KoAT2 Proof Output

Initial Problem

Start: f2
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇
Temp_Vars: S, T, U, V, W, X
Locations: f1, f13, f2, f20, f31, f45, f60
Transitions:
t₁₆: f13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₁
t₃: f13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f20(X₀, X₁, 1+X₁, S, T, 1, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₁ ≤ X₀
t₀: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f1(1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₀ ≤ 1 ∧ 1 ≤ X₀
t₁: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f13(X₀, 1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₀ ≤ 0
t₂: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f13(X₀, 1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 2 ≤ X₀
t₄: f20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f20(X₀, X₁, X₂, S*T+X₃, U*V+X₄, 1+X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₅ ≤ X₁
t₁₃: f20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f31(X₀, X₁, X₂, X₃, X₄, 1, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ 0
t₁₄: f20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f31(X₀, X₁, X₂, X₃, X₄, 1, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₁ ≤ X₅ ∧ 1 ≤ X₄
t₁₅: f20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f31(X₀, X₁, X₂, X₃, 0, 1, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₁ ≤ X₅ ∧ 0 ≤ X₄ ∧ X₄ ≤ 0
t₁₀: f31(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f1(X₀, X₁, X₀, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₁ ≤ X₅ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₅: f31(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f31(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₅ ≤ X₁
t₁₁: f31(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f45(X₀, X₁, X₂, X₃, X₄, 1, S, T, U, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₅
t₁₂: f31(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f45(X₀, X₁, X₂, X₃, X₄, 1, S, T, U, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₅
t₆: f45(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f45(X₀, X₁, X₂, X₃, X₄, 1+X₅, S*T+X₆, U*V+X₇, W*X+X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₅ ≤ X₁
t₉: f45(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f60(X₀, X₁, X₂, X₃, X₄, 1, X₆, X₇, X₈, S, X₁, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, T, U) :|: 2⋅V ≤ 1+X₁ ∧ 2⋅W ≤ 1+X₁ ∧ 1+X₁ ≤ X₅ ∧ 2+X₁ ≤ 3⋅V ∧ 2+X₁ ≤ 3⋅W ∧ W ≤ S ∧ S ≤ V
t₈: f60(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f13(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₉ ≤ X₅
t₇: f60(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f60(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆, X₇, X₈, X₉, X₁₀-1, S, T, U, V, X₁₀, X₁₆, X₁₇) :|: X₅ ≤ X₉

Preprocessing

Eliminate variables [X; X₃; X₆; X₇; X₈; X₁₀; X₁₁; X₁₂; X₁₃; X₁₄; X₁₅; X₁₆; X₁₇] that do not contribute to the problem

Found invariant X₄ ≤ 3 ∧ X₄ ≤ X₂ ∧ X₂+X₄ ≤ 6 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 5 ∧ X₄ ≤ 1+X₀ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 2+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ 3 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 5 ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f45

Found invariant X₁ ≤ 2 ∧ 1 ≤ X₁ for location f13

Found invariant X₀ ≤ 3 for location f1

Found invariant X₅ ≤ 1 ∧ X₅ ≤ X₄ ∧ X₄+X₅ ≤ 3 ∧ 1+X₅ ≤ X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ X₁ ∧ X₁+X₅ ≤ 2 ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₂+X₅ ∧ X₂ ≤ 1+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₄ ≤ 2 ∧ X₄ ≤ X₂ ∧ X₂+X₄ ≤ 4 ∧ X₄ ≤ 1+X₁ ∧ X₁+X₄ ≤ 3 ∧ X₄ ≤ 1+X₀ ∧ 1 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ 2 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 3 ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f60

