Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₀ ≤ 10
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 10 < X₀
t₁: l2(X₀, X₁, X₂) → l1(0, X₁, X₂)
t₄: l3(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂)
t₅: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)

Preprocessing

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

Found invariant 11 ≤ X₀ for location l5

Found invariant 0 ≤ X₀ for location l1

Found invariant 11 ≤ X₀ for location l4

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₂: l0(X₀) → l2(X₀)
t₁₃: l1(X₀) → l3(X₀) :|: X₀ ≤ 10 ∧ 0 ≤ X₀
t₁₄: l1(X₀) → l4(X₀) :|: 10 < X₀ ∧ 0 ≤ X₀
t₁₅: l2(X₀) → l1(0)
t₁₆: l3(X₀) → l1(X₀+1) :|: X₀ ≤ 10 ∧ 0 ≤ X₀
t₁₇: l4(X₀) → l5(X₀) :|: 11 ≤ X₀

Found invariant X₀ ≤ 11 ∧ 11 ≤ X₀ for location l5

Found invariant X₀ ≤ 11 ∧ 0 ≤ X₀ for location l1

Found invariant X₀ ≤ 11 ∧ 11 ≤ X₀ for location l4

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₃ 24 {O(1)}

TWN-Loops:

entry: t₁₅: l2(X₀) → l1(0)
results in twn-loop: twn:Inv: [0 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀] , (X₀) -> (X₀+1) :|: X₀ ≤ 10
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₀ < 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 10 ∧ 10 ≤ X₀

Stabilization-Threshold for: X₀ ≤ 10
alphas_abs: 10
M: 0
N: 1
Bound: 22 {O(1)}

relevant size-bounds w.r.t. t₁₅:
Runtime-bound of t₁₅: 1 {O(1)}
Results in: 24 {O(1)}

24 {O(1)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₆ 24 {O(1)}

relevant size-bounds w.r.t. t₁₅:
Runtime-bound of t₁₅: 1 {O(1)}
Results in: 24 {O(1)}

24 {O(1)}

All Bounds

Timebounds

Overall timebound:52 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 24 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 24 {O(1)}
t₁₇: 1 {O(1)}

Costbounds

Overall costbound: 52 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 24 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 24 {O(1)}
t₁₇: 1 {O(1)}

Sizebounds

t₁₂, X₀: X₀ {O(n)}
t₁₃, X₀: 10 {O(1)}
t₁₄, X₀: 11 {O(1)}
t₁₅, X₀: 0 {O(1)}
t₁₆, X₀: 11 {O(1)}
t₁₇, X₀: 11 {O(1)}