Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(C, 0)
t₁: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₁ ≤ 9
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: 10 ≤ X₁

Preprocessing

Eliminate variables {C,X₀} that do not contribute to the problem

Found invariant X₁ ≤ 10 ∧ 10 ≤ X₁ for location l2

Found invariant X₁ ≤ 10 ∧ 0 ≤ X₁ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₁) → l1(0)
t₈: l1(X₁) → l1(X₁+1) :|: X₁ ≤ 9 ∧ X₁ ≤ 10 ∧ 0 ≤ X₁
t₉: l1(X₁) → l2(X₁) :|: 10 ≤ X₁ ∧ X₁ ≤ 10 ∧ 0 ≤ X₁

Found invariant X₁ ≤ 10 ∧ 10 ≤ X₁ for location l2

Found invariant X₁ ≤ 10 ∧ 0 ≤ X₁ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₈ 22 {O(1)}

TWN-Loops:

entry: t₇: l0(X₁) → l1(0)
results in twn-loop: twn:Inv: [X₁ ≤ 10 ∧ 0 ≤ X₁] , (X₁) -> (X₁+1) :|: X₁ ≤ 9
order: [X₁]
closed-form:
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁ < 9 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 9 ∧ 9 ≤ X₁

Stabilization-Threshold for: X₁ ≤ 9
alphas_abs: 9
M: 0
N: 1
Bound: 20 {O(1)}

relevant size-bounds w.r.t. t₇:
Runtime-bound of t₇: 1 {O(1)}
Results in: 22 {O(1)}

22 {O(1)}

All Bounds

Timebounds

Overall timebound:24 {O(1)}
t₇: 1 {O(1)}
t₈: 22 {O(1)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: 24 {O(1)}
t₇: 1 {O(1)}
t₈: 22 {O(1)}
t₉: 1 {O(1)}

Sizebounds

t₇, X₁: 0 {O(1)}
t₈, X₁: 10 {O(1)}
t₉, X₁: 10 {O(1)}