Initial Problem
Start: f0
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, C1, X, Y, Z
Locations: f0, f16, f18, f28, f35, f37, f52, f76
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f16(1, X, Y, Z, A1, B1, C1, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₀ ≤ 1 ∧ 1 ≤ X₀
t₃: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f28(X₀, X, Y, Z, A1, B1, C1, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₀ ≤ 0
t₄: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f28(X₀, X, Y, Z, A1, B1, C1, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 2 ≤ X₀
t₁: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₈ ≤ X₇
t₂₃: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 1+X₇ ≤ X₈
t₂₂: f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1+X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 1+X₉ ≤ X₁₀
t₂: f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, 1+X₁₀, 2+X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₁₀ ≤ X₉
t₅: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, 2+X₇-X₈, 1, 0, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₈ ≤ X₇ ∧ X₈ ≤ 0
t₆: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, 2+X₇-X₈, 1, 0, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 2 ≤ X₈ ∧ X₈ ≤ X₇
t₇: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1, X₉, X₁₀, X₁₁, 1, 1, 0, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₈ ≤ 1 ∧ 1 ≤ X₇ ∧ 1 ≤ X₈
t₁₉: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f76(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 1+X₇ ≤ X₈ ∧ 2+X₀ ≤ 0
t₂₀: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f76(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 1+X₇ ≤ X₈ ∧ 0 ≤ X₀
t₂₁: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f76(-1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 0 ≤ 1+X₀ ∧ 1+X₀ ≤ 0 ∧ 1+X₇ ≤ X₈
t₁₈: f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1+X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 1+X₁₅ ≤ 3⋅X ∧ 2+X ≤ X₁₆ ∧ 2⋅X ≤ X₁₅
t₈: f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₁₆ ≤ 1+X ∧ 1+X₁₅ ≤ 3⋅X ∧ 2⋅X ≤ X₁₅
t₁₇: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f35(X₀, X₁, X₂, X₃, X₁₃, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X, Y, X₁₅, 1+X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, 2+X₂₂) :|: 1+X₉ ≤ X₁₀
