Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₂: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ X₁
t₀: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁+1 ≤ X₀

Preprocessing

Found invariant 1+X₁ ≤ X₀ for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₂: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ X₁
t₀: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁+1 ≤ X₀

Found invariant 1+X₁ ≤ X₀ for location l2

Time-Bound by TWN-Loops:

TWN-Loops: t₁ 2⋅X₀+2⋅X₁+4 {O(n)}

TWN-Loops:

entry: t₂: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀+1,X₁) :|: X₀ ≤ X₁
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

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

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

relevant size-bounds w.r.t. t₂:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+4 {O(n)}

2⋅X₀+2⋅X₁+4 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+6 {O(n)}
t₂: 1 {O(1)}
t₀: 1 {O(1)}
t₁: 2⋅X₀+2⋅X₁+4 {O(n)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+6 {O(n)}
t₂: 1 {O(1)}
t₀: 1 {O(1)}
t₁: 2⋅X₀+2⋅X₁+4 {O(n)}

Sizebounds

t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₀, X₀: 2⋅X₁+4⋅X₀+4 {O(n)}
t₀, X₁: 2⋅X₁ {O(n)}
t₁, X₀: 2⋅X₁+3⋅X₀+4 {O(n)}
t₁, X₁: X₁ {O(n)}