KoAT2 Proof Output

Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: f0, f10, f13, f16, f31, f7
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄) → f7(400, 0, X₂, X₃, X₄)
t₂: f10(X₀, X₁, X₂, X₃, X₄) → f13(X₀, X₁, X₂, 0, X₄) :|: X₂ ≤ 4
t₉: f10(X₀, X₁, X₂, X₃, X₄) → f7(X₀, 1+X₁, X₂, X₃, X₄) :|: 5 ≤ X₂
t₈: f13(X₀, X₁, X₂, X₃, X₄) → f10(X₀, X₁, 1+X₂, X₃, X₄) :|: 5 ≤ X₃
t₃: f13(X₀, X₁, X₂, X₃, X₄) → f16(X₀, X₁, X₂, X₃, 0) :|: X₃ ≤ 4
t₇: f16(X₀, X₁, X₂, X₃, X₄) → f13(X₀, X₁, X₂, 1+X₃, X₄) :|: 5 ≤ X₄
t₄: f16(X₀, X₁, X₂, X₃, X₄) → f16(X₀, X₁, X₂, X₃, 1+X₄) :|: X₄ ≤ 4 ∧ 1+F ≤ X₀
t₅: f16(X₀, X₁, X₂, X₃, X₄) → f16(X₀, X₁, X₂, X₃, 1+X₄) :|: X₄ ≤ 4
t₆: f16(X₀, X₁, X₂, X₃, X₄) → f31(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 4
t₁: f7(X₀, X₁, X₂, X₃, X₄) → f10(X₀, X₁, 0, X₃, X₄) :|: X₁ ≤ 4
t₁₀: f7(X₀, X₁, X₂, X₃, X₄) → f31(X₀, X₁, X₂, X₃, X₄) :|: 5 ≤ X₁

Preprocessing

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 400 ≤ X₀+X₂ ∧ X₀ ≤ 400+X₂ ∧ 0 ≤ X₁ ∧ 400 ≤ X₀+X₁ ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400 ∧ 400 ≤ X₀ for location f10

Found invariant X₄ ≤ 5 ∧ X₄ ≤ 5+X₃ ∧ X₃+X₄ ≤ 9 ∧ X₄ ≤ 5+X₂ ∧ X₄ ≤ 5+X₁ ∧ 395+X₄ ≤ X₀ ∧ X₀+X₄ ≤ 405 ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ 4+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ 400 ≤ X₀+X₄ ∧ X₀ ≤ 400+X₄ ∧ X₃ ≤ 4 ∧ X₃ ≤ 4+X₂ ∧ X₃ ≤ 4+X₁ ∧ 396+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 404 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 400 ≤ X₀+X₃ ∧ X₀ ≤ 400+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 400 ≤ X₀+X₂ ∧ X₀ ≤ 400+X₂ ∧ 0 ≤ X₁ ∧ 400 ≤ X₀+X₁ ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400 ∧ 400 ≤ X₀ for location f16

Found invariant X₃ ≤ 5 ∧ X₃ ≤ 5+X₂ ∧ X₃ ≤ 5+X₁ ∧ 395+X₃ ≤ X₀ ∧ X₀+X₃ ≤ 405 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 400 ≤ X₀+X₃ ∧ X₀ ≤ 400+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 400 ≤ X₀+X₂ ∧ X₀ ≤ 400+X₂ ∧ 0 ≤ X₁ ∧ 400 ≤ X₀+X₁ ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400 ∧ 400 ≤ X₀ for location f13

Found invariant 0 ≤ X₁ ∧ 400 ≤ X₀+X₁ ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400 ∧ 400 ≤ X₀ for location f31

Found invariant 0 ≤ X₁ ∧ 400 ≤ X₀+X₁ ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400 ∧ 400 ≤ X₀ for location f7