t₁₁: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, 1+X₁₀, X, X₁₂, X₁₃, X₁₄, X₁₅, 1, Y, Z, A1, B1, X₂₁, X₂₂) :|: X₁₆ ≤ 1 ∧ 1 ≤ X₁₆ ∧ X₁₀ ≤ X₉ ∧ X₁₀ ≤ 0
t₁₂: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, 1+X₁₀, X, X₁₂, X₁₃, X₁₄, X₁₅, 1, Y, Z, A1, B1, X₂₁, X₂₂) :|: X₁₆ ≤ 1 ∧ 1 ≤ X₁₆ ∧ 2 ≤ X₁₀ ∧ X₁₀ ≤ X₉
t₁₃: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, 2, 1, X₁₂, X₁₃, X₁₄, X₁₅, 1, X, Y, Z, A1, X₂₁, X₂₂) :|: X₁₀ ≤ 1 ∧ X₁₆ ≤ 1 ∧ 1 ≤ X₉ ∧ 1 ≤ X₁₀ ∧ 1 ≤ X₁₆
t₉: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₁₀ ≤ X₉ ∧ X₁₆ ≤ 0
t₁₀: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 2 ≤ X₁₆ ∧ X₁₀ ≤ X₉
t₁₄: f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, 1+X₁₀, 2+X₉-X₁₀, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X, Y, Z, A1, B1, X₂₂) :|: X₁₀ ≤ 0
t₁₅: f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, 1+X₁₀, 2+X₉-X₁₀, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X, Y, Z, A1, B1, X₂₂) :|: 2 ≤ X₁₀
t₁₆: f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, 2, 1, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X, Y, Z, A1, B1, X₂₂) :|: X₁₀ ≤ 1 ∧ 1 ≤ X₁₀
Preprocessing
Eliminate variables [A1; B1; C1; Y; Z; X₁; X₂; X₃; X₄; X₅; X₆; X₁₁; X₁₂; X₁₃; X₁₄; X₁₇; X₁₈; X₁₉; X₂₀; X₂₁; X₂₂] that do not contribute to the problem
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location f18
Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location f16
Found invariant X₂ ≤ X₁ for location f35
Found invariant 1+X₁ ≤ X₂ for location f76
Found invariant X₂ ≤ X₁ for location f37
Found invariant X₄ ≤ X₃ ∧ X₂ ≤ X₁ for location f52
Problem after Preprocessing
Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: X
Locations: f0, f16, f18, f28, f35, f37, f52, f76
Transitions:
t₅₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f16(1, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1 ∧ 1 ≤ X₀
t₅₁: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0
t₅₂: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2 ≤ X₀
t₅₃: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₅₄: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₅₅: f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f16(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆) :|: 1+X₃ ≤ X₄ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁
t₅₆: f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f18(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆) :|: X₄ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁
