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(X₀+1, X₂, X₂) :|: X₀+1 ≤ X₁

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(X₀+1, X₂, X₂) :|: X₀+1 ≤ X₁

Time-Bound by TWN-Loops:

TWN-Loops: t₁ 2⋅X₀+2⋅X₂+4 {O(n)}

TWN-Loops:

entry: t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀+1,X₂,X₂) :|: X₀+1 ≤ X₁
order: [X₀; X₂; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₂: X₂
X₁: [[n == 0]] * X₁ + [[n != 0]] * X₂

Termination: true
Formula:

1 < 0
∨ X₀+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ X₀+1

Stabilization-Threshold for: X₀+1 ≤ X₁
alphas_abs: X₀+X₂
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+2 {O(n)}

relevant size-bounds w.r.t. t₀:
X₀: X₀ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₂+4 {O(n)}

2⋅X₀+2⋅X₂+4 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₂+5 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₀+2⋅X₂+4 {O(n)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₂+5 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₀+2⋅X₂+4 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 2⋅X₂+3⋅X₀+4 {O(n)}
t₁, X₁: 2⋅X₂ {O(n)}
t₁, X₂: X₂ {O(n)}