Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₂-1, X₁, X₂, X₁, X₄) :|: X₂ < 1
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₂-1, X₁, X₂, X₁, X₄) :|: 1 < X₂
t₉: l2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₁, X₃, X₁) :|: 0 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 0
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 0 ≤ X₄
t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀
t₁₀: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄-X₀) :|: X₃ ≤ 0 ∧ 0 ≤ X₃
t₁₄: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: X₃ < 0
t₁₅: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: 0 < X₃
t₁₂: l8(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃-X₀, X₄)
Preprocessing
Found invariant X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l6
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l5
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l8
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l4
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₂-1, X₁, X₂, X₁, X₄) :|: X₂ < 1 ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₂-1, X₁, X₂, X₁, X₄) :|: 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₉: l2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₁, X₃, X₁) :|: 0 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 0 ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₀: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄-X₀) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₄: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: X₃ < 0 ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₅: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: 0 < X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₂: l8(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃-X₀, X₄) :|: X₄ ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
MPRF for transition t₅: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₂-1, X₁, X₂, X₁, X₄) :|: 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄-X₀) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
2⋅X₁+3 {O(n)}
MPRF for transition t₁₅: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: 0 < X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
X₁+1 {O(n)}
Chain transitions t₁₅: l6→l1 and t₅: l1→l5 to t₁₆₆: l6→l5
Chain transitions t₁₄: l6→l1 and t₅: l1→l5 to t₁₆₇: l6→l5
Chain transitions t₁₄: l6→l1 and t₄: l1→l5 to t₁₆₈: l6→l5
Chain transitions t₁₅: l6→l1 and t₄: l1→l5 to t₁₆₉: l6→l5
Chain transitions t₁₃: l6→l1 and t₄: l1→l5 to t₁₇₀: l6→l5
Chain transitions t₁₃: l6→l1 and t₅: l1→l5 to t₁₇₁: l6→l5
Chain transitions t₁₃: l6→l1 and t₃: l1→l4 to t₁₇₂: l6→l4
Chain transitions t₁₄: l6→l1 and t₃: l1→l4 to t₁₇₃: l6→l4
Chain transitions t₁₅: l6→l1 and t₃: l1→l4 to t₁₇₄: l6→l4
Chain transitions t₂: l3→l1 and t₃: l1→l4 to t₁₇₅: l3→l4
Chain transitions t₂: l3→l1 and t₄: l1→l5 to t₁₇₆: l3→l5
Chain transitions t₂: l3→l1 and t₅: l1→l5 to t₁₇₇: l3→l5
Chain transitions t₁₂: l8→l5 and t₁₀: l5→l8 to t₁₇₈: l8→l8
Chain transitions t₁₇₁: l6→l5 and t₁₀: l5→l8 to t₁₇₉: l6→l8
Chain transitions t₁₇₁: l6→l5 and t₁₁: l5→l6 to t₁₈₀: l6→l6
Chain transitions t₁₂: l8→l5 and t₁₁: l5→l6 to t₁₈₁: l8→l6
