Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀ ≤ 3
t₂: l1(X₀, X₁, X₂, X₃) → l1(X₀+1, X₀, X₀+1, E) :|: X₀ ≤ 3
t₃: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 4 ≤ X₀ ∧ E+1 ≤ 0
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 4 ≤ X₀

Preprocessing

Eliminate variables {X₁,X₂,X₃} that do not contribute to the problem

Found invariant X₀ ≤ 4 ∧ 4 ≤ X₀ for location l2

Found invariant X₀ ≤ 4 ∧ 0 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars: E
Locations: l0, l1, l2
Transitions:
t₁₁: l0(X₀) → l1(0)
t₁₂: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 3 ∧ X₀ ≤ 4 ∧ 0 ≤ X₀
t₁₃: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 3 ∧ X₀ ≤ 4 ∧ 0 ≤ X₀
t₁₄: l1(X₀) → l2(X₀) :|: 4 ≤ X₀ ∧ E+1 ≤ 0 ∧ X₀ ≤ 4 ∧ 0 ≤ X₀
t₁₅: l1(X₀) → l2(X₀) :|: 4 ≤ X₀ ∧ X₀ ≤ 4 ∧ 0 ≤ X₀

Found invariant X₀ ≤ 4 ∧ 4 ≤ X₀ for location l2

Found invariant X₀ ≤ 4 ∧ 0 ≤ X₀ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₁₂ 10 {O(1)}

TWN-Loops:

entry: t₁₁: l0(X₀) → l1(0)
results in twn-loop: twn:Inv: [X₀ ≤ 4 ∧ 0 ≤ X₀ ∧ X₀ ≤ 4 ∧ 0 ≤ X₀] , (X₀) -> (X₀+1) :|: X₀ ≤ 3 ∨ X₀ ≤ 3
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 3 ∧ 3 ≤ X₀
∨ 1 < 0
∨ X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 3 ∧ 3 ≤ X₀

Stabilization-Threshold for: X₀ ≤ 3
alphas_abs: 3
M: 0
N: 1
Bound: 8 {O(1)}

relevant size-bounds w.r.t. t₁₁:
Runtime-bound of t₁₁: 1 {O(1)}
Results in: 10 {O(1)}

10 {O(1)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₃ 10 {O(1)}

relevant size-bounds w.r.t. t₁₁:
Runtime-bound of t₁₁: 1 {O(1)}
Results in: 10 {O(1)}

10 {O(1)}

All Bounds

Timebounds

Overall timebound:23 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 10 {O(1)}
t₁₃: 10 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}

Costbounds

Overall costbound: 23 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 10 {O(1)}
t₁₃: 10 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}

Sizebounds

t₁₁, X₀: 0 {O(1)}
t₁₂, X₀: 4 {O(1)}
t₁₃, X₀: 4 {O(1)}
t₁₄, X₀: 4 {O(1)}
t₁₅, X₀: 4 {O(1)}