KoAT2 Proof Output

Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀
Temp_Vars: L, M
Locations: f0, f12, f15, f28, f30, f33, f42, f45, f59, f69, f71, f73, f82
Transitions:
t₂: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₃: f12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f15(X₀, X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₀
t₂₉: f12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁
t₂₆: f15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f12(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0
t₂₇: f15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f12(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 1 ≤ X₂
t₂₈: f15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f12(X₀, 1+X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₄: f15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f15(X₀, X₁, X₂, 1+X₃, L, L, X₆, X₇, X₈, X₉, X₁₀) :|: L ≤ X₂ ∧ X₃ ≤ X₀
t₅: f15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f15(X₀, X₁, L, 1+X₃, L, L, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₂ ≤ L ∧ X₃ ≤ X₀
t₆: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f30(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₃ ≤ X₀
t₂₅: f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f82(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₃
t₇: f30(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f33(X₀, X₁, X₂, X₃, X₄, X₅, L, X₇, X₈, X₉, X₁₀) :|: 1+X₁ ≤ X₃
t₂₄: f30(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f42(X₀, X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₃ ≤ X₁
t₂₃: f33(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f30(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₇
t₈: f33(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f33(X₀, X₁, X₂, X₃, X₄, X₅, L, 1+X₇, X₈, X₉, X₁₀) :|: 1+X₇ ≤ X₁
t₉: f42(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f45(X₀, X₁, X₂, X₃, X₄, X₅, L, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₀
t₂₀: f42(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f59(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁₀
t₂₁: f42(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f59(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁ ∧ 1+X₁₀ ≤ X₃
t₂₂: f42(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₃) :|: 1+X₀ ≤ X₁ ∧ X₁₀ ≤ X₃ ∧ X₃ ≤ X₁₀
t₁₈: f45(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f42(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, M, L, X₁₀) :|: 1+M ≤ X₂ ∧ X₃ ≤ X₇
t₁₉: f45(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f42(X₀, 1+X₁, L, X₃, X₄, X₅, X₆, X₇, L, M, X₁) :|: X₂ ≤ L ∧ X₃ ≤ X₇
t₁₀: f45(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f45(X₀, X₁, X₂, X₃, X₄, X₅, L, 1+X₇, X₈, X₉, X₁₀) :|: 1+X₇ ≤ X₃
t₁₁: f59(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f59(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇, L, X₉, X₁₀) :|: X₇ ≤ X₀
t₁₇: f59(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₇
t₀: f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+L ≤ 0
t₁: f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₁₅: f71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f28(X₀, X₁, X₂, 1+X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₂: f71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f73(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, L, X₉, X₁₀) :|: 1+X₃ ≤ X₀
t₁₃: f71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f73(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, L, X₉, X₁₀) :|: 1+X₀ ≤ X₃
t₁₆: f73(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f28(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁
t₁₄: f73(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f73(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₀

Preprocessing

Eliminate variables [X₄; X₅; X₆; X₈; X₉] that do not contribute to the problem

Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location f42

Found invariant 1 ≤ 0 for location f45

Found invariant 1 ≤ 0 for location f33

Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location f73

Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location f71

Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location f59

Found invariant 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location f82

Found invariant 0 ≤ X₂ ∧ X₁ ≤ X₀ for location f15

Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location f69

Found invariant 1+X₀ ≤ X₁ for location f28

Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location f30

Cut unsatisfiable transition [t₆₇: f15→f12; t₇₄: f30→f33; t₇₆: f33→f30; t₇₇: f33→f33; t₇₈: f42→f45; t₈₂: f45→f42; t₈₃: f45→f42; t₈₄: f45→f45; t₉₁: f71→f73; t₉₃: f73→f73]