Problem after Preprocessing

Start: f2
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: S, T, U, V, W
Locations: f1, f13, f2, f20, f31, f45, f60
Transitions:
t₃₅: f13(X₀, X₁, X₂, X₃, X₄, X₅) → f1(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ X₁ ≤ 2 ∧ 1 ≤ X₁
t₃₆: f13(X₀, X₁, X₂, X₃, X₄, X₅) → f20(X₀, X₁, 1+X₁, T, 1, X₅) :|: X₁ ≤ X₀ ∧ X₁ ≤ 2 ∧ 1 ≤ X₁
t₃₇: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f1(1, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 1 ∧ 1 ≤ X₀
t₃₈: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f13(X₀, 1, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0
t₃₉: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f13(X₀, 1, X₂, X₃, X₄, X₅) :|: 2 ≤ X₀
t₄₀: f20(X₀, X₁, X₂, X₃, X₄, X₅) → f20(X₀, X₁, X₂, U*V+X₃, 1+X₄, X₅) :|: X₄ ≤ X₁ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂
t₄₁: f20(X₀, X₁, X₂, X₃, X₄, X₅) → f31(X₀, X₁, X₂, X₃, 1, X₅) :|: 1+X₁ ≤ X₄ ∧ 1+X₃ ≤ 0 ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂
t₄₂: f20(X₀, X₁, X₂, X₃, X₄, X₅) → f31(X₀, X₁, X₂, X₃, 1, X₅) :|: 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂
t₄₃: f20(X₀, X₁, X₂, X₃, X₄, X₅) → f31(X₀, X₁, X₂, 0, 1, X₅) :|: 1+X₁ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂
t₄₄: f31(X₀, X₁, X₂, X₃, X₄, X₅) → f1(X₀, X₁, X₀, X₃, X₄, X₅) :|: 1+X₁ ≤ X₄ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂
t₄₅: f31(X₀, X₁, X₂, X₃, X₄, X₅) → f31(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ X₁ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂
t₄₆: f31(X₀, X₁, X₂, X₃, X₄, X₅) → f45(X₀, X₁, X₂, X₃, 1, X₅) :|: 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₄ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂
t₄₇: f31(X₀, X₁, X₂, X₃, X₄, X₅) → f45(X₀, X₁, X₂, X₃, 1, X₅) :|: 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂
t₄₈: f45(X₀, X₁, X₂, X₃, X₄, X₅) → f45(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ X₁ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂
t₄₉: f45(X₀, X₁, X₂, X₃, X₄, X₅) → f60(X₀, X₁, X₂, X₃, 1, S) :|: 2⋅V ≤ 1+X₁ ∧ 2⋅W ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 2+X₁ ≤ 3⋅V ∧ 2+X₁ ≤ 3⋅W ∧ W ≤ S ∧ S ≤ V ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂
t₅₀: f60(X₀, X₁, X₂, X₃, X₄, X₅) → f13(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₅ ≤ X₄ ∧ X₂+X₄ ≤ 4 ∧ X₁+X₂ ≤ 3 ∧ X₁+X₄ ≤ 3 ∧ X₂+X₅ ≤ 3 ∧ X₄+X₅ ≤ 3 ∧ X₁+X₅ ≤ 2 ∧ X₂ ≤ 2 ∧ X₄ ≤ 2 ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1 ∧ X₂ ≤ 1+X₄ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₅ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₂+X₅ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₅ ≤ X₄
t₅₁: f60(X₀, X₁, X₂, X₃, X₄, X₅) → f60(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ X₅ ∧ X₂+X₄ ≤ 4 ∧ X₁+X₂ ≤ 3 ∧ X₁+X₄ ≤ 3 ∧ X₂+X₅ ≤ 3 ∧ X₄+X₅ ≤ 3 ∧ X₁+X₅ ≤ 2 ∧ X₂ ≤ 2 ∧ X₄ ≤ 2 ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1 ∧ X₂ ≤ 1+X₄ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₅ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₂+X₅ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₅ ≤ X₄

MPRF for transition t₃₆: f13(X₀, X₁, X₂, X₃, X₄, X₅) → f20(X₀, X₁, 1+X₁, T, 1, X₅) :|: X₁ ≤ X₀ ∧ X₁ ≤ 2 ∧ 1 ≤ X₁ of depth 1:

new bound:

4 {O(1)}

MPRF:

• f13: [3-X₁]
• f20: [3-X₂]
• f31: [3-X₂]
• f45: [3-X₂]
• f60: [3-X₂]

MPRF for transition t₄₀: f20(X₀, X₁, X₂, X₃, X₄, X₅) → f20(X₀, X₁, X₂, Temp_Int₈₀₁+X₃, 1+X₄, X₅) :|: X₄ ≤ X₁ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂ of depth 1:

new bound:

6 {O(1)}

MPRF:

• f13: [5-X₁]
• f20: [7-X₂-X₄]
• f31: [7-2⋅X₂]
• f45: [5-2⋅X₁]
• f60: [9-6⋅X₅]

MPRF for transition t₄₁: f20(X₀, X₁, X₂, X₃, X₄, X₅) → f31(X₀, X₁, X₂, X₃, 1, X₅) :|: 1+X₁ ≤ X₄ ∧ 1+X₃ ≤ 0 ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂ of depth 1:

new bound:

5 {O(1)}

MPRF:

• f13: [4-X₁]
• f20: [5-X₂]
• f31: [4-X₂]
• f45: [3-X₁]
• f60: [3-X₁]

MPRF for transition t₄₂: f20(X₀, X₁, X₂, X₃, X₄, X₅) → f31(X₀, X₁, X₂, X₃, 1, X₅) :|: 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂ of depth 1:

new bound:

X₀+4 {O(n)}

MPRF:

• f13: [3+X₀-X₁]
• f20: [4+X₀-X₂]
• f31: [3+X₀-X₂]
• f45: [3+X₀-X₂]
• f60: [2+X₀-X₁]

MPRF for transition t₄₃: f20(X₀, X₁, X₂, X₃, X₄, X₅) → f31(X₀, X₁, X₂, 0, 1, X₅) :|: 1+X₁ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂ of depth 1:

new bound:

X₀+4 {O(n)}

MPRF:

• f13: [3+X₀-X₁]
• f20: [4+X₀-X₂]
• f31: [3+X₀-X₂]
• f45: [2+X₀-X₁]
• f60: [2+X₀-X₁]

MPRF for transition t₄₅: f31(X₀, X₁, X₂, X₃, X₄, X₅) → f31(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ X₁ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂ of depth 1:

new bound:

5 {O(1)}

MPRF:

• f13: [4-X₁]
• f20: [4-X₁]
• f31: [7+X₁-2⋅X₂-X₄]
• f45: [7+X₁-3⋅X₂]
• f60: [7+X₁-3⋅X₂]

MPRF for transition t₄₆: f31(X₀, X₁, X₂, X₃, X₄, X₅) → f45(X₀, X₁, X₂, X₃, 1, X₅) :|: 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₄ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂ of depth 1:

new bound:

4 {O(1)}

MPRF:

• f13: [3-X₁]
• f20: [3-X₁]
• f31: [3-X₁]
• f45: [3-X₂]
• f60: [3-X₂]

MPRF for transition t₄₇: f31(X₀, X₁, X₂, X₃, X₄, X₅) → f45(X₀, X₁, X₂, X₃, 1, X₅) :|: 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂ of depth 1:

new bound:

4 {O(1)}

MPRF:

• f13: [3-X₁]
• f20: [3-X₁]
• f31: [3-X₁]
• f45: [2-X₁]
• f60: [4+X₁-2⋅X₂]

MPRF for transition t₄₈: f45(X₀, X₁, X₂, X₃, X₄, X₅) → f45(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ X₁ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂ of depth 1:

new bound:

X₀+3 {O(n)}

MPRF:

• f13: [2+X₀-X₁]
• f20: [3+X₀-X₂]
• f31: [3+X₀-X₂]
• f45: [4+X₀-X₂-X₄]
• f60: [4+X₀-2⋅X₂]

MPRF for transition t₄₉: f45(X₀, X₁, X₂, X₃, X₄, X₅) → f60(X₀, X₁, X₂, X₃, 1, S) :|: 2⋅V ≤ 1+X₁ ∧ 2⋅W ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 2+X₁ ≤ 3⋅V ∧ 2+X₁ ≤ 3⋅W ∧ W ≤ S ∧ S ≤ V ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂ of depth 1:

new bound:

4 {O(1)}

MPRF:

• f13: [3-X₁]
• f20: [3-X₁]
• f31: [4-X₂]
• f45: [4-X₂]
• f60: [2-X₁]