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: f0, f10, f13, f16, f31, f7
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄) → f7(400, 0, X₂, X₃, X₄)
t₂: f10(X₀, X₁, X₂, X₃, X₄) → f13(X₀, X₁, X₂, 0, X₄) :|: X₂ ≤ 4 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₂
t₉: f10(X₀, X₁, X₂, X₃, X₄) → f7(X₀, 1+X₁, X₂, X₃, X₄) :|: 5 ≤ X₂ ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₂
t₈: f13(X₀, X₁, X₂, X₃, X₄) → f10(X₀, X₁, 1+X₂, X₃, X₄) :|: 5 ≤ X₃ ∧ X₀+X₃ ≤ 405 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ X₀ ≤ 400+X₃ ∧ X₃ ≤ 5+X₁ ∧ X₃ ≤ 5+X₂ ∧ X₃ ≤ 5 ∧ 395+X₃ ≤ X₀ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 400 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₃: f13(X₀, X₁, X₂, X₃, X₄) → f16(X₀, X₁, X₂, X₃, 0) :|: X₃ ≤ 4 ∧ X₀+X₃ ≤ 405 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ X₀ ≤ 400+X₃ ∧ X₃ ≤ 5+X₁ ∧ X₃ ≤ 5+X₂ ∧ X₃ ≤ 5 ∧ 395+X₃ ≤ X₀ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 400 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₇: f16(X₀, X₁, X₂, X₃, X₄) → f13(X₀, X₁, X₂, 1+X₃, X₄) :|: 5 ≤ X₄ ∧ X₀+X₄ ≤ 405 ∧ X₀+X₃ ≤ 404 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ X₀ ≤ 400+X₃ ∧ X₀ ≤ 400+X₄ ∧ X₃+X₄ ≤ 9 ∧ X₄ ≤ 5+X₁ ∧ X₄ ≤ 5+X₂ ∧ X₄ ≤ 5+X₃ ∧ X₄ ≤ 5 ∧ X₃ ≤ 4+X₁ ∧ X₃ ≤ 4+X₂ ∧ X₃ ≤ 4 ∧ X₃ ≤ 4+X₄ ∧ 395+X₄ ≤ X₀ ∧ 396+X₃ ≤ X₀ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 400 ≤ X₀+X₃ ∧ 400 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₄
t₄: f16(X₀, X₁, X₂, X₃, X₄) → f16(X₀, X₁, X₂, X₃, 1+X₄) :|: X₄ ≤ 4 ∧ 1+F ≤ X₀ ∧ X₀+X₄ ≤ 405 ∧ X₀+X₃ ≤ 404 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ X₀ ≤ 400+X₃ ∧ X₀ ≤ 400+X₄ ∧ X₃+X₄ ≤ 9 ∧ X₄ ≤ 5+X₁ ∧ X₄ ≤ 5+X₂ ∧ X₄ ≤ 5+X₃ ∧ X₄ ≤ 5 ∧ X₃ ≤ 4+X₁ ∧ X₃ ≤ 4+X₂ ∧ X₃ ≤ 4 ∧ X₃ ≤ 4+X₄ ∧ 395+X₄ ≤ X₀ ∧ 396+X₃ ≤ X₀ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 400 ≤ X₀+X₃ ∧ 400 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₄
t₅: f16(X₀, X₁, X₂, X₃, X₄) → f16(X₀, X₁, X₂, X₃, 1+X₄) :|: X₄ ≤ 4 ∧ X₀+X₄ ≤ 405 ∧ X₀+X₃ ≤ 404 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ X₀ ≤ 400+X₃ ∧ X₀ ≤ 400+X₄ ∧ X₃+X₄ ≤ 9 ∧ X₄ ≤ 5+X₁ ∧ X₄ ≤ 5+X₂ ∧ X₄ ≤ 5+X₃ ∧ X₄ ≤ 5 ∧ X₃ ≤ 4+X₁ ∧ X₃ ≤ 4+X₂ ∧ X₃ ≤ 4 ∧ X₃ ≤ 4+X₄ ∧ 395+X₄ ≤ X₀ ∧ 396+X₃ ≤ X₀ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 400 ≤ X₀+X₃ ∧ 400 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₄
t₆: f16(X₀, X₁, X₂, X₃, X₄) → f31(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 4 ∧ X₀+X₄ ≤ 405 ∧ X₀+X₃ ≤ 404 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ X₀ ≤ 400+X₃ ∧ X₀ ≤ 400+X₄ ∧ X₃+X₄ ≤ 9 ∧ X₄ ≤ 5+X₁ ∧ X₄ ≤ 5+X₂ ∧ X₄ ≤ 5+X₃ ∧ X₄ ≤ 5 ∧ X₃ ≤ 4+X₁ ∧ X₃ ≤ 4+X₂ ∧ X₃ ≤ 4 ∧ X₃ ≤ 4+X₄ ∧ 395+X₄ ≤ X₀ ∧ 396+X₃ ≤ X₀ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 400 ≤ X₀+X₃ ∧ 400 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₄
t₁: f7(X₀, X₁, X₂, X₃, X₄) → f10(X₀, X₁, 0, X₃, X₄) :|: X₁ ≤ 4 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₁₀: f7(X₀, X₁, X₂, X₃, X₄) → f31(X₀, X₁, X₂, X₃, X₄) :|: 5 ≤ X₁ ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 0 ≤ X₁

MPRF for transition t₁: f7(X₀, X₁, X₂, X₃, X₄) → f10(X₀, X₁, 0, X₃, X₄) :|: X₁ ≤ 4 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

