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) :|: 0 < X₁
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ ≤ 0
t₁: l2(X₀, X₁, X₂) → l1(X₂, 1, X₂)
t₄: l3(X₀, X₁, X₂) → l1(X₀-1, 1, X₂) :|: 0 < X₀ ∧ 0 < X₀
t₅: l3(X₀, X₁, X₂) → l1(X₀, 1, X₂) :|: 0 < X₀ ∧ X₀ ≤ 0
t₆: l3(X₀, X₁, X₂) → l1(X₀-1, 0, X₂) :|: X₀ ≤ 0 ∧ 0 < X₀
t₇: l3(X₀, X₁, X₂) → l1(X₀, 0, X₂) :|: X₀ ≤ 0 ∧ X₀ ≤ 0
t₈: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
Cut unsatisfiable transition t₅: l3→l1
Cut unsatisfiable transition t₆: l3→l1
Found invariant X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l5
Found invariant X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 0 ≤ X₁ for location l1
Found invariant X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l4
Found invariant X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ for location l3
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) :|: 0 < X₁ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 0 ≤ X₁
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 0 ≤ X₁
t₁: l2(X₀, X₁, X₂) → l1(X₂, 1, X₂)
t₄: l3(X₀, X₁, X₂) → l1(X₀-1, 1, X₂) :|: 0 < X₀ ∧ 0 < X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₇: l3(X₀, X₁, X₂) → l1(X₀, 0, X₂) :|: X₀ ≤ 0 ∧ X₀ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₈: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁
new bound:
X₂ {O(n)}
MPRF:
l3 [X₀ ]
l1 [X₀ ]
new bound:
1 {O(1)}
MPRF:
l3 [1 ]
l1 [X₁ ]
Found invariant X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l5
Found invariant X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 0 ≤ X₁ for location l1
Found invariant X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l4
Found invariant X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₁:
X₀: X₂ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₂+5 {O(n)}
Overall timebound:3⋅X₂+10 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₂+5 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₂ {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
Overall costbound: 3⋅X₂+10 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₂+5 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₂ {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₂, X₀: X₂ {O(n)}
t₂, X₁: 1 {O(1)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: X₂ {O(n)}
t₃, X₁: 0 {O(1)}
t₃, X₂: X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: 1 {O(1)}
t₁, X₂: X₂ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: 1 {O(1)}
t₄, X₂: X₂ {O(n)}
t₇, X₀: X₂ {O(n)}
t₇, X₁: 0 {O(1)}
t₇, X₂: X₂ {O(n)}
t₈, X₀: X₂ {O(n)}
t₈, X₁: 0 {O(1)}
t₈, X₂: X₂ {O(n)}