Cut unreachable locations [f33; f45] from the program graph

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: L
Locations: f0, f12, f15, f28, f30, f42, f59, f69, f71, f73, f82
Transitions:
t₆₄: f0(X₀, X₁, X₂, X₃, X₄, X₅) → f12(X₀, X₁, X₂, X₃, X₄, X₅)
t₆₅: f12(X₀, X₁, X₂, X₃, X₄, X₅) → f15(X₀, X₁, 0, X₃, X₄, X₅) :|: X₁ ≤ X₀
t₆₆: f12(X₀, X₁, X₂, X₃, X₄, X₅) → f28(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁
t₆₈: f15(X₀, X₁, X₂, X₃, X₄, X₅) → f12(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂
t₆₉: f15(X₀, X₁, X₂, X₃, X₄, X₅) → f12(X₀, 1+X₁, 0, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₁ ≤ X₀
t₇₀: f15(X₀, X₁, X₂, X₃, X₄, X₅) → f15(X₀, X₁, X₂, 1+X₃, X₄, X₅) :|: L ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂
t₇₁: f15(X₀, X₁, X₂, X₃, X₄, X₅) → f15(X₀, X₁, L, 1+X₃, X₄, X₅) :|: 1+X₂ ≤ L ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂
t₇₂: f28(X₀, X₁, X₂, X₃, X₄, X₅) → f30(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁
t₇₃: f28(X₀, X₁, X₂, X₃, X₄, X₅) → f82(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁
t₇₅: f30(X₀, X₁, X₂, X₃, X₄, X₅) → f42(X₀, X₁, 0, X₃, X₄, X₅) :|: X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀
t₇₉: f42(X₀, X₁, X₂, X₃, X₄, X₅) → f59(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₀: f42(X₀, X₁, X₂, X₃, X₄, X₅) → f59(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₅ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₁: f42(X₀, X₁, X₂, X₃, X₄, X₅) → f69(X₀, X₁, X₂, X₃, X₄, X₃) :|: 1+X₀ ≤ X₁ ∧ X₅ ≤ X₃ ∧ X₃ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₅: f59(X₀, X₁, X₂, X₃, X₄, X₅) → f59(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₆: f59(X₀, X₁, X₂, X₃, X₄, X₅) → f69(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₇: f69(X₀, X₁, X₂, X₃, X₄, X₅) → f71(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+L ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₈: f69(X₀, X₁, X₂, X₃, X₄, X₅) → f71(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₉: f71(X₀, X₁, X₂, X₃, X₄, X₅) → f28(X₀, X₁, X₂, 1+X₀, X₄, X₅) :|: X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₉₀: f71(X₀, X₁, X₂, X₃, X₄, X₅) → f73(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₉₂: f73(X₀, X₁, X₂, X₃, X₄, X₅) → f28(X₀, X₁, X₂, 1+X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 2+X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0

MPRF for transition t₆₅: f12(X₀, X₁, X₂, X₃, X₄, X₅) → f15(X₀, X₁, 0, X₃, X₄, X₅) :|: X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• f12: [1+X₀-X₁]
• f15: [X₀-X₁]

MPRF for transition t₆₈: f15(X₀, X₁, X₂, X₃, X₄, X₅) → f12(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• f12: [1+X₀-X₁]
• f15: [1+X₀-X₁]

MPRF for transition t₆₉: f15(X₀, X₁, X₂, X₃, X₄, X₅) → f12(X₀, 1+X₁, 0, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• f12: [1+X₀-X₁]
• f15: [1+X₀-X₁]

MPRF for transition t₇₀: f15(X₀, X₁, X₂, X₃, X₄, X₅) → f15(X₀, X₁, X₂, 1+X₃, X₄, X₅) :|: L ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₀+X₃+1 {O(n)}

MPRF:

• f12: [1+X₀-X₃]
• f15: [1+X₀-X₃]

MPRF for transition t₇₁: f15(X₀, X₁, X₂, X₃, X₄, X₅) → f15(X₀, X₁, L, 1+X₃, X₄, X₅) :|: 1+X₂ ≤ L ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₀+X₃+1 {O(n)}

MPRF:

• f12: [1+X₀-X₃]
• f15: [1+X₀-X₃]

MPRF for transition t₇₂: f28(X₀, X₁, X₂, X₃, X₄, X₅) → f30(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ of depth 1:

new bound:

7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}

MPRF:

• f28: [X₁-X₃]
• f30: [X₁-1-X₃]
• f42: [X₁-1-X₃]
• f59: [X₁-1-X₃]
• f69: [X₁-1-X₃]
• f71: [X₁-1-X₃]
• f73: [X₁-1-X₃]

MPRF for transition t₇₅: f30(X₀, X₁, X₂, X₃, X₄, X₅) → f42(X₀, X₁, 0, X₃, X₄, X₅) :|: X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ of depth 1:

new bound:

7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}

MPRF:

• f28: [X₁-X₃]
• f30: [X₁-X₃]
• f42: [X₁-1-X₃]
• f59: [X₁-1-X₃]
• f69: [X₁-1-X₃]
• f71: [X₁-1-X₃]
• f73: [X₁-1-X₃]

MPRF for transition t₇₉: f42(X₀, X₁, X₂, X₃, X₄, X₅) → f59(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

3⋅X₅+4⋅X₀+7⋅X₃+4 {O(n)}

MPRF:

• f28: [X₅-X₃]
• f30: [X₅-X₃]
• f42: [X₅-X₃]
• f59: [X₅-1-X₃]
• f69: [X₅-1-X₃]
• f71: [X₅-1-X₃]
• f73: [X₅-1-X₃]

MPRF for transition t₈₀: f42(X₀, X₁, X₂, X₃, X₄, X₅) → f59(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₅ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₀+7⋅X₃+5 {O(n)}

MPRF:

• f28: [1+X₀-X₃]
• f30: [1+X₀-X₃]
• f42: [1+X₀-X₃]
• f59: [X₀-X₃]
• f69: [X₀-X₃]
• f71: [X₀-X₃]
• f73: [X₀-X₃]

MPRF for transition t₈₁: f42(X₀, X₁, X₂, X₃, X₄, X₅) → f69(X₀, X₁, X₂, X₃, X₄, X₃) :|: 1+X₀ ≤ X₁ ∧ X₅ ≤ X₃ ∧ X₃ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₀+7⋅X₃+5 {O(n)}

MPRF:

• f28: [1+X₀-X₃]
• f30: [1+X₀-X₃]
• f42: [1+X₀-X₃]
• f59: [X₀-X₃]
• f69: [X₀-X₃]
• f71: [X₀-X₃]
• f73: [X₀-X₃]

MPRF for transition t₈₅: f59(X₀, X₁, X₂, X₃, X₄, X₅) → f59(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

3⋅X₀+3⋅X₄+1 {O(n)}

MPRF:

• f28: [1+X₀-X₄]
• f30: [1+X₀-X₄]
• f42: [1+X₀-X₄]
• f59: [1+X₀-X₄]
• f69: [1+X₀-X₄]
• f71: [1+X₀-X₄]
• f73: [1+X₀-X₄]

MPRF for transition t₈₆: f59(X₀, X₁, X₂, X₃, X₄, X₅) → f69(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}

MPRF:

• f28: [1+X₁-X₃]
• f30: [1+X₁-X₃]
• f42: [1+X₁-X₃]
• f59: [1+X₁-X₃]
• f69: [X₁-X₃]
• f71: [X₁-X₃]
• f73: [X₁-X₃]

MPRF for transition t₈₇: f69(X₀, X₁, X₂, X₃, X₄, X₅) → f71(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+L ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}

MPRF:

• f28: [1+X₁-X₃]
• f30: [1+X₁-X₃]
• f42: [1+X₁-X₃]
• f59: [1+X₁-X₃]
• f69: [1+X₁-X₃]
• f71: [X₁-X₃]
• f73: [X₁-X₃]

MPRF for transition t₈₈: f69(X₀, X₁, X₂, X₃, X₄, X₅) → f71(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

14⋅X₁+15⋅X₀+7⋅X₃+12 {O(n)}

MPRF:

• f28: [2⋅X₁-X₀-X₃]
• f30: [2⋅X₁-X₀-X₃]
• f42: [2⋅X₁-X₀-X₃]
• f59: [2⋅X₁-X₀-X₃]
• f69: [2⋅X₁-X₀-X₃]
• f71: [2⋅X₁-1-X₀-X₃]
• f73: [2⋅X₁-1-X₀-X₃]