5 {O(1)}

MPRF:

• f10: [4-X₁]
• f13: [4-X₁]
• f16: [4-X₁]
• f7: [5-X₁]

MPRF for transition t₂: f10(X₀, X₁, X₂, X₃, X₄) → f13(X₀, X₁, X₂, 0, X₄) :|: X₂ ≤ 4 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

25 {O(1)}

MPRF:

• f10: [5-X₂]
• f13: [4-X₂]
• f16: [4-X₂]
• f7: [-X₂]

MPRF for transition t₉: f10(X₀, X₁, X₂, X₃, X₄) → f7(X₀, 1+X₁, X₂, X₃, X₄) :|: 5 ≤ X₂ ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

10 {O(1)}

MPRF:

• f10: [2]
• f13: [2]
• f16: [2]
• f7: [1]

MPRF for transition t₃: f13(X₀, X₁, X₂, X₃, X₄) → f16(X₀, X₁, X₂, X₃, 0) :|: X₃ ≤ 4 ∧ X₀+X₃ ≤ 405 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ X₀ ≤ 400+X₃ ∧ X₃ ≤ 5+X₁ ∧ X₃ ≤ 5+X₂ ∧ X₃ ≤ 5 ∧ 395+X₃ ≤ X₀ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 400 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₃+10000 {O(n)}

MPRF:

• f10: [-X₃]
• f13: [400-X₃]
• f16: [399-X₃]
• f7: [-X₃]

MPRF for transition t₄: f16(X₀, X₁, X₂, X₃, X₄) → f16(X₀, X₁, X₂, X₃, 1+X₄) :|: X₄ ≤ 4 ∧ 1+F ≤ X₀ ∧ X₀+X₄ ≤ 405 ∧ X₀+X₃ ≤ 404 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ X₀ ≤ 400+X₃ ∧ X₀ ≤ 400+X₄ ∧ X₃+X₄ ≤ 9 ∧ X₄ ≤ 5+X₁ ∧ X₄ ≤ 5+X₂ ∧ X₄ ≤ 5+X₃ ∧ X₄ ≤ 5 ∧ X₃ ≤ 4+X₁ ∧ X₃ ≤ 4+X₂ ∧ X₃ ≤ 4 ∧ X₃ ≤ 4+X₄ ∧ 395+X₄ ≤ X₀ ∧ 396+X₃ ≤ X₀ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 400 ≤ X₀+X₃ ∧ 400 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

5⋅X₃+676 {O(n)}

MPRF:

• f10: [26-5⋅X₃]
• f13: [26-5⋅X₃]
• f16: [26-5⋅X₃-X₄]
• f7: [26-5⋅X₃]

MPRF for transition t₅: f16(X₀, X₁, X₂, X₃, X₄) → f16(X₀, X₁, X₂, X₃, 1+X₄) :|: X₄ ≤ 4 ∧ X₀+X₄ ≤ 405 ∧ X₀+X₃ ≤ 404 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ X₀ ≤ 400+X₃ ∧ X₀ ≤ 400+X₄ ∧ X₃+X₄ ≤ 9 ∧ X₄ ≤ 5+X₁ ∧ X₄ ≤ 5+X₂ ∧ X₄ ≤ 5+X₃ ∧ X₄ ≤ 5 ∧ X₃ ≤ 4+X₁ ∧ X₃ ≤ 4+X₂ ∧ X₃ ≤ 4 ∧ X₃ ≤ 4+X₄ ∧ 395+X₄ ≤ X₀ ∧ 396+X₃ ≤ X₀ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 400 ≤ X₀+X₃ ∧ 400 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

5⋅X₃+625 {O(n)}

MPRF:

• f10: [-5⋅X₃]
• f13: [25-5⋅X₃]
• f16: [25-5⋅X₃-X₄]
• f7: [-5⋅X₃]

MPRF for transition t₇: f16(X₀, X₁, X₂, X₃, X₄) → f13(X₀, X₁, X₂, 1+X₃, X₄) :|: 5 ≤ X₄ ∧ X₀+X₄ ≤ 405 ∧ X₀+X₃ ≤ 404 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ X₀ ≤ 400+X₃ ∧ X₀ ≤ 400+X₄ ∧ X₃+X₄ ≤ 9 ∧ X₄ ≤ 5+X₁ ∧ X₄ ≤ 5+X₂ ∧ X₄ ≤ 5+X₃ ∧ X₄ ≤ 5 ∧ X₃ ≤ 4+X₁ ∧ X₃ ≤ 4+X₂ ∧ X₃ ≤ 4 ∧ X₃ ≤ 4+X₄ ∧ 395+X₄ ≤ X₀ ∧ 396+X₃ ≤ X₀ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 400 ≤ X₀+X₃ ∧ 400 ≤ X₀+X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₃+130 {O(n)}