Chain transitions t₁₇₀: l6→l5 and t₁₁: l5→l6 to t₁₈₂: l6→l6
Chain transitions t₁₇₀: l6→l5 and t₁₀: l5→l8 to t₁₈₃: l6→l8
Chain transitions t₁₆₉: l6→l5 and t₁₁: l5→l6 to t₁₈₄: l6→l6
Chain transitions t₁₆₉: l6→l5 and t₁₀: l5→l8 to t₁₈₅: l6→l8
Chain transitions t₁₆₈: l6→l5 and t₁₁: l5→l6 to t₁₈₆: l6→l6
Chain transitions t₁₆₈: l6→l5 and t₁₀: l5→l8 to t₁₈₇: l6→l8
Chain transitions t₁₆₇: l6→l5 and t₁₁: l5→l6 to t₁₈₈: l6→l6
Chain transitions t₁₆₇: l6→l5 and t₁₀: l5→l8 to t₁₈₉: l6→l8
Chain transitions t₁₆₆: l6→l5 and t₁₁: l5→l6 to t₁₉₀: l6→l6
Chain transitions t₁₆₆: l6→l5 and t₁₀: l5→l8 to t₁₉₁: l6→l8
Chain transitions t₁₇₇: l3→l5 and t₁₁: l5→l6 to t₁₉₂: l3→l6
Chain transitions t₁₇₇: l3→l5 and t₁₀: l5→l8 to t₁₉₃: l3→l8
Chain transitions t₁₇₆: l3→l5 and t₁₁: l5→l6 to t₁₉₄: l3→l6
Chain transitions t₁₇₆: l3→l5 and t₁₀: l5→l8 to t₁₉₅: l3→l8
Analysing control-flow refined program
Cut unsatisfiable transition t₁₄: l6→l1
Cut unsatisfiable transition t₁₆₇: l6→l5
Cut unsatisfiable transition t₁₆₈: l6→l5
Cut unsatisfiable transition t₁₆₉: l6→l5
Cut unsatisfiable transition t₁₇₀: l6→l5
Cut unsatisfiable transition t₁₇₃: l6→l4
Cut unsatisfiable transition t₁₇₄: l6→l4
Cut unsatisfiable transition t₁₇₆: l3→l5
Cut unsatisfiable transition t₁₈₀: l6→l6
Cut unsatisfiable transition t₁₈₂: l6→l6
Cut unsatisfiable transition t₁₈₃: l6→l8
Cut unsatisfiable transition t₁₈₄: l6→l6
Cut unsatisfiable transition t₁₈₅: l6→l8
Cut unsatisfiable transition t₁₈₆: l6→l6
Cut unsatisfiable transition t₁₈₇: l6→l8
Cut unsatisfiable transition t₁₈₈: l6→l6
Cut unsatisfiable transition t₁₈₉: l6→l8
Cut unsatisfiable transition t₁₉₀: l6→l6
Cut unsatisfiable transition t₁₉₂: l3→l6
Cut unsatisfiable transition t₁₉₄: l3→l6
Cut unsatisfiable transition t₁₉₅: l3→l8
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l6
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l8
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l4
MPRF for transition t₁₇₉: l6(X₀, X₁, X₂, X₃, X₄) -{3}> l8(X₀-1, X₁, X₀, X₁, X₄-X₀) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 < X₀ ∧ X₀ ≤ 1+X₁ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁+X₀ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₁+X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₁₈₁: l8(X₀, X₁, X₂, X₃, X₄) -{2}> l6(X₀, X₁, X₂, X₃-X₀, X₄) :|: X₃ < 2⋅X₀ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₁₉₁: l6(X₀, X₁, X₂, X₃, X₄) -{3}> l8(X₀-1, X₁, X₀, X₁, X₄) :|: 0 < X₃ ∧ 1 < X₀ ∧ X₀ ≤ 1+X₁ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF for transition t₁₇₈: l8(X₀, X₁, X₂, X₃, X₄) -{2}> l8(X₀, X₁, X₂, X₃-X₀, X₄) :|: 2⋅X₀ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁⋅X₁+2⋅X₁+1 {O(n^2)}
Analysing control-flow refined program
Cut unsatisfiable transition t₄₇₈: l1→n_l5___10
Cut unsatisfiable transition t₅₁₂: n_l1___3→l4
Cut unreachable locations [n_l5___10; n_l5___7; n_l8___5; n_l8___8] from the program graph
Found invariant X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l6___6
Found invariant X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___1
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l8___2
Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___9
