ≤ X₁+1 ∧ X₁+1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: X₀ ≤ X₁+1
alphas_abs: 1+X₁
M: 5
N: 2
Bound: 2⋅X₁+8 {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:
X₁: X₁ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₁+14 {O(n)}
2⋅X₁+14 {O(n)}
All Bounds
Timebounds
Overall timebound:2⋅X₁+15 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₁+14 {O(n)}
Costbounds
Overall costbound: 2⋅X₁+15 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₁+14 {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: 2^(2⋅X₁+14)⋅X₀ {O(EXP)}
t₁, X₁: 3⋅X₁+14 {O(n)}