Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂
Temp_Vars: A1, B1, X, Y, Z
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₁₂: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l1(X₀, X₁, X₂, Y, X₄, 0, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, 0) :|: Y ≤ 0
t₁₃: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l1(X₀, X₁, X₂, Y, X₄, 0, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, 0) :|: 1 ≤ Y
t₁₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l1(X₀+1, X₁, 1, X₃, X₄, X₅, X₆, X, Y, Z, A1, X₄, X, X, X, X, X₁₇, X₁₇, 1, 1, 1, 0, X₂₂) :|: X ≤ 0 ∧ X₀+1 ≤ X₁
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l2(X₀, X₁, B1, X₃, X₄, X₅, X₆, X, Y, Z, A1, X₄, X, X, X, X, X₁₇, 0, B1, B1, B1, 0, X₂₂) :|: X₀+1 ≤ X₁ ∧ X ≤ 0 ∧ 2 ≤ B1
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l2(X₀, X₁, B1, X₃, X₄, X₅, X₆, X, Y, Z, A1, X₄, X, X, X, X, X₁₇, 0, B1, B1, B1, 0, X₂₂) :|: X₀+1 ≤ X₁ ∧ X ≤ 0 ∧ B1 ≤ 0
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₁ ≤ X₀
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X, Y, Z, A1, X₄, X, X, X, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 1 ≤ X ∧ X₀+1 ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 3 ≤ X₂
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₂ ≤ 1
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, 2, X₃, X₄+1, X₅, X₇, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₂ ≤ 2 ∧ 2 ≤ X₂
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l4(X₀, X₁, X₂, X₃, 0, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 1 ≤ X₃
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l4(X₀, X₁, X₂, X₃, 0, 0, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₃ ≤ 0
t₃: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂)
t₄: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂)
Cut unreachable locations [l5; l6] from the program graph
Eliminate variables {A1,Z,X₄,X₅,X₆,X₇,X₈,X₉,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₁₆,X₁₇,X₁₈,X₁₉,X₂₀,X₂₁,X₂₂} that do not contribute to the problem
Found invariant 1+X₀ ≤ X₁ for location l2
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: B1, X, Y
Locations: l0, l1, l2, l3, l4
Transitions:
t₃₀: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, Y) :|: Y ≤ 0
t₃₁: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, Y) :|: 1 ≤ Y
t₃₆: l1(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, 1, X₃) :|: X ≤ 0 ∧ X₀+1 ≤ X₁
t₃₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, B1, X₃) :|: X₀+1 ≤ X₁ ∧ X ≤ 0 ∧ 2 ≤ B1
t₃₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, B1, X₃) :|: X₀+1 ≤ X₁ ∧ X ≤ 0 ∧ B1 ≤ 0
t₃₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₃₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 ≤ X ∧ X₀+1 ≤ X₁
t₃₇: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 3 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₃₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₂ ≤ 1 ∧ 1+X₀ ≤ X₁
t₃₉: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, 2, X₃) :|: X₂ ≤ 2 ∧ 2 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₄₀: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃
t₄₁: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0
t₄₂: l4(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
new bound:
2⋅X₀+2⋅X₁ {O(n)}
MPRF:
l1 [X₁-X₀ ]
Found invariant 1+X₀ ≤ X₁ for location l2
Overall timebound:inf {Infinity}
t₃₀: 1 {O(1)}
t₃₁: 1 {O(1)}
t₃₂: 1 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: 1 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 2⋅X₀+2⋅X₁ {O(n)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}
t₄₁: 1 {O(1)}
t₄₂: inf {Infinity}
Overall costbound: inf {Infinity}
t₃₀: 1 {O(1)}
t₃₁: 1 {O(1)}
t₃₂: 1 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: 1 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 2⋅X₀+2⋅X₁ {O(n)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}
t₄₁: 1 {O(1)}
t₄₂: inf {Infinity}
t₃₀, X₀: X₀ {O(n)}
t₃₀, X₁: X₁ {O(n)}
t₃₀, X₂: X₂ {O(n)}
t₃₁, X₀: X₀ {O(n)}
t₃₁, X₁: X₁ {O(n)}
t₃₁, X₂: X₂ {O(n)}
t₃₂, X₀: 2⋅X₁+6⋅X₀ {O(n)}
t₃₂, X₁: 4⋅X₁ {O(n)}
t₃₂, X₂: 2⋅X₂+1 {O(n)}
t₃₃, X₀: 2⋅X₁+6⋅X₀ {O(n)}
t₃₃, X₁: 4⋅X₁ {O(n)}
t₃₃, X₂: 2⋅X₂+1 {O(n)}
t₃₄, X₀: 2⋅X₁+6⋅X₀ {O(n)}
t₃₄, X₁: 4⋅X₁ {O(n)}
t₃₅, X₀: 2⋅X₁+6⋅X₀ {O(n)}
t₃₅, X₁: 4⋅X₁ {O(n)}
t₃₆, X₀: 2⋅X₁+4⋅X₀ {O(n)}
t₃₆, X₁: 2⋅X₁ {O(n)}
t₃₆, X₂: 1 {O(1)}
t₃₇, X₀: 2⋅X₁+6⋅X₀ {O(n)}
t₃₇, X₁: 4⋅X₁ {O(n)}
t₃₈, X₀: 2⋅X₁+6⋅X₀ {O(n)}
t₃₈, X₁: 4⋅X₁ {O(n)}
t₃₉, X₀: 2⋅X₁+6⋅X₀ {O(n)}
t₃₉, X₁: 4⋅X₁ {O(n)}
t₃₉, X₂: 2 {O(1)}
t₄₀, X₀: 10⋅X₁+30⋅X₀ {O(n)}
t₄₀, X₁: 20⋅X₁ {O(n)}
t₄₁, X₀: 10⋅X₁+30⋅X₀ {O(n)}
t₄₁, X₁: 20⋅X₁ {O(n)}
t₄₂, X₀: 20⋅X₁+60⋅X₀ {O(n)}
t₄₂, X₁: 40⋅X₁ {O(n)}