Found invariant 1+X₄ ≤ X₁ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___4
Found invariant X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l1___3
Found invariant X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l4
MPRF for transition t₄₈₀: n_l1___3(X₀, X₁, X₂, X₃, X₄) → n_l5___9(X₂-1, X₁, X₂, X₁, X₄) :|: 0 < X₁ ∧ 1 < X₂ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₄₈₁: n_l1___4(X₀, X₁, X₂, X₃, X₄) → n_l5___9(X₂-1, X₁, X₂, X₁, X₄) :|: 0 < X₁ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀+X₄ ≤ X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₁+4 {O(n)}
MPRF for transition t₄₈₂: n_l5___1(X₀, X₁, X₂, X₃, X₄) → n_l6___6(X₀, X₁, X₀+1, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ 0 < X₀ ∧ 0 ≤ X₃ ∧ X₃ < X₀ ∧ X₀+1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₁+2 {O(n)}
MPRF for transition t₄₈₇: n_l5___9(X₀, X₁, X₂, X₃, X₄) → n_l8___2(X₀, X₁, X₀+1, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ 0 < X₀ ∧ 0 < X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₄₈₈: n_l6___6(X₀, X₁, X₂, X₃, X₄) → n_l1___3(X₀, X₁, X₀, X₃, X₄) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ 0 < X₃ ∧ X₀+1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₄₈₉: n_l6___6(X₀, X₁, X₂, X₃, X₄) → n_l1___4(X₀, X₁, X₀, 0, X₄-X₀) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
TWN: t₄₈₃: n_l5___1→n_l8___2
cycle: [t₄₈₃: n_l5___1→n_l8___2; t₄₉₀: n_l8___2→n_l5___1]
loop: (1 < X₂ ∧ X₀+1 ≤ X₂ ∧ X₀+1 ≤ X₂ ∧ 0 ≤ 0 ∧ 0 < X₀ ∧ X₀ ≤ X₃ ∧ 2⋅X₀ ≤ X₃ ∧ 0 ≤ 0,(X₀,X₂,X₃) -> (X₀,X₀+1,X₃-X₀)
order: [X₀; X₂; X₃]
closed-form:
X₀: X₀
X₂: [[n == 0]] * X₂ + [[n != 0]] * X₀+1
X₃: X₃ + [[n != 0]] * -X₀ * n^1
Termination: true
Formula:
X₀ < 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ X₀ < X₃ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₀ < 0 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 < X₀
∨ 2⋅X₀ < X₃ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ < 0 ∧ 0 < X₀
∨ 2⋅X₀ < X₃ ∧ X₀ < X₃ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ 2⋅X₀ < X₃ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 < X₀
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 2⋅X₀ ≤ X₃ ∧ X₃ ≤ 2⋅X₀ ∧ X₀ < 0 ∧ 0 < X₀
∨ 2⋅X₀ ≤ X₃ ∧ X₃ ≤ 2⋅X₀ ∧ X₀ < X₃ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ 2⋅X₀ ≤ X₃ ∧ X₃ ≤ 2⋅X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 < X₀
Stabilization-Threshold for: 2⋅X₀ ≤ X₃
alphas_abs: 2⋅X₀+X₃
M: 0
N: 1
Bound: 2⋅X₃+4⋅X₀+2 {O(n)}
Stabilization-Threshold for: X₀ ≤ X₃
alphas_abs: X₀+X₃
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₃+2 {O(n)}
TWN - Lifting for t₄₈₃: n_l5___1→n_l8___2 of 4⋅X₃+6⋅X₀+8 {O(n)}
relevant size-bounds w.r.t. t₄₈₇:
X₀: X₁ {O(n)}
X₃: 3⋅X₁ {O(n)}
Runtime-bound of t₄₈₇: X₁ {O(n)}
Results in: 18⋅X₁⋅X₁+8⋅X₁ {O(n^2)}
TWN: t₄₉₀: n_l8___2→n_l5___1
TWN - Lifting for t₄₉₀: n_l8___2→n_l5___1 of 4⋅X₃+6⋅X₀+8 {O(n)}
relevant size-bounds w.r.t. t₄₈₇:
X₀: X₁ {O(n)}
X₃: 3⋅X₁ {O(n)}
Runtime-bound of t₄₈₇: X₁ {O(n)}
Results in: 18⋅X₁⋅X₁+8⋅X₁ {O(n^2)}
CFR: Improvement to new bound with the following program:
new bound:
Infinite