t₅₇: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₁ ∧ X₂ ≤ 0
t₅₈: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2 ≤ X₂ ∧ X₂ ≤ X₁
t₅₉: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f35(X₀, X₁, 1, X₃, X₄, X₅, X₆) :|: X₂ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂
t₆₀: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f76(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ 0
t₆₁: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f76(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₁ ≤ X₂ ∧ 0 ≤ X₀
t₆₂: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f76(-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ 1+X₀ ∧ 1+X₀ ≤ 0 ∧ 1+X₁ ≤ X₂
t₆₃: f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f28(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆) :|: 1+X₅ ≤ 3⋅X ∧ 2+X ≤ X₆ ∧ 2⋅X ≤ X₅ ∧ X₂ ≤ X₁
t₆₄: f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 1+X ∧ 1+X₅ ≤ 3⋅X ∧ 2⋅X ≤ X₅ ∧ X₂ ≤ X₁
t₆₅: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f35(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆) :|: 1+X₃ ≤ X₄ ∧ X₂ ≤ X₁
t₆₆: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, 1+X₄, X₅, 1) :|: X₆ ≤ 1 ∧ 1 ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 0 ∧ X₂ ≤ X₁
t₆₇: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, 1+X₄, X₅, 1) :|: X₆ ≤ 1 ∧ 1 ≤ X₆ ∧ 2 ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₂ ≤ X₁
t₆₈: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, 2, X₅, 1) :|: X₄ ≤ 1 ∧ X₆ ≤ 1 ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₆ ∧ X₂ ≤ X₁
t₆₉: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ X₃ ∧ X₆ ≤ 0 ∧ X₂ ≤ X₁
t₇₀: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2 ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₂ ≤ X₁
t₇₁: f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆) :|: X₄ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₃
t₇₂: f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆) :|: 2 ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₃
t₇₃: f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, 2, X₅, X₆) :|: X₄ ≤ 1 ∧ 1 ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₃
MPRF for transition t₅₃: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF:
• f16: [1+X₁-X₂]
• f18: [X₁-X₂]