MPRF for transition t₈₉: f71(X₀, X₁, X₂, X₃, X₄, X₅) → f28(X₀, X₁, X₂, 1+X₀, X₄, X₅) :|: X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}

MPRF:

• f28: [X₁-X₃]
• f30: [X₁-X₃]
• f42: [X₁-X₃]
• f59: [X₁-X₃]
• f69: [X₁-X₃]
• f71: [X₁-X₃]
• f73: [X₁-X₃]

MPRF for transition t₉₀: f71(X₀, X₁, X₂, X₃, X₄, X₅) → f73(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₀+7⋅X₃+4 {O(n)}

MPRF:

• f28: [X₀-X₃]
• f30: [X₀-X₃]
• f42: [X₀-X₃]
• f59: [X₀-X₃]
• f69: [X₀-X₃]
• f71: [X₀-X₃]
• f73: [X₀-1-X₃]

MPRF for transition t₉₂: f73(X₀, X₁, X₂, X₃, X₄, X₅) → f28(X₀, X₁, X₂, 1+X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 2+X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₀+7⋅X₃+4 {O(n)}

MPRF:

• f28: [X₀-X₃]
• f30: [X₀-X₃]
• f42: [X₀-X₃]
• f59: [X₀-X₃]
• f69: [X₀-X₃]
• f71: [X₀-X₃]
• f73: [X₀-X₃]

All Bounds

Timebounds

Overall timebound:3⋅X₄+3⋅X₅+52⋅X₁+79⋅X₃+95⋅X₀+85 {O(n)}
t₆₄: 1 {O(1)}
t₆₅: X₀+X₁+1 {O(n)}
t₆₆: 1 {O(1)}
t₆₈: X₀+X₁+1 {O(n)}
t₆₉: X₀+X₁+1 {O(n)}
t₇₀: X₀+X₃+1 {O(n)}
t₇₁: X₀+X₃+1 {O(n)}
t₇₂: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₃: 1 {O(1)}
t₇₅: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₉: 3⋅X₅+4⋅X₀+7⋅X₃+4 {O(n)}
t₈₀: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₁: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₅: 3⋅X₀+3⋅X₄+1 {O(n)}
t₈₆: 7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}
t₈₇: 7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}
t₈₈: 14⋅X₁+15⋅X₀+7⋅X₃+12 {O(n)}
t₈₉: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₉₀: 7⋅X₀+7⋅X₃+4 {O(n)}
t₉₂: 7⋅X₀+7⋅X₃+4 {O(n)}

Costbounds

Overall costbound: 3⋅X₄+3⋅X₅+52⋅X₁+79⋅X₃+95⋅X₀+85 {O(n)}
t₆₄: 1 {O(1)}
t₆₅: X₀+X₁+1 {O(n)}
t₆₆: 1 {O(1)}
t₆₈: X₀+X₁+1 {O(n)}
t₆₉: X₀+X₁+1 {O(n)}
t₇₀: X₀+X₃+1 {O(n)}
t₇₁: X₀+X₃+1 {O(n)}
t₇₂: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₃: 1 {O(1)}
t₇₅: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₉: 3⋅X₅+4⋅X₀+7⋅X₃+4 {O(n)}
t₈₀: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₁: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₅: 3⋅X₀+3⋅X₄+1 {O(n)}
t₈₆: 7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}
t₈₇: 7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}
t₈₈: 14⋅X₁+15⋅X₀+7⋅X₃+12 {O(n)}
t₈₉: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₉₀: 7⋅X₀+7⋅X₃+4 {O(n)}
t₉₂: 7⋅X₀+7⋅X₃+4 {O(n)}

