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
Locations: f1, f2, f26, f32, f5, f52, f55, f62, f9
Transitions:
t₀: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 2 ≤ X₀
t₄: f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f26(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₃ ≤ X₀
t₁₆: f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃
t₅: f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f32(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, 0, 0, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₃ ≤ X₀
t₆: f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f32(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, S, (S)², (S)²+X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+S ≤ 0 ∧ X₃ ≤ X₀
t₇: f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f32(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, S, (S)², (S)²+X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1 ≤ S ∧ X₃ ≤ X₀
t₁₄: f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, S, T, T, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃
t₁₅: f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, -S, T, S, X₁₇) :|: 1+X₀ ≤ X₃
t₂₀: f5(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+S ≤ 0 ∧ X₀ ≤ X₁
t₂₁: f5(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 ≤ S ∧ X₀ ≤ X₁
t₂₂: f5(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) :|: X₀ ≤ X₁
t₁: f5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f9(X₀, X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₁ ≤ X₀
t₁₃: f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f5(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₁₀
t₈: f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f55(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₁₀ ≤ X₀
t₉: f55(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f55(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, X₇, X₈, S*T+X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₃ ≤ X₀
t₁₂: f55(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f62(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, S, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₉ ≤ T+T*U ∧ 1+X₉ ≤ U*V+V ∧ 1+X₀ ≤ X₃ ∧ V ≤ S ∧ S ≤ T ∧ T*U ≤ X₉ ∧ U*V ≤ X₉
t₁₁: f62(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, 1+X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃
t₁₀: f62(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f62(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₃ ≤ X₀
t₁₈: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0
t₁₉: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃ ∧ 1 ≤ X₂
t₁₇: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f5(X₀, 1+X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, 0) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₂: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f9(X₀, X₁, X₂, 1+X₃, X₂, S, S, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+S ≤ X₂ ∧ X₃ ≤ X₀
t₃: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f9(X₀, X₁, S, 1+X₃, X₂, S, S, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₂ ≤ S ∧ X₃ ≤ X₀

Preprocessing

Cut unsatisfiable transition [t₄: f26→f26; t₁₀: f62→f62]

Eliminate variables [X₄; X₅; X₆; X₇; X₈; X₁₁; X₁₂; X₁₃; X₁₄; X₁₅; X₁₆; X₁₇] that do not contribute to the problem

Found invariant 1+X₅ ≤ X₃ ∧ X₅ ≤ X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location f55

Found invariant 2 ≤ X₀ for location f5

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location f52

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location f32

Found invariant 1+X₅ ≤ X₃ ∧ X₅ ≤ X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location f62

Found invariant 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location f9

Found invariant 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location f1

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location f26

Cut unsatisfiable transition [t₅₃: f32→f32; t₅₄: f32→f32; t₅₅: f32→f32; t₆₄: f55→f55; t₆₇: f9→f26]

Problem after Preprocessing

Start: f2
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: S, T, U, V
Locations: f1, f2, f26, f32, f5, f52, f55, f62, f9
Transitions:
t₅₁: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f5(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2 ≤ X₀
t₅₂: f26(X₀, X₁, X₂, X₃, X₄, X₅) → f32(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃
t₅₆: f32(X₀, X₁, X₂, X₃, X₄, X₅) → f52(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃
t₅₇: f32(X₀, X₁, X₂, X₃, X₄, X₅) → f52(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃
t₅₈: f5(X₀, X₁, X₂, X₃, X₄, X₅) → f1(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+S ≤ 0 ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₅₉: f5(X₀, X₁, X₂, X₃, X₄, X₅) → f1(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ S ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₆₀: f5(X₀, X₁, X₂, X₃, X₄, X₅) → f1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀
t₆₁: f5(X₀, X₁, X₂, X₃, X₄, X₅) → f9(X₀, X₁, 0, X₃, X₄, X₅) :|: 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₂: f52(X₀, X₁, X₂, X₃, X₄, X₅) → f5(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₅ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃
t₆₃: f52(X₀, X₁, X₂, X₃, X₄, X₅) → f55(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃
t₆₅: f55(X₀, X₁, X₂, X₃, X₄, X₅) → f62(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₄ ≤ T+T*U ∧ 1+X₄ ≤ U*V+V ∧ 1+X₀ ≤ X₃ ∧ V ≤ S ∧ S ≤ T ∧ T*U ≤ X₄ ∧ U*V ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₅ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₅ ≤ X₀
t₆₆: f62(X₀, X₁, X₂, X₃, X₄, X₅) → f52(X₀, X₁, X₂, X₃, X₄, 1+X₅) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₅ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₅ ≤ X₀
t₆₈: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f26(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₂
t₆₉: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f5(X₀, 1+X₁, 0, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂
t₇₀: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f9(X₀, X₁, X₂, 1+X₃, X₄, X₅) :|: 1+S ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₂
t₇₁: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f9(X₀, X₁, S, 1+X₃, X₄, X₅) :|: X₂ ≤ S ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₂