MPRF for transition t₅₀: f60(X₀, X₁, X₂, X₃, X₄, X₅) → f13(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₅ ≤ X₄ ∧ X₂+X₄ ≤ 4 ∧ X₁+X₂ ≤ 3 ∧ X₁+X₄ ≤ 3 ∧ X₂+X₅ ≤ 3 ∧ X₄+X₅ ≤ 3 ∧ X₁+X₅ ≤ 2 ∧ X₂ ≤ 2 ∧ X₄ ≤ 2 ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1 ∧ X₂ ≤ 1+X₄ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₅ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₂+X₅ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₅ ≤ X₄ of depth 1:

new bound:

3 {O(1)}

MPRF:

• f13: [2-X₁]
• f20: [3-X₂]
• f31: [3-X₂]
• f45: [2-X₁]
• f60: [2-X₁]

MPRF for transition t₅₁: f60(X₀, X₁, X₂, X₃, X₄, X₅) → f60(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ X₅ ∧ X₂+X₄ ≤ 4 ∧ X₁+X₂ ≤ 3 ∧ X₁+X₄ ≤ 3 ∧ X₂+X₅ ≤ 3 ∧ X₄+X₅ ≤ 3 ∧ X₁+X₅ ≤ 2 ∧ X₂ ≤ 2 ∧ X₄ ≤ 2 ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1 ∧ X₂ ≤ 1+X₄ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₅ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₅ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₂+X₅ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₅ ≤ X₄ of depth 1:

new bound:

4 {O(1)}

MPRF:

• f13: [3-X₁]
• f20: [3-X₁]
• f31: [3-X₁]
• f45: [3-X₁]
• f60: [3+X₂-2⋅X₁-X₄]

knowledge_propagation leads to new time bound 6 {O(1)} for transition t₄₂: f20(X₀, X₁, X₂, X₃, X₄, X₅) → f31(X₀, X₁, X₂, X₃, 1, X₅) :|: 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂

knowledge_propagation leads to new time bound 6 {O(1)} for transition t₄₃: f20(X₀, X₁, X₂, X₃, X₄, X₅) → f31(X₀, X₁, X₂, 0, 1, X₅) :|: 1+X₁ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ X₂+X₄ ≤ 6 ∧ X₁+X₂ ≤ 5 ∧ X₁+X₄ ≤ 5 ∧ X₂ ≤ 3 ∧ X₄ ≤ 3 ∧ X₁ ≤ 2 ∧ X₂ ≤ 2+X₄ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₄ ≤ 1+X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₂

All Bounds

Timebounds

Overall timebound:X₀+59 {O(n)}
t₃₅: 1 {O(1)}
t₃₆: 4 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 6 {O(1)}
t₄₁: 5 {O(1)}
t₄₂: 6 {O(1)}
t₄₃: 6 {O(1)}
t₄₄: 1 {O(1)}
t₄₅: 5 {O(1)}
t₄₆: 4 {O(1)}
t₄₇: 4 {O(1)}
t₄₈: X₀+3 {O(n)}
t₄₉: 4 {O(1)}
t₅₀: 3 {O(1)}
t₅₁: 4 {O(1)}

Costbounds

Overall costbound: X₀+59 {O(n)}
t₃₅: 1 {O(1)}
t₃₆: 4 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 6 {O(1)}
t₄₁: 5 {O(1)}
t₄₂: 6 {O(1)}
t₄₃: 6 {O(1)}
t₄₄: 1 {O(1)}
t₄₅: 5 {O(1)}
t₄₆: 4 {O(1)}
t₄₇: 4 {O(1)}
t₄₈: X₀+3 {O(n)}
t₄₉: 4 {O(1)}
t₅₀: 3 {O(1)}
t₅₁: 4 {O(1)}

