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, X₁+1, X₂+1) :|: X₁+X₂+1 ≤ X₀

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, X₁+1, X₂+1) :|: X₁+X₂+1 ≤ X₀

Time-Bound by TWN-Loops:

TWN-Loops: t₀ 2⋅X₀+2⋅X₁+2⋅X₂+4 {O(n)}

TWN-Loops:

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

Termination: true
Formula:

2 < 0
∨ X₁+X₂+1 < X₀ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ 0 ∧ 0 ≤ 2 ∧ X₁+X₂+1 ≤ X₀ ∧ X₀ ≤ X₁+X₂+1

Stabilization-Threshold for: X₁+X₂+1 ≤ X₀
alphas_abs: X₁+X₂+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2⋅X₂+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⋅X₁+2⋅X₂+4 {O(n)}

2⋅X₀+2⋅X₁+2⋅X₂+4 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+2⋅X₂+5 {O(n)}
t₁: 1 {O(1)}
t₀: 2⋅X₀+2⋅X₁+2⋅X₂+4 {O(n)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+2⋅X₂+5 {O(n)}
t₁: 1 {O(1)}
t₀: 2⋅X₀+2⋅X₁+2⋅X₂+4 {O(n)}

Sizebounds

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