MPRF for transition t₅₂: f26(X₀, X₁, X₂, X₃, X₄, X₅) → f32(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

• f26: [X₀-X₁]
• f32: [X₀-1-X₁]
• f5: [X₀-X₁]
• f52: [X₀-1-X₁]
• f55: [X₀-1-X₁]
• f62: [X₀-1-X₁]
• f9: [X₀-X₁]

MPRF for transition t₅₆: f32(X₀, X₁, X₂, X₃, X₄, X₅) → f52(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

• f26: [X₀-X₁]
• f32: [X₀-X₁]
• f5: [X₀-X₁]
• f52: [X₀-1-X₁]
• f55: [X₀-1-X₁]
• f62: [X₀-1-X₁]
• f9: [X₀-X₁]

MPRF for transition t₅₇: f32(X₀, X₁, X₂, X₃, X₄, X₅) → f52(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

• f26: [X₀-X₁]
• f32: [X₀-X₁]
• f5: [X₀-X₁]
• f52: [X₀-1-X₁]
• f55: [X₀-1-X₁]
• f62: [X₀-1-X₁]
• f9: [X₀-X₁]

MPRF for transition t₆₁: f5(X₀, X₁, X₂, X₃, X₄, X₅) → f9(X₀, X₁, 0, X₃, X₄, X₅) :|: 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

• f26: [X₀-1-X₁]
• f32: [X₀-1-X₁]
• f5: [X₀-X₁]
• f52: [X₀-1-X₁]
• f55: [X₀-1-X₁]
• f62: [X₀-1-X₁]
• f9: [X₀-1-X₁]

MPRF for transition t₆₂: f52(X₀, X₁, X₂, X₃, X₄, X₅) → f5(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₅ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• f26: [1+X₀-X₁]
• f32: [1+X₀-X₁]
• f5: [1+X₀-X₁]
• f52: [1+X₀-X₁]
• f55: [1+X₀-X₁]
• f62: [1+X₀-X₁]
• f9: [1+X₀-X₁]

MPRF for transition t₆₃: f52(X₀, X₁, X₂, X₃, X₄, X₅) → f55(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃ of depth 1:

new bound:

2⋅X₀+X₅ {O(n)}

MPRF:

• f26: [2⋅X₀-X₅]
• f32: [2⋅X₀-X₅]
• f5: [2⋅X₀-X₅]
• f52: [2⋅X₀-X₅]
• f55: [2⋅X₀-1-X₅]
• f62: [2⋅X₀-1-X₅]
• f9: [2⋅X₀-X₅]

MPRF for transition t₆₅: f55(X₀, X₁, X₂, X₃, X₄, X₅) → f62(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₄ ≤ T+TU ∧ 1+X₄ ≤ UV+V ∧ 1+X₀ ≤ X₃ ∧ V ≤ S ∧ S ≤ T ∧ TU ≤ X₄ ∧ UV ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₅ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₅ ≤ X₀ of depth 1:

new bound:

2⋅X₅+3⋅X₀ {O(n)}

MPRF:

• f26: [3⋅X₀-2⋅X₅]
• f32: [3⋅X₀-2⋅X₅]
• f5: [3⋅X₀-2⋅X₅]
• f52: [3⋅X₀-2⋅X₅]
• f55: [3⋅X₀-1-2⋅X₅]
• f62: [3⋅X₀-2-2⋅X₅]
• f9: [3⋅X₀-2⋅X₅]