Sizebounds

t₆₄, X₀: X₀ {O(n)}
t₆₄, X₁: X₁ {O(n)}
t₆₄, X₂: X₂ {O(n)}
t₆₄, X₃: X₃ {O(n)}
t₆₄, X₄: X₄ {O(n)}
t₆₄, X₅: X₅ {O(n)}
t₆₅, X₀: X₀ {O(n)}
t₆₅, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₆₅, X₂: 0 {O(1)}
t₆₅, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₆₅, X₄: X₄ {O(n)}
t₆₅, X₅: X₅ {O(n)}
t₆₆, X₀: 3⋅X₀ {O(n)}
t₆₆, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₆₆, X₃: 4⋅X₀+7⋅X₃+4 {O(n)}
t₆₆, X₄: 3⋅X₄ {O(n)}
t₆₆, X₅: 3⋅X₅ {O(n)}
t₆₈, X₀: X₀ {O(n)}
t₆₈, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₆₈, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₆₈, X₄: X₄ {O(n)}
t₆₈, X₅: X₅ {O(n)}
t₆₉, X₀: X₀ {O(n)}
t₆₉, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₆₉, X₂: 0 {O(1)}
t₆₉, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₆₉, X₄: X₄ {O(n)}
t₆₉, X₅: X₅ {O(n)}
t₇₀, X₀: X₀ {O(n)}
t₇₀, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₇₀, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₇₀, X₄: X₄ {O(n)}
t₇₀, X₅: X₅ {O(n)}
t₇₁, X₀: X₀ {O(n)}
t₇₁, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₇₁, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₇₁, X₄: X₄ {O(n)}
t₇₁, X₅: X₅ {O(n)}
t₇₂, X₀: 3⋅X₀ {O(n)}
t₇₂, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₂, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₇₂, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₇₂, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₇₃, X₀: 9⋅X₀ {O(n)}
t₇₃, X₁: 12⋅X₀+21⋅X₁+12 {O(n)}
t₇₃, X₃: 10⋅X₀+7⋅X₃+6 {O(n)}
t₇₃, X₄: 15⋅X₄+6⋅X₀+2 {O(n)}
t₇₃, X₅: 22⋅X₀+28⋅X₃+9⋅X₅+16 {O(n)}
t₇₅, X₀: 3⋅X₀ {O(n)}
t₇₅, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₅, X₂: 0 {O(1)}
t₇₅, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₇₅, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₇₅, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₇₉, X₀: 3⋅X₀ {O(n)}
t₇₉, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₉, X₂: 0 {O(1)}
t₇₉, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₇₉, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₇₉, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₈₀, X₀: 3⋅X₀ {O(n)}
t₈₀, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₀, X₂: 0 {O(1)}
t₈₀, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₀, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₈₀, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₈₁, X₀: 3⋅X₀ {O(n)}
t₈₁, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₁, X₂: 0 {O(1)}
t₈₁, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₁, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₈₁, X₅: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₅, X₀: 3⋅X₀ {O(n)}
t₈₅, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₅, X₂: 0 {O(1)}
t₈₅, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₅, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₈₅, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₈₆, X₀: 3⋅X₀ {O(n)}
t₈₆, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₆, X₂: 0 {O(1)}
t₈₆, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₆, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₈₆, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₈₇, X₀: 3⋅X₀ {O(n)}
t₈₇, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₇, X₂: 0 {O(1)}
t₈₇, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₇, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₈₇, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₈₈, X₀: 3⋅X₀ {O(n)}
t₈₈, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₈, X₂: 0 {O(1)}
t₈₈, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₈, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₈₈, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₈₉, X₀: 6⋅X₀ {O(n)}
t₈₉, X₁: 14⋅X₁+8⋅X₀+8 {O(n)}
t₈₉, X₂: 0 {O(1)}
t₈₉, X₃: 6⋅X₀+2 {O(n)}
t₈₉, X₄: 12⋅X₄+6⋅X₀+2 {O(n)}
t₈₉, X₅: 22⋅X₀+28⋅X₃+6⋅X₅+16 {O(n)}
t₉₀, X₀: 3⋅X₀ {O(n)}
t₉₀, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₉₀, X₂: 0 {O(1)}
t₉₀, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₉₀, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₉₀, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₉₂, X₀: 3⋅X₀ {O(n)}
t₉₂, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₉₂, X₂: 0 {O(1)}
t₉₂, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₉₂, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₉₂, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}