MPRF:

• f10: [5-X₃]
• f13: [5-X₃]
• f16: [5-X₃]
• f7: [5-X₃]

MPRF for transition t₈: f13(X₀, X₁, X₂, X₃, X₄) → f10(X₀, X₁, 1+X₂, X₃, X₄) :|: 5 ≤ X₃ ∧ X₀+X₃ ≤ 405 ∧ X₀ ≤ 400 ∧ X₀ ≤ 400+X₁ ∧ X₀ ≤ 400+X₂ ∧ X₀ ≤ 400+X₃ ∧ X₃ ≤ 5+X₁ ∧ X₃ ≤ 5+X₂ ∧ X₃ ≤ 5 ∧ 395+X₃ ≤ X₀ ∧ 400 ≤ X₀ ∧ 400 ≤ X₀+X₁ ∧ 400 ≤ X₀+X₂ ∧ 400 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

25 {O(1)}

MPRF:

• f10: [0]
• f13: [1]
• f16: [X₀-399]
• f7: [0]

All Bounds

Timebounds

Overall timebound:12⋅X₃+11499 {O(n)}
t₀: 1 {O(1)}
t₁: 5 {O(1)}
t₂: 25 {O(1)}
t₃: X₃+10000 {O(n)}
t₄: 5⋅X₃+676 {O(n)}
t₅: 5⋅X₃+625 {O(n)}
t₆: 1 {O(1)}
t₇: X₃+130 {O(n)}
t₈: 25 {O(1)}
t₉: 10 {O(1)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 12⋅X₃+11499 {O(n)}
t₀: 1 {O(1)}
t₁: 5 {O(1)}
t₂: 25 {O(1)}
t₃: X₃+10000 {O(n)}
t₄: 5⋅X₃+676 {O(n)}
t₅: 5⋅X₃+625 {O(n)}
t₆: 1 {O(1)}
t₇: X₃+130 {O(n)}
t₈: 25 {O(1)}
t₉: 10 {O(1)}
t₁₀: 1 {O(1)}

Sizebounds

t₀, X₀: 400 {O(1)}
t₀, X₁: 0 {O(1)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₁, X₀: 400 {O(1)}
t₁, X₁: 4 {O(1)}
t₁, X₂: 0 {O(1)}
t₁, X₃: X₃+5 {O(n)}
t₁, X₄: X₄+5 {O(n)}
t₂, X₀: 400 {O(1)}
t₂, X₁: 4 {O(1)}
t₂, X₂: 4 {O(1)}
t₂, X₃: 0 {O(1)}
t₂, X₄: X₄+10 {O(n)}
t₃, X₀: 400 {O(1)}
t₃, X₁: 4 {O(1)}
t₃, X₂: 4 {O(1)}
t₃, X₃: 4 {O(1)}
t₃, X₄: 0 {O(1)}
t₄, X₀: 400 {O(1)}
t₄, X₁: 4 {O(1)}
t₄, X₂: 4 {O(1)}
t₄, X₃: 4 {O(1)}
t₄, X₄: 5 {O(1)}
t₅, X₀: 400 {O(1)}
t₅, X₁: 4 {O(1)}
t₅, X₂: 4 {O(1)}
t₅, X₃: 4 {O(1)}
t₅, X₄: 5 {O(1)}
t₆, X₀: 400 {O(1)}
t₆, X₁: 12 {O(1)}
t₆, X₂: 12 {O(1)}
t₆, X₃: 4 {O(1)}
t₆, X₄: 4 {O(1)}
t₇, X₀: 400 {O(1)}
t₇, X₁: 4 {O(1)}
t₇, X₂: 4 {O(1)}
t₇, X₃: 5 {O(1)}
t₇, X₄: 5 {O(1)}
t₈, X₀: 400 {O(1)}
t₈, X₁: 4 {O(1)}
t₈, X₂: 5 {O(1)}
t₈, X₃: 5 {O(1)}
t₈, X₄: 5 {O(1)}
t₉, X₀: 400 {O(1)}
t₉, X₁: 5 {O(1)}
t₉, X₂: 5 {O(1)}
t₉, X₃: 5 {O(1)}
t₉, X₄: 5 {O(1)}
t₁₀, X₀: 400 {O(1)}
t₁₀, X₁: 5 {O(1)}
t₁₀, X₂: 5 {O(1)}
t₁₀, X₃: 5 {O(1)}
t₁₀, X₄: 5 {O(1)}