Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₁: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀, X₀+X₁) :|: 1 ≤ X₀ ∧ X₁+1 ≤ X₀

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₁: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀, X₀+X₁) :|: 1 ≤ X₀ ∧ X₁+1 ≤ X₀

Time-Bound by TWN-Loops:

TWN-Loops: t₀ 2⋅X₀+2⋅X₁+5 {O(n)}

TWN-Loops:

entry: t₁: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀,X₀+X₁) :|: 1 ≤ X₀ ∧ X₁+1 ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * X₀ * n^1

Termination: true
Formula:

X₀ < 0 ∧ 1 < X₀
∨ X₀ < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ X₁+1 < X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₀
∨ X₁+1 < X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 < X₀
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1

Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₁:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+5 {O(n)}

2⋅X₀+2⋅X₁+5 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+6 {O(n)}
t₁: 1 {O(1)}
t₀: 2⋅X₀+2⋅X₁+5 {O(n)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+6 {O(n)}
t₁: 1 {O(1)}
t₀: 2⋅X₀+2⋅X₁+5 {O(n)}

Sizebounds

t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: 4⋅X₀⋅X₀+4⋅X₀⋅X₁+12⋅X₀+X₁ {O(n^2)}