KoAT2 Proof Output

Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: H, I
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(5, 13, 0, 0, X₄, X₅, X₆)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₂+1, X₄, X₅, X₆) :|: X₃+1 ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆) :|: X₃+1 ≤ X₀ ∧ X₃+1 ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆) :|: X₃+1 ≤ X₀ ∧ 1+X₂ ≤ X₃
t₁₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, 0, X₄, X₅, X₆) :|: X₀ ≤ X₃
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, 0, X₅, X₆) :|: X₃+1 ≤ X₀
t₁₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, 0, X₄, X₅, X₆) :|: X₀ ≤ X₃
t₁₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆) :|: X₁ ≤ X₄
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄+1, H, I) :|: X₄+1 ≤ X₁
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃+1, X₄, H, I) :|: X₃+1 ≤ X₁
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, H, I) :|: X₃+1 ≤ X₁
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, 0, X₄, X₅, X₆) :|: X₁ ≤ X₃
t₉: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ X₃
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆) :|: X₃+1 ≤ X₀

Preprocessing

Cut unsatisfiable transition t₂: l1→l1

Eliminate variables {H,I,X₅,X₆} that do not contribute to the problem

Found invariant X₃ ≤ 5 ∧ X₃ ≤ 5+X₂ ∧ X₂+X₃ ≤ 5 ∧ 8+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 18 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 10 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ for location l2

Found invariant X₃ ≤ 12 ∧ X₃ ≤ 12+X₂ ∧ X₂+X₃ ≤ 12 ∧ 1+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 25 ∧ X₃ ≤ 7+X₀ ∧ X₀+X₃ ≤ 17 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ for location l5

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ for location l4

Found invariant 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ 4+X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 13 ≤ X₁+X₄ ∧ X₁ ≤ 13+X₄ ∧ 5 ≤ X₀+X₄ ∧ X₀ ≤ 5+X₄ ∧ X₃ ≤ 4 ∧ X₃ ≤ 4+X₂ ∧ X₂+X₃ ≤ 4 ∧ 9+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 17 ∧ 1+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 9 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₃₆: l0(X₀, X₁, X₂, X₃, X₄) → l1(5, 13, 0, 0, X₄)
t₃₇: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₂+1, X₄) :|: X₃+1 ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 5 ∧ X₃ ≤ 5+X₂ ∧ X₂+X₃ ≤ 5 ∧ 8+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 18 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 10 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀
t₃₈: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃+1, X₄) :|: X₃+1 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₃ ≤ 5 ∧ X₃ ≤ 5+X₂ ∧ X₂+X₃ ≤ 5 ∧ 8+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 18 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 10 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀
t₃₉: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, 0, X₄) :|: X₀ ≤ X₃ ∧ X₃ ≤ 5 ∧ X₃ ≤ 5+X₂ ∧ X₂+X₃ ≤ 5 ∧ 8+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 18 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 10 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀
t₄₀: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, 0) :|: X₃+1 ≤ X₀ ∧ X₃ ≤ 5 ∧ X₃ ≤ 5+X₂ ∧ X₂+X₃ ≤ 5 ∧ 8+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 18 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 10 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀
t₄₁: l2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, 0, X₄) :|: X₀ ≤ X₃ ∧ X₃ ≤ 5 ∧ X₃ ≤ 5+X₂ ∧ X₂+X₃ ≤ 5 ∧ 8+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 18 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 10 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀
t₄₂: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃+1, X₄) :|: X₁ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ 4+X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 13 ≤ X₁+X₄ ∧ X₁ ≤ 13+X₄ ∧ 5 ≤ X₀+X₄ ∧ X₀ ≤ 5+X₄ ∧ X₃ ≤ 4 ∧ X₃ ≤ 4+X₂ ∧ X₂+X₃ ≤ 4 ∧ 9+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 17 ∧ 1+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 9 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀
t₄₃: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄+1) :|: X₄+1 ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ 4+X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 13 ≤ X₁+X₄ ∧ X₁ ≤ 13+X₄ ∧ 5 ≤ X₀+X₄ ∧ X₀ ≤ 5+X₄ ∧ X₃ ≤ 4 ∧ X₃ ≤ 4+X₂ ∧ X₂+X₃ ≤ 4 ∧ 9+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 17 ∧ 1+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 9 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀
t₄₄: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃+1, X₄) :|: X₃+1 ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀
t₄₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₃+1 ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀
t₄₆: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, 0, X₄) :|: X₁ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀
t₄₇: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃ ∧ X₃ ≤ 5 ∧ X₃ ≤ 5+X₂ ∧ X₂+X₃ ≤ 5 ∧ 8+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 18 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 10 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀
t₄₈: l6(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃+1, X₄) :|: X₃+1 ≤ X₀ ∧ X₃ ≤ 5 ∧ X₃ ≤ 5+X₂ ∧ X₂+X₃ ≤ 5 ∧ 8+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 18 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 10 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₃₇: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₂+1, X₄) :|: X₃+1 ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 5 ∧ X₃ ≤ 5+X₂ ∧ X₂+X₃ ≤ 5 ∧ 8+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 18 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 10 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀

MPRF for transition t₃₈: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃+1, X₄) :|: X₃+1 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₃ ≤ 5 ∧ X₃ ≤ 5+X₂ ∧ X₂+X₃ ≤ 5 ∧ 8+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 18 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 10 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ of depth 1:

new bound:

21 {O(1)}

MPRF for transition t₄₀: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, 0) :|: X₃+1 ≤ X₀ ∧ X₃ ≤ 5 ∧ X₃ ≤ 5+X₂ ∧ X₂+X₃ ≤ 5 ∧ 8+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 18 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 10 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ of depth 1:

new bound:

6 {O(1)}

MPRF for transition t₄₂: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃+1, X₄) :|: X₁ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ 4+X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 13 ≤ X₁+X₄ ∧ X₁ ≤ 13+X₄ ∧ 5 ≤ X₀+X₄ ∧ X₀ ≤ 5+X₄ ∧ X₃ ≤ 4 ∧ X₃ ≤ 4+X₂ ∧ X₂+X₃ ≤ 4 ∧ 9+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 17 ∧ 1+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 9 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ of depth 1:

new bound:

21 {O(1)}

TWN: t₄₃: l3→l3

cycle: [t₄₃: l3→l3]
loop: (X₄+1 ≤ X₁,(X₁,X₄) -> (X₁,X₄+1)
order: [X₁; X₄]
closed-form:

X₁: X₁
X₄: X₄ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₄+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₄+1 ≤ X₁ ∧ X₁ ≤ X₄+1

Stabilization-Threshold for: X₄+1 ≤ X₁

alphas_abs: X₄+1+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₄+4 {O(n)}

TWN - Lifting for t₄₃: l3→l3 of 2⋅X₁+2⋅X₄+6 {O(n)}

relevant size-bounds w.r.t. t₄₀:
X₁: 13 {O(1)}
X₄: 0 {O(1)}
Runtime-bound of t₄₀: 6 {O(1)}
Results in: 192 {O(1)}

MPRF for transition t₄₄: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃+1, X₄) :|: X₃+1 ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ of depth 1:

new bound:

13 {O(1)}

MPRF for transition t₄₈: l6(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃+1, X₄) :|: X₃+1 ≤ X₀ ∧ X₃ ≤ 5 ∧ X₃ ≤ 5+X₂ ∧ X₂+X₃ ≤ 5 ∧ 8+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 18 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 10 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 13 ≤ X₁+X₃ ∧ X₁ ≤ 13+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₀ ≤ 5+X₃ ∧ X₂ ≤ 0 ∧ 13+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 13 ∧ 5+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 5 ∧ 0 ≤ X₂ ∧ 13 ≤ X₁+X₂ ∧ X₁ ≤ 13+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 5+X₂ ∧ X₁ ≤ 13 ∧ X₁ ≤ 8+X₀ ∧ X₀+X₁ ≤ 18 ∧ 13 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ 8+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ of depth 1:

new bound:

6 {O(1)}

All Bounds

Timebounds

Overall timebound:266 {O(1)}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 21 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 6 {O(1)}
t₄₁: 1 {O(1)}
t₄₂: 21 {O(1)}
t₄₃: 192 {O(1)}
t₄₄: 13 {O(1)}
t₄₅: 1 {O(1)}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}
t₄₈: 6 {O(1)}

Costbounds

Overall costbound: 266 {O(1)}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 21 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 6 {O(1)}
t₄₁: 1 {O(1)}
t₄₂: 21 {O(1)}
t₄₃: 192 {O(1)}
t₄₄: 13 {O(1)}
t₄₅: 1 {O(1)}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}
t₄₈: 6 {O(1)}

Sizebounds

t₃₆, X₀: 5 {O(1)}
t₃₆, X₁: 13 {O(1)}
t₃₆, X₂: 0 {O(1)}
t₃₆, X₃: 0 {O(1)}
t₃₆, X₄: X₄ {O(n)}
t₃₇, X₀: 5 {O(1)}
t₃₇, X₁: 13 {O(1)}
t₃₇, X₂: 0 {O(1)}
t₃₇, X₃: 1 {O(1)}
t₃₇, X₄: X₄ {O(n)}
t₃₈, X₀: 5 {O(1)}
t₃₈, X₁: 13 {O(1)}
t₃₈, X₂: 0 {O(1)}
t₃₈, X₃: 5 {O(1)}
t₃₈, X₄: X₄ {O(n)}
t₃₉, X₀: 5 {O(1)}
t₃₉, X₁: 13 {O(1)}
t₃₉, X₂: 0 {O(1)}
t₃₉, X₃: 0 {O(1)}
t₃₉, X₄: X₄ {O(n)}
t₄₀, X₀: 5 {O(1)}
t₄₀, X₁: 13 {O(1)}
t₄₀, X₂: 0 {O(1)}
t₄₀, X₃: 4 {O(1)}
t₄₀, X₄: 0 {O(1)}
t₄₁, X₀: 5 {O(1)}
t₄₁, X₁: 13 {O(1)}
t₄₁, X₂: 0 {O(1)}
t₄₁, X₃: 0 {O(1)}
t₄₁, X₄: 13 {O(1)}
t₄₂, X₀: 5 {O(1)}
t₄₂, X₁: 13 {O(1)}
t₄₂, X₂: 0 {O(1)}
t₄₂, X₃: 5 {O(1)}
t₄₂, X₄: 13 {O(1)}
t₄₃, X₀: 5 {O(1)}
t₄₃, X₁: 13 {O(1)}
t₄₃, X₂: 0 {O(1)}
t₄₃, X₃: 4 {O(1)}
t₄₃, X₄: 13 {O(1)}
t₄₄, X₀: 5 {O(1)}
t₄₄, X₁: 13 {O(1)}
t₄₄, X₂: 0 {O(1)}
t₄₄, X₃: 13 {O(1)}
t₄₄, X₄: 13 {O(1)}
t₄₅, X₀: 5 {O(1)}
t₄₅, X₁: 13 {O(1)}
t₄₅, X₂: 0 {O(1)}
t₄₅, X₃: 12 {O(1)}
t₄₅, X₄: 26 {O(1)}
t₄₆, X₀: 5 {O(1)}
t₄₆, X₁: 13 {O(1)}
t₄₆, X₂: 0 {O(1)}
t₄₆, X₃: 0 {O(1)}
t₄₆, X₄: 13 {O(1)}
t₄₇, X₀: 5 {O(1)}
t₄₇, X₁: 13 {O(1)}
t₄₇, X₂: 0 {O(1)}
t₄₇, X₃: 5 {O(1)}
t₄₇, X₄: 13 {O(1)}
t₄₈, X₀: 5 {O(1)}
t₄₈, X₁: 13 {O(1)}
t₄₈, X₂: 0 {O(1)}
t₄₈, X₃: 5 {O(1)}
t₄₈, X₄: 13 {O(1)}