KoAT2 Proof Output

Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: H, I
Locations: f0, f12, f15, f23, f26, f30, f52
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f12(2, H, I, 0, X₄, X₅, X₆)
t₁: f12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f15(X₀, X₁, X₂, X₃, 0, X₅, X₆) :|: 1+X₃ ≤ X₀
t₁₅: f12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f23(X₀, X₁, X₂, 0, X₄, X₅, X₆) :|: X₀ ≤ X₃
t₁₄: f15(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f12(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆) :|: X₀ ≤ X₄
t₂: f15(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f15(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆) :|: 1+X₄ ≤ X₀
t₃: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f26(X₀, X₁, X₂, X₃, 0, X₅, X₆) :|: 1+X₃ ≤ X₀
t₈: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f52(X₀, X₁, X₂, X₃, X₄, X₅, 0) :|: X₀ ≤ X₃
t₉: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f52(X₀, X₁, X₂, X₃, X₄, X₅, 1) :|: H ≤ 49 ∧ X₀ ≤ X₃
t₁₀: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f52(X₀, X₁, X₂, X₃, X₄, X₅, 1) :|: X₀ ≤ X₃
t₁₁: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f52(X₀, X₁, X₂, X₃, X₄, X₅, 1) :|: H ≤ 42 ∧ X₀ ≤ X₃
t₁₂: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f52(X₀, X₁, X₂, X₃, X₄, X₅, 1) :|: H ≤ 21 ∧ X₀ ≤ X₃
t₁₃: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f52(X₀, X₁, X₂, X₃, X₄, X₅, 1) :|: H ≤ 18 ∧ X₀ ≤ X₃
t₇: f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f23(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆) :|: X₀ ≤ X₄
t₄: f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f30(X₀, X₁, X₂, X₃, X₄, 0, X₆) :|: 1+X₄ ≤ X₀
t₆: f30(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f26(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆) :|: X₀ ≤ X₅
t₅: f30(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f30(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆) :|: 1+X₅ ≤ X₀

Preprocessing

Eliminate variables [I; X₁; X₂; X₆] that do not contribute to the problem

Found invariant X₂ ≤ 2 ∧ X₂ ≤ 2+X₁ ∧ X₁+X₂ ≤ 3 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 4 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 2+X₂ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 3 ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location f15

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location f23

Found invariant X₃ ≤ 2 ∧ X₃ ≤ 2+X₂ ∧ X₂+X₃ ≤ 3 ∧ X₃ ≤ 2+X₁ ∧ X₁+X₃ ≤ 3 ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 4 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ 2+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 2 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 3 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 2+X₂ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 3 ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location f30

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location f52

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location f12

Found invariant X₂ ≤ 2 ∧ X₂ ≤ 2+X₁ ∧ X₁+X₂ ≤ 3 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 4 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 2+X₂ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 3 ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location f26

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: H
Locations: f0, f12, f15, f23, f26, f30, f52
Transitions:
t₃₃: f0(X₀, X₁, X₂, X₃) → f12(2, 0, X₂, X₃)
t₃₄: f12(X₀, X₁, X₂, X₃) → f15(X₀, X₁, 0, X₃) :|: 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₃₅: f12(X₀, X₁, X₂, X₃) → f23(X₀, 0, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₃₆: f15(X₀, X₁, X₂, X₃) → f12(X₀, 1+X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ X₀+X₂ ≤ 4 ∧ X₀+X₁ ≤ 3 ∧ X₁+X₂ ≤ 3 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2+X₂ ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ 2 ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₂
t₃₇: f15(X₀, X₁, X₂, X₃) → f15(X₀, X₁, 1+X₂, X₃) :|: 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 4 ∧ X₀+X₁ ≤ 3 ∧ X₁+X₂ ≤ 3 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2+X₂ ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ 2 ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₂
t₃₈: f23(X₀, X₁, X₂, X₃) → f26(X₀, X₁, 0, X₃) :|: 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₃₉: f23(X₀, X₁, X₂, X₃) → f52(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₄₀: f23(X₀, X₁, X₂, X₃) → f52(X₀, X₁, X₂, X₃) :|: H ≤ 49 ∧ X₀ ≤ X₁ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₄₁: f23(X₀, X₁, X₂, X₃) → f52(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₄₂: f23(X₀, X₁, X₂, X₃) → f52(X₀, X₁, X₂, X₃) :|: H ≤ 42 ∧ X₀ ≤ X₁ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₄₃: f23(X₀, X₁, X₂, X₃) → f52(X₀, X₁, X₂, X₃) :|: H ≤ 21 ∧ X₀ ≤ X₁ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₄₄: f23(X₀, X₁, X₂, X₃) → f52(X₀, X₁, X₂, X₃) :|: H ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₄₅: f26(X₀, X₁, X₂, X₃) → f23(X₀, 1+X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ X₀+X₂ ≤ 4 ∧ X₀+X₁ ≤ 3 ∧ X₁+X₂ ≤ 3 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2+X₂ ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ 2 ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₂
t₄₆: f26(X₀, X₁, X₂, X₃) → f30(X₀, X₁, X₂, 0) :|: 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 4 ∧ X₀+X₁ ≤ 3 ∧ X₁+X₂ ≤ 3 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2+X₂ ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ 2 ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₂
t₄₇: f30(X₀, X₁, X₂, X₃) → f26(X₀, X₁, 1+X₂, X₃) :|: X₀ ≤ X₃ ∧ X₀+X₃ ≤ 4 ∧ X₀+X₁ ≤ 3 ∧ X₀+X₂ ≤ 3 ∧ X₁+X₃ ≤ 3 ∧ X₂+X₃ ≤ 3 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2+X₂ ∧ X₀ ≤ 2+X₃ ∧ X₃ ≤ 2+X₁ ∧ X₁+X₂ ≤ 2 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2 ∧ X₂ ≤ 1+X₁ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₂ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ 1+X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₄₈: f30(X₀, X₁, X₂, X₃) → f30(X₀, X₁, X₂, 1+X₃) :|: 1+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 4 ∧ X₀+X₁ ≤ 3 ∧ X₀+X₂ ≤ 3 ∧ X₁+X₃ ≤ 3 ∧ X₂+X₃ ≤ 3 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2+X₂ ∧ X₀ ≤ 2+X₃ ∧ X₃ ≤ 2+X₁ ∧ X₁+X₂ ≤ 2 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2 ∧ X₂ ≤ 1+X₁ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₂ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ 1+X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃

MPRF for transition t₃₄: f12(X₀, X₁, X₂, X₃) → f15(X₀, X₁, 0, X₃) :|: 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

3 {O(1)}

MPRF:

• f12: [1+X₀-X₁]
• f15: [X₀-X₁]

MPRF for transition t₃₆: f15(X₀, X₁, X₂, X₃) → f12(X₀, 1+X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ X₀+X₂ ≤ 4 ∧ X₀+X₁ ≤ 3 ∧ X₁+X₂ ≤ 3 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2+X₂ ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ 2 ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

4 {O(1)}

MPRF:

• f12: [2+X₀-X₁]
• f15: [4-X₁]

MPRF for transition t₃₇: f15(X₀, X₁, X₂, X₃) → f15(X₀, X₁, 1+X₂, X₃) :|: 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 4 ∧ X₀+X₁ ≤ 3 ∧ X₁+X₂ ≤ 3 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2+X₂ ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ 2 ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

5 {O(1)}

MPRF:

• f12: [3+X₀-2⋅X₁]
• f15: [3+X₀-2⋅X₁-X₂]

MPRF for transition t₃₈: f23(X₀, X₁, X₂, X₃) → f26(X₀, X₁, 0, X₃) :|: 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

3 {O(1)}

MPRF:

• f23: [3-X₁]
• f26: [2-X₁]
• f30: [2-X₁]

MPRF for transition t₄₅: f26(X₀, X₁, X₂, X₃) → f23(X₀, 1+X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ X₀+X₂ ≤ 4 ∧ X₀+X₁ ≤ 3 ∧ X₁+X₂ ≤ 3 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2+X₂ ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ 2 ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

2 {O(1)}

MPRF:

• f23: [X₀-X₁]
• f26: [2-X₁]
• f30: [X₀-X₁]

MPRF for transition t₄₆: f26(X₀, X₁, X₂, X₃) → f30(X₀, X₁, X₂, 0) :|: 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 4 ∧ X₀+X₁ ≤ 3 ∧ X₁+X₂ ≤ 3 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2+X₂ ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ 2 ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

7 {O(1)}

MPRF:

• f23: [7-2⋅X₁]
• f26: [7-2⋅X₁-X₂]
• f30: [6-2⋅X₁-X₂]

MPRF for transition t₄₇: f30(X₀, X₁, X₂, X₃) → f26(X₀, X₁, 1+X₂, X₃) :|: X₀ ≤ X₃ ∧ X₀+X₃ ≤ 4 ∧ X₀+X₁ ≤ 3 ∧ X₀+X₂ ≤ 3 ∧ X₁+X₃ ≤ 3 ∧ X₂+X₃ ≤ 3 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2+X₂ ∧ X₀ ≤ 2+X₃ ∧ X₃ ≤ 2+X₁ ∧ X₁+X₂ ≤ 2 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2 ∧ X₂ ≤ 1+X₁ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₂ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ 1+X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

27 {O(1)}

MPRF:

• f23: [27-8⋅X₁]
• f26: [27-8⋅X₁-4⋅X₂]
• f30: [22+X₀-7⋅X₁-4⋅X₂]