MPRF for transition t₆₆: f62(X₀, X₁, X₂, X₃, X₄, X₅) → f52(X₀, X₁, X₂, X₃, X₄, 1+X₅) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₅ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₅ ≤ X₀ of depth 1:

new bound:

2⋅X₅+3⋅X₀ {O(n)}

MPRF:

• f26: [3⋅X₀-2⋅X₅]
• f32: [3⋅X₀-2⋅X₅]
• f5: [3⋅X₀-2⋅X₅]
• f52: [3⋅X₀-2⋅X₅]
• f55: [3⋅X₀-2⋅X₅]
• f62: [3⋅X₀-1-2⋅X₅]
• f9: [3⋅X₀-2⋅X₅]

MPRF for transition t₆₈: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f26(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

• f26: [X₀-1-X₁]
• f32: [X₀-1-X₁]
• f5: [X₀-X₁]
• f52: [X₀-1-X₁]
• f55: [X₀-1-X₁]
• f62: [X₀-1-X₁]
• f9: [X₀-X₁]

MPRF for transition t₆₉: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f5(X₀, 1+X₁, 0, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

• f26: [X₀-X₁]
• f32: [X₀-X₁]
• f5: [X₀-X₁]
• f52: [X₀-X₁]
• f55: [X₀-X₁]
• f62: [X₀-X₁]
• f9: [X₀-X₁]

MPRF for transition t₇₀: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f9(X₀, X₁, X₂, 1+X₃, X₄, X₅) :|: 1+S ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₀+X₃ {O(n)}

MPRF:

• f26: [2⋅X₀-X₃]
• f32: [2⋅X₀-X₃]
• f5: [2⋅X₀-X₃]
• f52: [2⋅X₀-X₃]
• f55: [2⋅X₀-X₃]
• f62: [2⋅X₀-X₃]
• f9: [2⋅X₀-X₃]

MPRF for transition t₇₁: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f9(X₀, X₁, S, 1+X₃, X₄, X₅) :|: X₂ ≤ S ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₀+X₃ {O(n)}

MPRF:

• f26: [2⋅X₀-X₃]
• f32: [2⋅X₀-X₃]
• f5: [2⋅X₀-X₃]
• f52: [2⋅X₀-X₃]
• f55: [2⋅X₀-X₃]
• f62: [2⋅X₀-X₃]
• f9: [2⋅X₀-X₃]

All Bounds

Timebounds

Overall timebound:19⋅X₀+2⋅X₃+5⋅X₅+7⋅X₁+5 {O(n)}
t₅₁: 1 {O(1)}
t₅₂: X₀+X₁ {O(n)}
t₅₆: X₀+X₁ {O(n)}
t₅₇: X₀+X₁ {O(n)}
t₅₈: 1 {O(1)}
t₅₉: 1 {O(1)}
t₆₀: 1 {O(1)}
t₆₁: X₀+X₁ {O(n)}
t₆₂: X₀+X₁+1 {O(n)}
t₆₃: 2⋅X₀+X₅ {O(n)}
t₆₅: 2⋅X₅+3⋅X₀ {O(n)}
t₆₆: 2⋅X₅+3⋅X₀ {O(n)}
t₆₈: X₀+X₁ {O(n)}
t₆₉: X₀+X₁ {O(n)}
t₇₀: 2⋅X₀+X₃ {O(n)}
t₇₁: 2⋅X₀+X₃ {O(n)}

Costbounds

Overall costbound: 19⋅X₀+2⋅X₃+5⋅X₅+7⋅X₁+5 {O(n)}
t₅₁: 1 {O(1)}
t₅₂: X₀+X₁ {O(n)}
t₅₆: X₀+X₁ {O(n)}
t₅₇: X₀+X₁ {O(n)}
t₅₈: 1 {O(1)}
t₅₉: 1 {O(1)}
t₆₀: 1 {O(1)}
t₆₁: X₀+X₁ {O(n)}
t₆₂: X₀+X₁+1 {O(n)}
t₆₃: 2⋅X₀+X₅ {O(n)}
t₆₅: 2⋅X₅+3⋅X₀ {O(n)}
t₆₆: 2⋅X₅+3⋅X₀ {O(n)}
t₆₈: X₀+X₁ {O(n)}
t₆₉: X₀+X₁ {O(n)}
t₇₀: 2⋅X₀+X₃ {O(n)}
t₇₁: 2⋅X₀+X₃ {O(n)}

