Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₁: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂-1) :|: X₁+1 ≤ X₀ ∧ X₁+1 ≤ X₂

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₁: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂-1) :|: X₁+1 ≤ X₀ ∧ X₁+1 ≤ X₂

Time-Bound by TWN-Loops:

TWN-Loops: t₀ 2⋅X₀+2⋅X₂+4⋅X₁+6 {O(n)}

TWN-Loops:

entry: t₁: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀-1,X₁,X₂-1) :|: X₁+1 ≤ X₀ ∧ X₁+1 ≤ X₂
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1
∨ X₁+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁+1 < X₂ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1 ∧ 1 < 0
∨ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1 ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1

Stabilization-Threshold for: X₁+1 ≤ X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}
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)}
X₂: X₂ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₂+4⋅X₁+6 {O(n)}

2⋅X₀+2⋅X₂+4⋅X₁+6 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₂+4⋅X₁+7 {O(n)}
t₁: 1 {O(1)}
t₀: 2⋅X₀+2⋅X₂+4⋅X₁+6 {O(n)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₂+4⋅X₁+7 {O(n)}
t₁: 1 {O(1)}
t₀: 2⋅X₀+2⋅X₂+4⋅X₁+6 {O(n)}

Sizebounds

t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₀, X₀: 2⋅X₂+3⋅X₀+4⋅X₁+6 {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: 2⋅X₀+3⋅X₂+4⋅X₁+6 {O(n)}