MPRF for transition t₄₈: f30(X₀, X₁, X₂, X₃) → f30(X₀, X₁, X₂, 1+X₃) :|: 1+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 4 ∧ X₀+X₁ ≤ 3 ∧ X₀+X₂ ≤ 3 ∧ X₁+X₃ ≤ 3 ∧ X₂+X₃ ≤ 3 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2+X₂ ∧ X₀ ≤ 2+X₃ ∧ X₃ ≤ 2+X₁ ∧ X₁+X₂ ≤ 2 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2 ∧ X₂ ≤ 1+X₁ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₂ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ 1+X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

8 {O(1)}

MPRF:

• f23: [8-4⋅X₁]
• f26: [8-4⋅X₁-2⋅X₂]
• f30: [10-X₀-4⋅X₁-2⋅X₂-X₃]

All Bounds

Timebounds

Overall timebound:67 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: 3 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 4 {O(1)}
t₃₇: 5 {O(1)}
t₃₈: 3 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}
t₄₁: 1 {O(1)}
t₄₂: 1 {O(1)}
t₄₃: 1 {O(1)}
t₄₄: 1 {O(1)}
t₄₅: 2 {O(1)}
t₄₆: 7 {O(1)}
t₄₇: 27 {O(1)}
t₄₈: 8 {O(1)}

Costbounds

Overall costbound: 67 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: 3 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 4 {O(1)}
t₃₇: 5 {O(1)}
t₃₈: 3 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}
t₄₁: 1 {O(1)}
t₄₂: 1 {O(1)}
t₄₃: 1 {O(1)}
t₄₄: 1 {O(1)}
t₄₅: 2 {O(1)}
t₄₆: 7 {O(1)}
t₄₇: 27 {O(1)}
t₄₈: 8 {O(1)}

Sizebounds

t₃₃, X₀: 2 {O(1)}
t₃₃, X₁: 0 {O(1)}
t₃₃, X₂: X₂ {O(n)}
t₃₃, X₃: X₃ {O(n)}
t₃₄, X₀: 2 {O(1)}
t₃₄, X₁: 1 {O(1)}
t₃₄, X₂: 0 {O(1)}
t₃₄, X₃: X₃ {O(n)}
t₃₅, X₀: 2 {O(1)}
t₃₅, X₁: 0 {O(1)}
t₃₅, X₂: 2 {O(1)}
t₃₅, X₃: X₃ {O(n)}
t₃₆, X₀: 2 {O(1)}
t₃₆, X₁: 2 {O(1)}
t₃₆, X₂: 2 {O(1)}
t₃₆, X₃: X₃ {O(n)}
t₃₇, X₀: 2 {O(1)}
t₃₇, X₁: 1 {O(1)}
t₃₇, X₂: 2 {O(1)}
t₃₇, X₃: X₃ {O(n)}
t₃₈, X₀: 2 {O(1)}
t₃₈, X₁: 1 {O(1)}
t₃₈, X₂: 0 {O(1)}
t₃₈, X₃: X₃+2 {O(n)}
t₃₉, X₀: 2 {O(1)}
t₃₉, X₁: 2 {O(1)}
t₃₉, X₂: 2 {O(1)}
t₃₉, X₃: 2 {O(1)}
t₄₀, X₀: 2 {O(1)}
t₄₀, X₁: 2 {O(1)}
t₄₀, X₂: 2 {O(1)}
t₄₀, X₃: 2 {O(1)}
t₄₁, X₀: 2 {O(1)}
t₄₁, X₁: 2 {O(1)}
t₄₁, X₂: 2 {O(1)}
t₄₁, X₃: 2 {O(1)}
t₄₂, X₀: 2 {O(1)}
t₄₂, X₁: 2 {O(1)}
t₄₂, X₂: 2 {O(1)}
t₄₂, X₃: 2 {O(1)}
t₄₃, X₀: 2 {O(1)}
t₄₃, X₁: 2 {O(1)}
t₄₃, X₂: 2 {O(1)}
t₄₃, X₃: 2 {O(1)}
t₄₄, X₀: 2 {O(1)}
t₄₄, X₁: 2 {O(1)}
t₄₄, X₂: 2 {O(1)}
t₄₄, X₃: 2 {O(1)}
t₄₅, X₀: 2 {O(1)}
t₄₅, X₁: 2 {O(1)}
t₄₅, X₂: 2 {O(1)}
t₄₅, X₃: 2 {O(1)}
t₄₆, X₀: 2 {O(1)}
t₄₆, X₁: 1 {O(1)}
t₄₆, X₂: 1 {O(1)}
t₄₆, X₃: 0 {O(1)}
t₄₇, X₀: 2 {O(1)}
t₄₇, X₁: 1 {O(1)}
t₄₇, X₂: 2 {O(1)}
t₄₇, X₃: 2 {O(1)}
t₄₈, X₀: 2 {O(1)}
t₄₈, X₁: 1 {O(1)}
t₄₈, X₂: 1 {O(1)}
t₄₈, X₃: 2 {O(1)}