KoAT2 Proof Output

Initial Problem

Start: f0
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
Locations: f0, f10, f13, f29, f34, f53, f55, f61, f73
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 2 ≤ X₀
t₁: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f13(X₀, X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₁ ≤ X₀
t₂₀: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f73(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+S ≤ 0 ∧ X₀ ≤ X₁
t₂₁: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f73(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₀ ≤ X₁
t₁₇: f13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f10(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: f13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f13(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: f13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f13(X₀, X₁, S, 1+X₃, X₂, S, S, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₂ ≤ S ∧ X₃ ≤ X₀
t₁₈: f13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f29(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: f13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f29(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃ ∧ 1 ≤ X₂
t₄: f29(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f29(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₃ ≤ X₀
t₁₆: f29(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f34(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃
t₅: f34(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f34(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, 0, 0, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₃ ≤ X₀
t₆: f34(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f34(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, S, T, T+X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+S ≤ 0 ∧ X₃ ≤ X₀
t₇: f34(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f34(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, S, T, T+X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1 ≤ S ∧ X₃ ≤ X₀
t₁₄: f34(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f53(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, S, T, T, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃
t₁₅: f34(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f53(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, -S, T, S, X₁₇) :|: 1+U ≤ 0 ∧ 1+X₀ ≤ X₃
t₁₃: f53(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f10(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₁₀
t₈: f53(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, 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) → f61(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, S, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃
t₁₁: f61(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f53(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, 1+X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃
t₁₀: f61(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f61(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₃ ≤ X₀

Preprocessing

Cut unsatisfiable transition [t₄: f29→f29; t₁₀: f61→f61]

Eliminate variables [T; X₄; X₅; X₆; X₇; X₈; X₉; X₁₁; X₁₂; X₁₃; X₁₄; X₁₅; X₁₆; X₁₇] that do not contribute to the problem

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 f29

Found invariant 1+X₄ ≤ X₃ ∧ X₄ ≤ 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 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location f13

Found invariant 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location f73

Found invariant 2 ≤ X₀ for location f10

Found invariant 1+X₄ ≤ X₃ ∧ X₄ ≤ 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 f61

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 f53

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 f34

Cut unsatisfiable transition [t₅₆: f13→f29; t₅₉: f34→f34; t₆₀: f34→f34; t₆₁: f34→f34; t₆₆: f55→f55]

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: S, U
Locations: f0, f10, f13, f29, f34, f53, f55, f61, f73
Transitions:
t₄₉: f0(X₀, X₁, X₂, X₃, X₄) → f10(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₀
t₅₀: f10(X₀, X₁, X₂, X₃, X₄) → f13(X₀, X₁, 0, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₅₁: f10(X₀, X₁, X₂, X₃, X₄) → f73(X₀, X₁, X₂, X₃, X₄) :|: 1+S ≤ 0 ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₅₂: f10(X₀, X₁, X₂, X₃, X₄) → f73(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀
t₅₃: f13(X₀, X₁, X₂, X₃, X₄) → f10(X₀, 1+X₁, 0, X₃, X₄) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂
t₅₄: f13(X₀, X₁, X₂, X₃, X₄) → f13(X₀, X₁, X₂, 1+X₃, X₄) :|: 1+S ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₂
t₅₅: f13(X₀, X₁, X₂, X₃, X₄) → f13(X₀, X₁, S, 1+X₃, X₄) :|: X₂ ≤ S ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₂
t₅₇: f13(X₀, X₁, X₂, X₃, X₄) → f29(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₂
t₅₈: f29(X₀, X₁, X₂, X₃, X₄) → f34(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃
t₆₂: f34(X₀, X₁, X₂, X₃, X₄) → f53(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃
t₆₃: f34(X₀, X₁, X₂, X₃, X₄) → f53(X₀, X₁, X₂, X₃, X₄) :|: 1+U ≤ 0 ∧ 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃
t₆₄: f53(X₀, X₁, X₂, X₃, X₄) → f10(X₀, 1+X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 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: f53(X₀, X₁, X₂, X₃, X₄) → f55(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 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
t₆₇: f55(X₀, X₁, X₂, X₃, X₄) → f61(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₄ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₄ ≤ X₀
t₆₈: f61(X₀, X₁, X₂, X₃, X₄) → f53(X₀, X₁, X₂, X₃, 1+X₄) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₄ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₄ ≤ X₀

MPRF for transition t₅₀: f10(X₀, X₁, X₂, X₃, X₄) → f13(X₀, X₁, 0, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

• f10: [X₀-X₁]
• f13: [X₀-1-X₁]
• f29: [X₀-1-X₁]
• f34: [X₀-1-X₁]
• f53: [X₀-1-X₁]
• f55: [X₀-1-X₁]
• f61: [X₀-1-X₁]

MPRF for transition t₅₃: f13(X₀, X₁, X₂, X₃, X₄) → f10(X₀, 1+X₁, 0, X₃, X₄) :|: 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:

• f10: [X₀-X₁]
• f13: [X₀-X₁]
• f29: [X₀-X₁]
• f34: [X₀-X₁]
• f53: [X₀-X₁]
• f55: [X₀-X₁]
• f61: [X₀-X₁]

MPRF for transition t₅₄: f13(X₀, X₁, X₂, X₃, X₄) → f13(X₀, X₁, X₂, 1+X₃, X₄) :|: 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:

• f10: [2⋅X₀-X₃]
• f13: [2⋅X₀-X₃]
• f29: [2⋅X₀-X₃]
• f34: [2⋅X₀-X₃]
• f53: [2⋅X₀-X₃]
• f55: [2⋅X₀-X₃]
• f61: [2⋅X₀-X₃]

MPRF for transition t₅₅: f13(X₀, X₁, X₂, X₃, X₄) → f13(X₀, X₁, S, 1+X₃, X₄) :|: 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:

• f10: [2⋅X₀-X₃]
• f13: [2⋅X₀-X₃]
• f29: [2⋅X₀-X₃]
• f34: [2⋅X₀-X₃]
• f53: [2⋅X₀-X₃]
• f55: [2⋅X₀-X₃]
• f61: [2⋅X₀-X₃]

MPRF for transition t₅₇: f13(X₀, X₁, X₂, X₃, X₄) → f29(X₀, X₁, X₂, X₃, X₄) :|: 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:

• f10: [X₀-X₁]
• f13: [X₀-X₁]
• f29: [X₀-1-X₁]
• f34: [X₀-1-X₁]
• f53: [X₀-1-X₁]
• f55: [X₀-1-X₁]
• f61: [X₀-1-X₁]

MPRF for transition t₅₈: f29(X₀, X₁, X₂, X₃, X₄) → f34(X₀, X₁, X₂, X₃, X₄) :|: 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:

• f10: [X₀-X₁]
• f13: [X₀-X₁]
• f29: [X₀-X₁]
• f34: [X₀-1-X₁]
• f53: [X₀-1-X₁]
• f55: [X₀-1-X₁]
• f61: [X₀-1-X₁]

MPRF for transition t₆₂: f34(X₀, X₁, X₂, X₃, X₄) → f53(X₀, X₁, X₂, X₃, X₄) :|: 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:

• f10: [X₀-X₁]
• f13: [X₀-X₁]
• f29: [X₀-X₁]
• f34: [X₀-X₁]
• f53: [X₀-1-X₁]
• f55: [X₀-1-X₁]
• f61: [X₀-1-X₁]

MPRF for transition t₆₃: f34(X₀, X₁, X₂, X₃, X₄) → f53(X₀, X₁, X₂, X₃, X₄) :|: 1+U ≤ 0 ∧ 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:

• f10: [X₀-X₁]
• f13: [X₀-X₁]
• f29: [X₀-X₁]
• f34: [X₀-X₁]
• f53: [X₀-1-X₁]
• f55: [X₀-1-X₁]
• f61: [X₀-1-X₁]

MPRF for transition t₆₄: f53(X₀, X₁, X₂, X₃, X₄) → f10(X₀, 1+X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₄ ∧ 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 {O(n)}

MPRF:

• f10: [X₀-X₁]
• f13: [X₀-X₁]
• f29: [X₀-X₁]
• f34: [X₀-X₁]
• f53: [X₀-X₁]
• f55: [X₀-X₁]
• f61: [X₀-X₁]

MPRF for transition t₆₅: f53(X₀, X₁, X₂, X₃, X₄) → f55(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 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:

X₀+X₄+2 {O(n)}

MPRF:

• f10: [2+X₀-X₄]
• f13: [2+X₀-X₄]
• f29: [2+X₀-X₄]
• f34: [2+X₀-X₄]
• f53: [2+X₀-X₄]
• f55: [1+X₀-X₄]
• f61: [1+X₀-X₄]

MPRF for transition t₆₇: f55(X₀, X₁, X₂, X₃, X₄) → f61(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₄ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₄ ≤ X₀ of depth 1:

new bound:

2⋅X₄+3⋅X₀ {O(n)}

MPRF:

• f10: [3⋅X₀-2⋅X₄]
• f13: [3⋅X₀-2⋅X₄]
• f29: [3⋅X₀-2⋅X₄]
• f34: [3⋅X₀-2⋅X₄]
• f53: [3⋅X₀-2⋅X₄]
• f55: [3⋅X₀-1-2⋅X₄]
• f61: [3⋅X₀-2-2⋅X₄]

MPRF for transition t₆₈: f61(X₀, X₁, X₂, X₃, X₄) → f53(X₀, X₁, X₂, X₃, 1+X₄) :|: 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₄ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₄ ≤ X₀ of depth 1:

new bound:

X₀+X₄+1 {O(n)}

MPRF:

• f10: [1+X₀-X₄]
• f13: [1+X₀-X₄]
• f29: [1+X₀-X₄]
• f34: [1+X₀-X₄]
• f53: [1+X₀-X₄]
• f55: [1+X₀-X₄]
• f61: [1+X₀-X₄]

All Bounds

Timebounds

Overall timebound:16⋅X₀+2⋅X₃+4⋅X₄+7⋅X₁+6 {O(n)}
t₄₉: 1 {O(1)}
t₅₀: X₀+X₁ {O(n)}
t₅₁: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: X₀+X₁ {O(n)}
t₅₄: 2⋅X₀+X₃ {O(n)}
t₅₅: 2⋅X₀+X₃ {O(n)}
t₅₇: X₀+X₁ {O(n)}
t₅₈: X₀+X₁ {O(n)}
t₆₂: X₀+X₁ {O(n)}
t₆₃: X₀+X₁ {O(n)}
t₆₄: X₀+X₁ {O(n)}
t₆₅: X₀+X₄+2 {O(n)}
t₆₇: 2⋅X₄+3⋅X₀ {O(n)}
t₆₈: X₀+X₄+1 {O(n)}

Costbounds

Overall costbound: 16⋅X₀+2⋅X₃+4⋅X₄+7⋅X₁+6 {O(n)}
t₄₉: 1 {O(1)}
t₅₀: X₀+X₁ {O(n)}
t₅₁: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: X₀+X₁ {O(n)}
t₅₄: 2⋅X₀+X₃ {O(n)}
t₅₅: 2⋅X₀+X₃ {O(n)}
t₅₇: X₀+X₁ {O(n)}
t₅₈: X₀+X₁ {O(n)}
t₆₂: X₀+X₁ {O(n)}
t₆₃: X₀+X₁ {O(n)}
t₆₄: X₀+X₁ {O(n)}
t₆₅: X₀+X₄+2 {O(n)}
t₆₇: 2⋅X₄+3⋅X₀ {O(n)}
t₆₈: X₀+X₄+1 {O(n)}

Sizebounds

t₄₉, X₀: X₀ {O(n)}
t₄₉, X₁: X₁ {O(n)}
t₄₉, X₂: X₂ {O(n)}
t₄₉, X₃: X₃ {O(n)}
t₄₉, X₄: X₄ {O(n)}
t₅₀, X₀: X₀ {O(n)}
t₅₀, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₀, X₂: 0 {O(1)}
t₅₀, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₀, X₄: 2⋅X₄+X₀+1 {O(n)}
t₅₁, X₀: 3⋅X₀ {O(n)}
t₅₁, X₁: 4⋅X₀+7⋅X₁ {O(n)}
t₅₁, X₃: 7⋅X₃+8⋅X₀ {O(n)}
t₅₁, X₄: 2⋅X₀+5⋅X₄+2 {O(n)}
t₅₂, X₀: 3⋅X₀ {O(n)}
t₅₂, X₁: 4⋅X₀+7⋅X₁ {O(n)}
t₅₂, X₃: 7⋅X₃+8⋅X₀ {O(n)}
t₅₂, X₄: 2⋅X₀+5⋅X₄+2 {O(n)}
t₅₃, X₀: X₀ {O(n)}
t₅₃, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₃, X₂: 0 {O(1)}
t₅₃, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₃, X₄: 2⋅X₄+X₀+1 {O(n)}
t₅₄, X₀: X₀ {O(n)}
t₅₄, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₄, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₄, X₄: 2⋅X₄+X₀+1 {O(n)}
t₅₅, X₀: X₀ {O(n)}
t₅₅, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₅, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₅, X₄: 2⋅X₄+X₀+1 {O(n)}
t₅₇, X₀: X₀ {O(n)}
t₅₇, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₇, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₇, X₄: 2⋅X₄+X₀+1 {O(n)}
t₅₈, X₀: X₀ {O(n)}
t₅₈, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₈, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₈, X₄: 2⋅X₄+X₀+1 {O(n)}
t₆₂, X₀: X₀ {O(n)}
t₆₂, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₂, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₂, X₄: 2⋅X₄+X₀+1 {O(n)}
t₆₃, X₀: X₀ {O(n)}
t₆₃, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₃, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₃, X₄: 2⋅X₄+X₀+1 {O(n)}
t₆₄, X₀: X₀ {O(n)}
t₆₄, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₄, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₄, X₄: 2⋅X₄+X₀+1 {O(n)}
t₆₅, X₀: X₀ {O(n)}
t₆₅, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₅, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₅, X₄: 2⋅X₄+X₀+1 {O(n)}
t₆₇, X₀: X₀ {O(n)}
t₆₇, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₇, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₇, X₄: 2⋅X₄+X₀+1 {O(n)}
t₆₈, X₀: X₀ {O(n)}
t₆₈, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₈, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₈, X₄: 2⋅X₄+X₀+1 {O(n)}