MPRF for transition t₅₅: f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f16(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆) :|: 1+X₃ ≤ X₄ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF:
• f16: [1+X₁-X₂]
• f18: [1+X₁-X₂]
MPRF for transition t₅₆: f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f18(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆) :|: X₄ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ of depth 1:
new bound:
X₃+X₄+1 {O(n)}
MPRF:
• f16: [1+X₃-X₄]
• f18: [1+X₃-X₄]
MPRF for transition t₅₇: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₁ ∧ X₂ ≤ 0 of depth 1:
new bound:
2⋅X₂+2 {O(n)}
MPRF:
• f28: [1-X₂]
• f35: [-X₂]
• f37: [-X₂]
• f52: [-X₂]
MPRF for transition t₅₈: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2 ≤ X₂ ∧ X₂ ≤ X₁ of depth 1:
new bound:
2⋅X₁+2⋅X₂+2 {O(n)}
MPRF:
• f28: [1+X₁-X₂]
• f35: [X₁-X₂]
• f37: [X₁-X₂]
• f52: [X₁-X₂]
MPRF for transition t₅₉: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f35(X₀, X₁, 1, X₃, X₄, X₅, X₆) :|: X₂ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ of depth 1:
new bound:
2⋅X₂+4 {O(n)}
MPRF:
• f28: [2-X₂]
• f35: [1-X₂]
• f37: [1-X₂]
• f52: [1-X₂]
MPRF for transition t₆₃: f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f28(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆) :|: 1+X₅ ≤ 3⋅X ∧ 2+X ≤ X₆ ∧ 2⋅X ≤ X₅ ∧ X₂ ≤ X₁ of depth 1:
new bound:
2⋅X₁+2⋅X₂+2 {O(n)}
MPRF:
• f28: [1+X₁-X₂]
• f35: [1+X₁-X₂]
• f37: [1+X₁-X₂]
• f52: [1+X₁-X₂]
MPRF for transition t₆₄: f35(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 1+X ∧ 1+X₅ ≤ 3⋅X ∧ 2⋅X ≤ X₅ ∧ X₂ ≤ X₁ of depth 1:
new bound:
2⋅X₅+2⋅X₆+2 {O(n)}
MPRF:
• f28: [1+X₅-X₆]
• f35: [1+X₅-X₆]
• f37: [X₅-X₆]
• f52: [X₅-X₆]
MPRF for transition t₆₆: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, 1+X₄, X₅, 1) :|: X₆ ≤ 1 ∧ 1 ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 0 ∧ X₂ ≤ X₁ of depth 1:
new bound:
2⋅X₄+2 {O(n)}
MPRF:
• f28: [1-X₄]
• f35: [1-X₄]
• f37: [1-X₄]
• f52: [-X₄]
MPRF for transition t₆₇: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, 1+X₄, X₅, 1) :|: X₆ ≤ 1 ∧ 1 ≤ X₆ ∧ 2 ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₂ ≤ X₁ of depth 1:
new bound:
2⋅X₄+4⋅X₃ {O(n)}
MPRF:
• f28: [2⋅X₃-X₄]
• f35: [2⋅X₃-X₄]
• f37: [2⋅X₃-X₄]
• f52: [2⋅X₃-X₄]
MPRF for transition t₆₈: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, 2, X₅, 1) :|: X₄ ≤ 1 ∧ X₆ ≤ 1 ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₆ ∧ X₂ ≤ X₁ of depth 1:
new bound:
2⋅X₄+4⋅X₃ {O(n)}
MPRF:
• f28: [2⋅X₃-X₄]
• f35: [2⋅X₃-X₄]
• f37: [2⋅X₃-X₄]
• f52: [2⋅X₃-X₄]
MPRF for transition t₆₉: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ X₃ ∧ X₆ ≤ 0 ∧ X₂ ≤ X₁ of depth 1:
new bound:
2⋅X₃+2⋅X₄+2 {O(n)}
MPRF:
• f28: [1+X₃-X₄]
• f35: [1+X₃-X₄]
• f37: [1+X₃-X₄]
• f52: [X₃-X₄]
MPRF for transition t₇₀: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2 ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₂ ≤ X₁ of depth 1:
new bound:
2⋅X₃+2⋅X₄+2 {O(n)}
MPRF:
• f28: [1+X₃-X₄]
• f35: [1+X₃-X₄]
• f37: [1+X₃-X₄]
• f52: [X₃-X₄]
MPRF for transition t₇₁: f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆) :|: X₄ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₃ of depth 1:
new bound:
2⋅X₄+2 {O(n)}
MPRF:
• f28: [1-X₄]
• f35: [1-X₄]
• f37: [1-X₄]
• f52: [1-X₄]
MPRF for transition t₇₂: f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆) :|: 2 ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₃ of depth 1:
new bound:
4⋅X₄+6⋅X₃ {O(n)}
MPRF:
• f28: [3⋅X₃-2⋅X₄]
• f35: [3⋅X₃-2⋅X₄]
• f37: [3⋅X₃-2⋅X₄]
• f52: [3⋅X₃-1-2⋅X₄]
MPRF for transition t₇₃: f52(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f37(X₀, X₁, X₂, X₃, 2, X₅, X₆) :|: X₄ ≤ 1 ∧ 1 ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₃ of depth 1:
new bound:
2⋅X₄+4⋅X₃ {O(n)}
MPRF:
• f28: [2⋅X₃-X₄]
• f35: [2⋅X₃-X₄]
• f37: [2⋅X₃-X₄]
• f52: [2⋅X₃-X₄]
knowledge_propagation leads to new time bound 14⋅X₄+18⋅X₃+2⋅X₅+2⋅X₆+6 {O(n)} for transition t₆₅: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f35(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆) :|: 1+X₃ ≤ X₄ ∧ X₂ ≤ X₁
All Bounds
Timebounds
Overall timebound:10⋅X₂+33⋅X₄+4⋅X₅+4⋅X₆+41⋅X₃+6⋅X₁+36 {O(n)}
t₅₀: 1 {O(1)}
t₅₁: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: X₁+X₂+1 {O(n)}
t₅₄: 1 {O(1)}
t₅₅: X₁+X₂+1 {O(n)}
t₅₆: X₃+X₄+1 {O(n)}
t₅₇: 2⋅X₂+2 {O(n)}
t₅₈: 2⋅X₁+2⋅X₂+2 {O(n)}
t₅₉: 2⋅X₂+4 {O(n)}
t₆₀: 1 {O(1)}
t₆₁: 1 {O(1)}
t₆₂: 1 {O(1)}
t₆₃: 2⋅X₁+2⋅X₂+2 {O(n)}
t₆₄: 2⋅X₅+2⋅X₆+2 {O(n)}
t₆₅: 14⋅X₄+18⋅X₃+2⋅X₅+2⋅X₆+6 {O(n)}
t₆₆: 2⋅X₄+2 {O(n)}
t₆₇: 2⋅X₄+4⋅X₃ {O(n)}
t₆₈: 2⋅X₄+4⋅X₃ {O(n)}
t₆₉: 2⋅X₃+2⋅X₄+2 {O(n)}
t₇₀: 2⋅X₃+2⋅X₄+2 {O(n)}
t₇₁: 2⋅X₄+2 {O(n)}
t₇₂: 4⋅X₄+6⋅X₃ {O(n)}
t₇₃: 2⋅X₄+4⋅X₃ {O(n)}
Costbounds
Overall costbound: 10⋅X₂+33⋅X₄+4⋅X₅+4⋅X₆+41⋅X₃+6⋅X₁+36 {O(n)}
t₅₀: 1 {O(1)}
t₅₁: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: X₁+X₂+1 {O(n)}
t₅₄: 1 {O(1)}
