Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4
Transitions:
t₄: l0(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(1+X₀, X₁, X₀, X₃) :|: X₀ ≤ 9
t₀: l1(X₀, X₁, X₂, X₃) → l2(X₀, E, X₂, X₃) :|: 10 ≤ X₀
t₂: l3(X₀, X₁, X₂, X₃) → l1(1, X₁, X₂, X₃) :|: E ≤ 9 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₃: l4(X₀, X₁, X₂, X₃) → l1(2, X₁, X₂, 2) :|: X₀ ≤ 9

Preprocessing

Cut unreachable locations [l3; l4] from the program graph

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

Found invariant X₀ ≤ 10 ∧ 10 ≤ X₀ for location l2

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₉: l0(X₀) → l1(0)
t₁₁: l1(X₀) → l1(1+X₀) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₁₀: l1(X₀) → l2(X₀) :|: 10 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀

Found invariant X₀ ≤ 10 ∧ 10 ≤ X₀ for location l2

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₁₁ 22 {O(1)}

TWN-Loops:

entry: t₉: l0(X₀) → l1(0)
results in twn-loop: twn:Inv: [X₀ ≤ 10 ∧ 0 ≤ X₀] , (X₀) -> (1+X₀) :|: X₀ ≤ 9
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₀ < 9 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 9 ∧ 9 ≤ X₀

Stabilization-Threshold for: X₀ ≤ 9
alphas_abs: 9
M: 0
N: 1
Bound: 20 {O(1)}

relevant size-bounds w.r.t. t₉:
Runtime-bound of t₉: 1 {O(1)}
Results in: 22 {O(1)}

22 {O(1)}

All Bounds

Timebounds

Overall timebound:24 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 22 {O(1)}

Costbounds

Overall costbound: 24 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 22 {O(1)}

Sizebounds

t₉, X₀: 0 {O(1)}
t₁₀, X₀: 10 {O(1)}
t₁₁, X₀: 10 {O(1)}