Sizebounds

t₃₅, X₀: 2⋅X₀+2 {O(n)}
t₃₅, X₁: 2 {O(1)}
t₃₅, X₂: X₂+2 {O(n)}
t₃₅, X₄: X₄+2 {O(n)}
t₃₅, X₅: X₅+1 {O(n)}
t₃₆, X₀: X₀+2 {O(n)}
t₃₆, X₁: 2 {O(1)}
t₃₆, X₂: 3 {O(1)}
t₃₆, X₄: 1 {O(1)}
t₃₆, X₅: X₅+1 {O(n)}
t₃₇, X₀: 1 {O(1)}
t₃₇, X₁: X₁ {O(n)}
t₃₇, X₂: X₂ {O(n)}
t₃₇, X₃: X₃ {O(n)}
t₃₇, X₄: X₄ {O(n)}
t₃₇, X₅: X₅ {O(n)}
t₃₈, X₀: X₀ {O(n)}
t₃₈, X₁: 1 {O(1)}
t₃₈, X₂: X₂ {O(n)}
t₃₈, X₃: X₃ {O(n)}
t₃₈, X₄: X₄ {O(n)}
t₃₈, X₅: X₅ {O(n)}
t₃₉, X₀: X₀ {O(n)}
t₃₉, X₁: 1 {O(1)}
t₃₉, X₂: X₂ {O(n)}
t₃₉, X₃: X₃ {O(n)}
t₃₉, X₄: X₄ {O(n)}
t₃₉, X₅: X₅ {O(n)}
t₄₀, X₀: X₀+2 {O(n)}
t₄₀, X₁: 2 {O(1)}
t₄₀, X₂: 3 {O(1)}
t₄₀, X₄: 3 {O(1)}
t₄₀, X₅: X₅+1 {O(n)}
t₄₁, X₀: X₀+2 {O(n)}
t₄₁, X₁: 2 {O(1)}
t₄₁, X₂: 3 {O(1)}
t₄₁, X₄: 1 {O(1)}
t₄₁, X₅: X₅+1 {O(n)}
t₄₂, X₀: X₀+2 {O(n)}
t₄₂, X₁: 2 {O(1)}
t₄₂, X₂: 3 {O(1)}
t₄₂, X₄: 1 {O(1)}
t₄₂, X₅: X₅+1 {O(n)}
t₄₃, X₀: X₀+2 {O(n)}
t₄₃, X₁: 2 {O(1)}
t₄₃, X₂: 3 {O(1)}
t₄₃, X₃: 0 {O(1)}
t₄₃, X₄: 1 {O(1)}
t₄₃, X₅: X₅+1 {O(n)}
t₄₄, X₀: 3 {O(1)}
t₄₄, X₁: 2 {O(1)}
t₄₄, X₂: 3 {O(1)}
t₄₄, X₄: 3 {O(1)}
t₄₄, X₅: 3⋅X₅+3 {O(n)}
t₄₅, X₀: X₀+2 {O(n)}
t₄₅, X₁: 2 {O(1)}
t₄₅, X₂: 3 {O(1)}
t₄₅, X₄: 3 {O(1)}
t₄₅, X₅: 3⋅X₅+3 {O(n)}
t₄₆, X₀: X₀+2 {O(n)}
t₄₆, X₁: 2 {O(1)}
t₄₆, X₂: 3 {O(1)}
t₄₆, X₄: 1 {O(1)}
t₄₆, X₅: 3⋅X₅+3 {O(n)}
t₄₇, X₀: 2 {O(1)}
t₄₇, X₁: 2 {O(1)}
t₄₇, X₂: 3 {O(1)}
t₄₇, X₄: 1 {O(1)}
t₄₇, X₅: 3⋅X₅+3 {O(n)}
t₄₈, X₀: X₀+2 {O(n)}
t₄₈, X₁: 2 {O(1)}
t₄₈, X₂: 3 {O(1)}
t₄₈, X₄: 3 {O(1)}
t₄₈, X₅: 6⋅X₅+6 {O(n)}
t₄₉, X₀: X₀+2 {O(n)}
t₄₉, X₁: 1 {O(1)}
t₄₉, X₂: 2 {O(1)}
t₄₉, X₄: 1 {O(1)}
t₄₉, X₅: 1 {O(1)}
t₅₀, X₀: X₀+2 {O(n)}
t₅₀, X₁: 2 {O(1)}
t₅₀, X₂: 2 {O(1)}
t₅₀, X₄: 2 {O(1)}
t₅₀, X₅: 1 {O(1)}
t₅₁, X₀: X₀+2 {O(n)}
t₅₁, X₁: 1 {O(1)}
t₅₁, X₂: 2 {O(1)}
t₅₁, X₄: 2 {O(1)}
t₅₁, X₅: 1 {O(1)}