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 < 20
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 20 ≤ X₀
t₁: l2(X₀, X₁, X₂) → l1(0, X₁, X₂)
t₄: l3(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₀ ≤ 9
t₅: l3(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: 9 < X₀
t₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
Eliminate variables {X₁,X₂} that do not contribute to the problem
Found invariant 20 ≤ X₀ for location l5
Found invariant 0 ≤ X₀ for location l1
Found invariant 20 ≤ X₀ for location l4
Found invariant X₀ ≤ 19 ∧ 0 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₄: l0(X₀) → l2(X₀)
t₁₅: l1(X₀) → l3(X₀) :|: X₀ < 20 ∧ 0 ≤ X₀
t₁₆: l1(X₀) → l4(X₀) :|: 20 ≤ X₀ ∧ 0 ≤ X₀
t₁₇: l2(X₀) → l1(0)
t₁₈: l3(X₀) → l1(X₀+1) :|: X₀ ≤ 9 ∧ X₀ ≤ 19 ∧ 0 ≤ X₀
t₁₉: l3(X₀) → l1(X₀+1) :|: 9 < X₀ ∧ X₀ ≤ 19 ∧ 0 ≤ X₀
t₂₀: l4(X₀) → l5(X₀) :|: 20 ≤ X₀
Found invariant X₀ ≤ 20 ∧ 20 ≤ X₀ for location l5
Found invariant X₀ ≤ 20 ∧ 0 ≤ X₀ for location l1
Found invariant X₀ ≤ 20 ∧ 20 ≤ X₀ for location l4
Found invariant X₀ ≤ 19 ∧ 0 ≤ X₀ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₁₇:
X₀: 0 {O(1)}
Runtime-bound of t₁₇: 1 {O(1)}
Results in: 84 {O(1)}
relevant size-bounds w.r.t. t₁₇:
X₀: 0 {O(1)}
Runtime-bound of t₁₇: 1 {O(1)}
Results in: 84 {O(1)}
relevant size-bounds w.r.t. t₁₇:
X₀: 0 {O(1)}
Runtime-bound of t₁₇: 1 {O(1)}
Results in: 84 {O(1)}
Overall timebound:256 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 84 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 84 {O(1)}
t₁₉: 84 {O(1)}
t₂₀: 1 {O(1)}
Overall costbound: 256 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 84 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 84 {O(1)}
t₁₉: 84 {O(1)}
t₂₀: 1 {O(1)}
t₁₄, X₀: X₀ {O(n)}
t₁₅, X₀: 19 {O(1)}
t₁₆, X₀: 20 {O(1)}
t₁₇, X₀: 0 {O(1)}
t₁₈, X₀: 10 {O(1)}
t₁₉, X₀: 20 {O(1)}
t₂₀, X₀: 20 {O(1)}