t₅₅: X₁+X₂+1 {O(n)}
t₅₆: X₃+X₄+1 {O(n)}
t₅₇: 2⋅X₂+2 {O(n)}
t₅₈: 2⋅X₁+2⋅X₂+2 {O(n)}
t₅₉: 2⋅X₂+4 {O(n)}
t₆₀: 1 {O(1)}
t₆₁: 1 {O(1)}
t₆₂: 1 {O(1)}
t₆₃: 2⋅X₁+2⋅X₂+2 {O(n)}
t₆₄: 2⋅X₅+2⋅X₆+2 {O(n)}
t₆₅: 14⋅X₄+18⋅X₃+2⋅X₅+2⋅X₆+6 {O(n)}
t₆₆: 2⋅X₄+2 {O(n)}
t₆₇: 2⋅X₄+4⋅X₃ {O(n)}
t₆₈: 2⋅X₄+4⋅X₃ {O(n)}
t₆₉: 2⋅X₃+2⋅X₄+2 {O(n)}
t₇₀: 2⋅X₃+2⋅X₄+2 {O(n)}
t₇₁: 2⋅X₄+2 {O(n)}
t₇₂: 4⋅X₄+6⋅X₃ {O(n)}
t₇₃: 2⋅X₄+4⋅X₃ {O(n)}
Sizebounds
t₅₀, X₀: 1 {O(1)}
t₅₀, X₁: X₁ {O(n)}
t₅₀, X₂: X₂ {O(n)}
t₅₀, X₃: X₃ {O(n)}
t₅₀, X₄: X₄ {O(n)}
t₅₀, X₅: X₅ {O(n)}
t₅₀, X₆: X₆ {O(n)}
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)}
t₅₁, X₆: X₆ {O(n)}
t₅₂, X₀: X₀ {O(n)}
t₅₂, X₁: X₁ {O(n)}
t₅₂, X₂: X₂ {O(n)}
t₅₂, X₃: X₃ {O(n)}
t₅₂, X₄: X₄ {O(n)}
t₅₂, X₅: X₅ {O(n)}
t₅₂, X₆: X₆ {O(n)}
t₅₃, X₀: 1 {O(1)}
t₅₃, X₁: X₁ {O(n)}
t₅₃, X₂: 2⋅X₂+X₁+1 {O(n)}
t₅₃, X₃: X₃ {O(n)}
t₅₃, X₄: 2⋅X₄+X₃+1 {O(n)}
t₅₃, X₅: X₅ {O(n)}
t₅₃, X₆: X₆ {O(n)}
t₅₄, X₀: 1 {O(1)}
t₅₄, X₁: 2⋅X₁ {O(n)}
t₅₄, X₂: 3⋅X₂+X₁+1 {O(n)}
t₅₄, X₃: 2⋅X₃ {O(n)}
t₅₄, X₄: 3⋅X₄+X₃+1 {O(n)}
t₅₄, X₅: 2⋅X₅ {O(n)}
t₅₄, X₆: 2⋅X₆ {O(n)}
t₅₅, X₀: 1 {O(1)}
t₅₅, X₁: X₁ {O(n)}
t₅₅, X₂: 2⋅X₂+X₁+1 {O(n)}
t₅₅, X₃: X₃ {O(n)}
t₅₅, X₄: 2⋅X₄+X₃+1 {O(n)}
t₅₅, X₅: X₅ {O(n)}
t₅₅, X₆: X₆ {O(n)}
t₅₆, X₀: 1 {O(1)}
t₅₆, X₁: X₁ {O(n)}
t₅₆, X₂: 2⋅X₂+X₁+1 {O(n)}
t₅₆, X₃: X₃ {O(n)}
t₅₆, X₄: 2⋅X₄+X₃+1 {O(n)}
t₅₆, X₅: X₅ {O(n)}
t₅₆, X₆: X₆ {O(n)}
t₅₇, X₀: 2⋅X₀ {O(n)}
t₅₇, X₁: 2⋅X₁ {O(n)}
t₅₇, X₂: 2⋅X₁+4⋅X₂+3 {O(n)}
t₅₇, X₃: 2⋅X₃ {O(n)}
t₅₇, X₄: 10⋅X₃+8⋅X₄+5 {O(n)}
t₅₇, X₅: 2⋅X₅ {O(n)}
t₅₇, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+4⋅X₆+9 {O(n)}
t₅₈, X₀: 2⋅X₀ {O(n)}
t₅₈, X₁: 2⋅X₁ {O(n)}
t₅₈, X₂: 2⋅X₁+4⋅X₂+3 {O(n)}
t₅₈, X₃: 2⋅X₃ {O(n)}
t₅₈, X₄: 10⋅X₃+8⋅X₄+5 {O(n)}
t₅₈, X₅: 2⋅X₅ {O(n)}
t₅₈, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+4⋅X₆+9 {O(n)}
t₅₉, X₀: 2⋅X₀ {O(n)}
t₅₉, X₁: 2⋅X₁ {O(n)}
t₅₉, X₂: 1 {O(1)}
t₅₉, X₃: 2⋅X₃ {O(n)}
t₅₉, X₄: 10⋅X₃+8⋅X₄+5 {O(n)}
t₅₉, X₅: 2⋅X₅ {O(n)}
t₅₉, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+4⋅X₆+9 {O(n)}
t₆₀, X₀: 3⋅X₀ {O(n)}
t₆₀, X₁: 3⋅X₁ {O(n)}
t₆₀, X₂: 2⋅X₁+5⋅X₂+3 {O(n)}
t₆₀, X₃: 3⋅X₃ {O(n)}
t₆₀, X₄: 10⋅X₃+9⋅X₄+5 {O(n)}
t₆₀, X₅: 3⋅X₅ {O(n)}
t₆₀, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+5⋅X₆+9 {O(n)}
t₆₁, X₀: 4⋅X₀+1 {O(n)}
t₆₁, X₁: 6⋅X₁ {O(n)}
t₆₁, X₂: 3⋅X₁+9⋅X₂+4 {O(n)}
t₆₁, X₃: 6⋅X₃ {O(n)}
t₆₁, X₄: 11⋅X₃+13⋅X₄+6 {O(n)}
t₆₁, X₅: 6⋅X₅ {O(n)}
t₆₁, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+8⋅X₆+9 {O(n)}