Sizebounds

t₅₁, X₀: X₀ {O(n)}
t₅₁, X₁: X₁ {O(n)}
t₅₁, X₂: X₂ {O(n)}
t₅₁, X₃: X₃ {O(n)}
t₅₁, X₄: X₄ {O(n)}
t₅₁, X₅: X₅ {O(n)}
t₅₂, X₀: X₀ {O(n)}
t₅₂, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₅₂, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₂, X₄: X₄ {O(n)}
t₅₂, X₅: 3⋅X₀+3⋅X₅ {O(n)}
t₅₆, X₀: X₀ {O(n)}
t₅₆, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₅₆, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₆, X₄: X₄ {O(n)}
t₅₆, X₅: 3⋅X₀+3⋅X₅ {O(n)}
t₅₇, X₀: X₀ {O(n)}
t₅₇, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₅₇, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₇, X₄: X₄ {O(n)}
t₅₇, X₅: 3⋅X₀+3⋅X₅ {O(n)}
t₅₈, X₀: 3⋅X₀ {O(n)}
t₅₈, X₁: 4⋅X₀+7⋅X₁+2 {O(n)}
t₅₈, X₃: 7⋅X₃+8⋅X₀ {O(n)}
t₅₈, X₄: 3⋅X₄ {O(n)}
t₅₈, X₅: 6⋅X₀+7⋅X₅ {O(n)}
t₅₉, X₀: 3⋅X₀ {O(n)}
t₅₉, X₁: 4⋅X₀+7⋅X₁+2 {O(n)}
t₅₉, X₃: 7⋅X₃+8⋅X₀ {O(n)}
t₅₉, X₄: 3⋅X₄ {O(n)}
t₅₉, X₅: 6⋅X₀+7⋅X₅ {O(n)}
t₆₀, X₀: 3⋅X₀ {O(n)}
t₆₀, X₁: 4⋅X₀+7⋅X₁+2 {O(n)}
t₆₀, X₃: 7⋅X₃+8⋅X₀ {O(n)}
t₆₀, X₄: 3⋅X₄ {O(n)}
t₆₀, X₅: 6⋅X₀+7⋅X₅ {O(n)}
t₆₁, X₀: X₀ {O(n)}
t₆₁, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₆₁, X₂: 0 {O(1)}
t₆₁, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₁, X₄: X₄ {O(n)}
t₆₁, X₅: 3⋅X₀+3⋅X₅ {O(n)}
t₆₂, X₀: X₀ {O(n)}
t₆₂, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₆₂, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₂, X₄: X₄ {O(n)}
t₆₂, X₅: 3⋅X₀+3⋅X₅ {O(n)}
t₆₃, X₀: X₀ {O(n)}
t₆₃, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₆₃, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₃, X₄: X₄ {O(n)}
t₆₃, X₅: 3⋅X₀+3⋅X₅ {O(n)}
t₆₅, X₀: X₀ {O(n)}
t₆₅, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₆₅, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₅, X₄: X₄ {O(n)}
t₆₅, X₅: 3⋅X₀+3⋅X₅ {O(n)}
t₆₆, X₀: X₀ {O(n)}
t₆₆, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₆₆, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₆, X₄: X₄ {O(n)}
t₆₆, X₅: 3⋅X₀+3⋅X₅ {O(n)}
t₆₈, X₀: X₀ {O(n)}
t₆₈, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₆₈, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₈, X₄: X₄ {O(n)}
t₆₈, X₅: 3⋅X₀+3⋅X₅ {O(n)}
t₆₉, X₀: X₀ {O(n)}
t₆₉, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₆₉, X₂: 0 {O(1)}
t₆₉, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₉, X₄: X₄ {O(n)}
t₆₉, X₅: 3⋅X₀+3⋅X₅ {O(n)}
t₇₀, X₀: X₀ {O(n)}
t₇₀, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₇₀, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₇₀, X₄: X₄ {O(n)}
t₇₀, X₅: 3⋅X₀+3⋅X₅ {O(n)}
t₇₁, X₀: X₀ {O(n)}
t₇₁, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₇₁, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₇₁, X₄: X₄ {O(n)}
t₇₁, X₅: 3⋅X₀+3⋅X₅ {O(n)}