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l7, n_l1___3, n_l1___4, n_l5___1, n_l5___9, n_l6___6, n_l8___2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₄₇₉: l1(X₀, X₁, X₂, X₃, X₄) → n_l5___9(X₂-1, X₁, X₂, X₁, X₄) :|: 0 < X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₉: l2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₁, X₃, X₁) :|: 0 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 0 ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₄₈₀: n_l1___3(X₀, X₁, X₂, X₃, X₄) → n_l5___9(X₂-1, X₁, X₂, X₁, X₄) :|: 0 < X₁ ∧ 1 < X₂ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₅₁₃: n_l1___4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₈₁: n_l1___4(X₀, X₁, X₂, X₃, X₄) → n_l5___9(X₂-1, X₁, X₂, X₁, X₄) :|: 0 < X₁ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀+X₄ ≤ X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₈₂: n_l5___1(X₀, X₁, X₂, X₃, X₄) → n_l6___6(X₀, X₁, X₀+1, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ 0 < X₀ ∧ 0 ≤ X₃ ∧ X₃ < X₀ ∧ X₀+1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₈₃: n_l5___1(X₀, X₁, X₂, X₃, X₄) → n_l8___2(X₀, X₁, X₀+1, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ 0 < X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₈₇: n_l5___9(X₀, X₁, X₂, X₃, X₄) → n_l8___2(X₀, X₁, X₀+1, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ 0 < X₀ ∧ 0 < X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₈₈: n_l6___6(X₀, X₁, X₂, X₃, X₄) → n_l1___3(X₀, X₁, X₀, X₃, X₄) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ 0 < X₃ ∧ X₀+1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₈₉: n_l6___6(X₀, X₁, X₂, X₃, X₄) → n_l1___4(X₀, X₁, X₀, 0, X₄-X₀) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₉₀: n_l8___2(X₀, X₁, X₂, X₃, X₄) → n_l5___1(X₀, X₁, X₀+1, X₃-X₀, X₄) :|: 1 < X₂ ∧ X₀+1 ≤ X₂ ∧ X₀+1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
CFR: Improvement to new bound with the following program:
new bound:
36⋅X₁⋅X₁+24⋅X₁+7 {O(n^2)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l7, n_l1___3, n_l1___4, n_l5___1, n_l5___9, n_l6___6, n_l8___2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₄₇₉: l1(X₀, X₁, X₂, X₃, X₄) → n_l5___9(X₂-1, X₁, X₂, X₁, X₄) :|: 0 < X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₉: l2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₁, X₃, X₁) :|: 0 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 0 ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₄₈₀: n_l1___3(X₀, X₁, X₂, X₃, X₄) → n_l5___9(X₂-1, X₁, X₂, X₁, X₄) :|: 0 < X₁ ∧ 1 < X₂ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₅₁₃: n_l1___4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₈₁: n_l1___4(X₀, X₁, X₂, X₃, X₄) → n_l5___9(X₂-1, X₁, X₂, X₁, X₄) :|: 0 < X₁ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀+X₄ ≤ X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₈₂: n_l5___1(X₀, X₁, X₂, X₃, X₄) → n_l6___6(X₀, X₁, X₀+1, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ 0 < X₀ ∧ 0 ≤ X₃ ∧ X₃ < X₀ ∧ X₀+1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₈₃: n_l5___1(X₀, X₁, X₂, X₃, X₄) → n_l8___2(X₀, X₁, X₀+1, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ 0 < X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₈₇: n_l5___9(X₀, X₁, X₂, X₃, X₄) → n_l8___2(X₀, X₁, X₀+1, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ 0 < X₀ ∧ 0 < X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₈₈: n_l6___6(X₀, X₁, X₂, X₃, X₄) → n_l1___3(X₀, X₁, X₀, X₃, X₄) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ 0 < X₃ ∧ X₀+1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₈₉: n_l6___6(X₀, X₁, X₂, X₃, X₄) → n_l1___4(X₀, X₁, X₀, 0, X₄-X₀) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₉₀: n_l8___2(X₀, X₁, X₂, X₃, X₄) → n_l5___1(X₀, X₁, X₀+1, X₃-X₀, X₄) :|: 1 < X₂ ∧ X₀+1 ≤ X₂ ∧ X₀+1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:36⋅X₁⋅X₁+24⋅X₁+17 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₄₇₉: 1 {O(1)}
t₄₈₀: X₁ {O(n)}
t₄₈₁: 2⋅X₁+4 {O(n)}
t₄₈₂: 2⋅X₁+2 {O(n)}
t₄₈₃: 18⋅X₁⋅X₁+8⋅X₁ {O(n^2)}
t₄₈₇: X₁ {O(n)}
t₄₈₈: X₁ {O(n)}
t₄₈₉: X₁+1 {O(n)}
t₄₉₀: 18⋅X₁⋅X₁+8⋅X₁ {O(n^2)}
t₅₁₃: 1 {O(1)}
Costbounds
Overall costbound: 36⋅X₁⋅X₁+24⋅X₁+17 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₄₇₉: 1 {O(1)}
t₄₈₀: X₁ {O(n)}
t₄₈₁: 2⋅X₁+4 {O(n)}
t₄₈₂: 2⋅X₁+2 {O(n)}
t₄₈₃: 18⋅X₁⋅X₁+8⋅X₁ {O(n^2)}
t₄₈₇: X₁ {O(n)}
t₄₈₈: X₁ {O(n)}
t₄₈₉: X₁+1 {O(n)}
t₄₉₀: 18⋅X₁⋅X₁+8⋅X₁ {O(n^2)}
t₅₁₃: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₁ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₁ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: 1 {O(1)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₁ {O(n)}
t₆, X₀: 1 {O(1)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 1 {O(1)}
t₆, X₃: 0 {O(1)}
t₆, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₇, X₀: X₀+1 {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}
t₇, X₂: 1 {O(1)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₁⋅X₁+4⋅X₁ {O(n^2)}
t₈, X₀: 1 {O(1)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 1 {O(1)}
t₈, X₃: 0 {O(1)}
t₈, X₄: 0 {O(1)}
t₉, X₀: 2⋅X₀+3 {O(n)}
t₉, X₁: 5⋅X₁ {O(n)}
t₉, X₂: X₂+3 {O(n)}
t₉, X₃: 2⋅X₃ {O(n)}
t₉, X₄: 2⋅X₁⋅X₁+7⋅X₁+X₄ {O(n^2)}
t₄₇₉, X₀: X₁ {O(n)}
t₄₇₉, X₁: X₁ {O(n)}
t₄₇₉, X₂: X₁ {O(n)}
t₄₇₉, X₃: X₁ {O(n)}
t₄₇₉, X₄: X₁ {O(n)}
t₄₈₀, X₀: X₁ {O(n)}
t₄₈₀, X₁: X₁ {O(n)}
t₄₈₀, X₂: X₁ {O(n)}
t₄₈₀, X₃: X₁ {O(n)}
t₄₈₀, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₈₁, X₀: X₁ {O(n)}
t₄₈₁, X₁: X₁ {O(n)}
t₄₈₁, X₂: X₁ {O(n)}
t₄₈₁, X₃: X₁ {O(n)}
t₄₈₁, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₈₂, X₀: X₁ {O(n)}
t₄₈₂, X₁: X₁ {O(n)}
t₄₈₂, X₂: X₁+1 {O(n)}
t₄₈₂, X₃: 3⋅X₁ {O(n)}
t₄₈₂, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₈₃, X₀: X₁ {O(n)}
t₄₈₃, X₁: X₁ {O(n)}
t₄₈₃, X₂: X₁+1 {O(n)}
t₄₈₃, X₃: 3⋅X₁ {O(n)}
t₄₈₃, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₈₇, X₀: X₁ {O(n)}
t₄₈₇, X₁: X₁ {O(n)}
t₄₈₇, X₂: 3⋅X₁+3 {O(n)}
t₄₈₇, X₃: 3⋅X₁ {O(n)}
t₄₈₇, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₈₈, X₀: X₁ {O(n)}
t₄₈₈, X₁: X₁ {O(n)}
t₄₈₈, X₂: X₁ {O(n)}
t₄₈₈, X₃: 3⋅X₁ {O(n)}
t₄₈₈, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₈₉, X₀: X₁ {O(n)}
t₄₈₉, X₁: X₁ {O(n)}
t₄₈₉, X₂: X₁ {O(n)}
t₄₈₉, X₃: 0 {O(1)}
t₄₈₉, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₉₀, X₀: X₁ {O(n)}
t₄₉₀, X₁: X₁ {O(n)}
t₄₉₀, X₂: 2⋅X₁+2 {O(n)}
t₄₉₀, X₃: 3⋅X₁ {O(n)}
t₄₉₀, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₅₁₃, X₀: 1 {O(1)}
t₅₁₃, X₁: X₁ {O(n)}
t₅₁₃, X₂: 1 {O(1)}
t₅₁₃, X₃: 0 {O(1)}
t₅₁₃, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}