Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars: K, L
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(K, 0, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀, X₁+1, X₂+1, 1, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₂ ≤ 15
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀, X₁, X₂+1, 0, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₂ ≤ 15
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₃, X₁, X₁, K, L, L, L) :|: 16 ≤ X₂

Preprocessing

Eliminate variables {K,L,X₀,X₁,X₃,X₄,X₅,X₆,X₇,X₈,X₉} that do not contribute to the problem

Found invariant X₂ ≤ 16 ∧ 16 ≤ X₂ for location l2

Found invariant X₂ ≤ 16 ∧ 0 ≤ X₂ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₉: l0(X₂) → l1(0)
t₁₀: l1(X₂) → l1(X₂+1) :|: X₂ ≤ 15 ∧ X₂ ≤ 16 ∧ 0 ≤ X₂
t₁₁: l1(X₂) → l1(X₂+1) :|: X₂ ≤ 15 ∧ X₂ ≤ 16 ∧ 0 ≤ X₂
t₁₂: l1(X₂) → l2(X₂) :|: 16 ≤ X₂ ∧ X₂ ≤ 16 ∧ 0 ≤ X₂

Found invariant X₂ ≤ 16 ∧ 16 ≤ X₂ for location l2

Found invariant X₂ ≤ 16 ∧ 0 ≤ X₂ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₁₀ 34 {O(1)}

TWN-Loops:

entry: t₉: l0(X₂) → l1(0)
results in twn-loop: twn:Inv: [X₂ ≤ 16 ∧ 0 ≤ X₂ ∧ X₂ ≤ 16 ∧ 0 ≤ X₂] , (X₂) -> (X₂+1) :|: X₂ ≤ 15 ∨ X₂ ≤ 15
order: [X₂]
closed-form:
X₂: X₂ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₂ < 15 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ ≤ 15 ∧ 15 ≤ X₂
∨ 1 < 0
∨ X₂ < 15 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ ≤ 15 ∧ 15 ≤ X₂

Stabilization-Threshold for: X₂ ≤ 15
alphas_abs: 15
M: 0
N: 1
Bound: 32 {O(1)}

relevant size-bounds w.r.t. t₉:
Runtime-bound of t₉: 1 {O(1)}
Results in: 34 {O(1)}

34 {O(1)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₁ 34 {O(1)}

relevant size-bounds w.r.t. t₉:
Runtime-bound of t₉: 1 {O(1)}
Results in: 34 {O(1)}

34 {O(1)}

All Bounds

Timebounds

Overall timebound:70 {O(1)}
t₉: 1 {O(1)}
t₁₀: 34 {O(1)}
t₁₁: 34 {O(1)}
t₁₂: 1 {O(1)}

Costbounds

Overall costbound: 70 {O(1)}
t₉: 1 {O(1)}
t₁₀: 34 {O(1)}
t₁₁: 34 {O(1)}
t₁₂: 1 {O(1)}

Sizebounds

t₉, X₂: 0 {O(1)}
t₁₀, X₂: 16 {O(1)}
t₁₁, X₂: 16 {O(1)}
t₁₂, X₂: 16 {O(1)}