t₆₂, X₀: 1 {O(1)}
t₆₂, X₁: 3⋅X₁ {O(n)}
t₆₂, X₂: 2⋅X₁+5⋅X₂+3 {O(n)}
t₆₂, X₃: 3⋅X₃ {O(n)}
t₆₂, X₄: 10⋅X₃+9⋅X₄+5 {O(n)}
t₆₂, X₅: 3⋅X₅ {O(n)}
t₆₂, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+5⋅X₆+9 {O(n)}
t₆₃, X₀: 2⋅X₀ {O(n)}
t₆₃, X₁: 2⋅X₁ {O(n)}
t₆₃, X₂: 2⋅X₁+4⋅X₂+3 {O(n)}
t₆₃, X₃: 2⋅X₃ {O(n)}
t₆₃, X₄: 10⋅X₃+8⋅X₄+5 {O(n)}
t₆₃, X₅: 2⋅X₅ {O(n)}
t₆₃, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+4⋅X₆+9 {O(n)}
t₆₄, X₀: 2⋅X₀ {O(n)}
t₆₄, X₁: 2⋅X₁ {O(n)}
t₆₄, X₂: 2⋅X₁+4⋅X₂+3 {O(n)}
t₆₄, X₃: 2⋅X₃ {O(n)}
t₆₄, X₄: 10⋅X₃+8⋅X₄+5 {O(n)}
t₆₄, X₅: 2⋅X₅ {O(n)}
t₆₄, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+4⋅X₆+9 {O(n)}
t₆₅, X₀: 2⋅X₀ {O(n)}
t₆₅, X₁: 2⋅X₁ {O(n)}
t₆₅, X₂: 2⋅X₁+4⋅X₂+3 {O(n)}
t₆₅, X₃: 2⋅X₃ {O(n)}
t₆₅, X₄: 10⋅X₃+8⋅X₄+5 {O(n)}
t₆₅, X₅: 2⋅X₅ {O(n)}
t₆₅, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+4⋅X₆+9 {O(n)}
t₆₆, X₀: 2⋅X₀ {O(n)}
t₆₆, X₁: 2⋅X₁ {O(n)}
t₆₆, X₂: 2⋅X₁+4⋅X₂+3 {O(n)}
t₆₆, X₃: 2⋅X₃ {O(n)}
t₆₆, X₄: 10⋅X₃+8⋅X₄+5 {O(n)}
t₆₆, X₅: 2⋅X₅ {O(n)}
t₆₆, X₆: 1 {O(1)}
t₆₇, X₀: 2⋅X₀ {O(n)}
t₆₇, X₁: 2⋅X₁ {O(n)}
t₆₇, X₂: 2⋅X₁+4⋅X₂+3 {O(n)}
t₆₇, X₃: 2⋅X₃ {O(n)}
t₆₇, X₄: 10⋅X₃+8⋅X₄+5 {O(n)}
t₆₇, X₅: 2⋅X₅ {O(n)}
t₆₇, X₆: 1 {O(1)}
t₆₈, X₀: 2⋅X₀ {O(n)}
t₆₈, X₁: 2⋅X₁ {O(n)}
t₆₈, X₂: 2⋅X₁+4⋅X₂+3 {O(n)}
t₆₈, X₃: 2⋅X₃ {O(n)}
t₆₈, X₄: 2 {O(1)}
t₆₈, X₅: 2⋅X₅ {O(n)}
t₆₈, X₆: 1 {O(1)}
t₆₉, X₀: 2⋅X₀ {O(n)}
t₆₉, X₁: 2⋅X₁ {O(n)}
t₆₉, X₂: 2⋅X₁+4⋅X₂+3 {O(n)}
t₆₉, X₃: 2⋅X₃ {O(n)}
t₆₉, X₄: 10⋅X₃+8⋅X₄+5 {O(n)}
t₆₉, X₅: 2⋅X₅ {O(n)}
t₆₉, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+4⋅X₆+9 {O(n)}
t₇₀, X₀: 2⋅X₀ {O(n)}
t₇₀, X₁: 2⋅X₁ {O(n)}
t₇₀, X₂: 2⋅X₁+4⋅X₂+3 {O(n)}
t₇₀, X₃: 2⋅X₃ {O(n)}
t₇₀, X₄: 10⋅X₃+8⋅X₄+5 {O(n)}
t₇₀, X₅: 2⋅X₅ {O(n)}
t₇₀, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+4⋅X₆+9 {O(n)}
t₇₁, X₀: 2⋅X₀ {O(n)}
t₇₁, X₁: 2⋅X₁ {O(n)}
t₇₁, X₂: 2⋅X₁+4⋅X₂+3 {O(n)}
t₇₁, X₃: 2⋅X₃ {O(n)}
t₇₁, X₄: 10⋅X₃+8⋅X₄+5 {O(n)}
t₇₁, X₅: 2⋅X₅ {O(n)}
t₇₁, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+4⋅X₆+9 {O(n)}
t₇₂, X₀: 2⋅X₀ {O(n)}
t₇₂, X₁: 2⋅X₁ {O(n)}
t₇₂, X₂: 2⋅X₁+4⋅X₂+3 {O(n)}
t₇₂, X₃: 2⋅X₃ {O(n)}
t₇₂, X₄: 10⋅X₃+8⋅X₄+5 {O(n)}
t₇₂, X₅: 2⋅X₅ {O(n)}
t₇₂, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+4⋅X₆+9 {O(n)}
t₇₃, X₀: 2⋅X₀ {O(n)}
t₇₃, X₁: 2⋅X₁ {O(n)}
t₇₃, X₂: 2⋅X₁+4⋅X₂+3 {O(n)}
t₇₃, X₃: 2⋅X₃ {O(n)}
t₇₃, X₄: 2 {O(1)}
t₇₃, X₅: 2⋅X₅ {O(n)}
t₇₃, X₆: 14⋅X₄+18⋅X₃+2⋅X₅+4⋅X₆+9 {O(n)}