Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: X₂ < 1
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: 1 < X₂
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ < 0
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₅
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 0 ∧ 0 ≤ X₅
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₁, X₃, X₁, X₅) :|: 1 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, nondef.0) :|: X₁ ≤ 1
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₀
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₃
t₁₁: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: X₃ < 0
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: 0 < X₃
t₁₃: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄-X₀, X₅) :|: X₃ ≤ 0 ∧ 0 ≤ X₃
t₁₄: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃-X₀, X₄, X₅)
Preprocessing
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l7
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 l5
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l4
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: X₂ < 1 ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ < 0
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₅
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 0 ∧ 0 ≤ X₅
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₁, X₃, X₁, X₅) :|: 1 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, nondef.0) :|: X₁ ≤ 1
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₀ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₁: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: X₃ < 0 ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: 0 < X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₃: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄-X₀, X₅) :|: 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: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃-X₀, X₄, X₅) :|: 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, X₅) → l4(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: 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+4 {O(n)}
MPRF for transition t₁₃: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄-X₀, X₅) :|: 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:
X₁+1 {O(n)}
Chain transitions t₁₃: l5→l1 and t₅: l1→l4 to t₁₆₁: l5→l4
Chain transitions t₁₂: l5→l1 and t₅: l1→l4 to t₁₆₂: l5→l4
Chain transitions t₁₂: l5→l1 and t₄: l1→l4 to t₁₆₃: l5→l4
Chain transitions t₁₃: l5→l1 and t₄: l1→l4 to t₁₆₄: l5→l4
Chain transitions t₁₁: l5→l1 and t₄: l1→l4 to t₁₆₅: l5→l4
Chain transitions t₁₁: l5→l1 and t₅: l1→l4 to t₁₆₆: l5→l4
Chain transitions t₁₁: l5→l1 and t₃: l1→l2 to t₁₆₇: l5→l2
Chain transitions t₁₂: l5→l1 and t₃: l1→l2 to t₁₆₈: l5→l2
Chain transitions t₁₃: l5→l1 and t₃: l1→l2 to t₁₆₉: l5→l2
Chain transitions t₂: l3→l1 and t₃: l1→l2 to t₁₇₀: l3→l2
Chain transitions t₂: l3→l1 and t₄: l1→l4 to t₁₇₁: l3→l4
Chain transitions t₂: l3→l1 and t₅: l1→l4 to t₁₇₂: l3→l4
Chain transitions t₁₄: l7→l4 and t₁₀: l4→l7 to t₁₇₃: l7→l7
Chain transitions t₁₆₆: l5→l4 and t₁₀: l4→l7 to t₁₇₄: l5→l7
Chain transitions t₁₆₆: l5→l4 and t₉: l4→l5 to t₁₇₅: l5→l5
Chain transitions t₁₄: l7→l4 and t₉: l4→l5 to t₁₇₆: l7→l5
Chain transitions t₁₆₅: l5→l4 and t₉: l4→l5 to t₁₇₇: l5→l5
Chain transitions t₁₆₅: l5→l4 and t₁₀: l4→l7 to t₁₇₈: l5→l7
Chain transitions t₁₆₄: l5→l4 and t₉: l4→l5 to t₁₇₉: l5→l5
Chain transitions t₁₆₄: l5→l4 and t₁₀: l4→l7 to t₁₈₀: l5→l7
Chain transitions t₁₆₃: l5→l4 and t₉: l4→l5 to t₁₈₁: l5→l5
Chain transitions t₁₆₃: l5→l4 and t₁₀: l4→l7 to t₁₈₂: l5→l7
Chain transitions t₁₆₂: l5→l4 and t₉: l4→l5 to t₁₈₃: l5→l5
Chain transitions t₁₆₂: l5→l4 and t₁₀: l4→l7 to t₁₈₄: l5→l7
Chain transitions t₁₆₁: l5→l4 and t₉: l4→l5 to t₁₈₅: l5→l5
Chain transitions t₁₆₁: l5→l4 and t₁₀: l4→l7 to t₁₈₆: l5→l7
Chain transitions t₁₇₂: l3→l4 and t₉: l4→l5 to t₁₈₇: l3→l5
Chain transitions t₁₇₂: l3→l4 and t₁₀: l4→l7 to t₁₈₈: l3→l7
Chain transitions t₁₇₁: l3→l4 and t₉: l4→l5 to t₁₈₉: l3→l5
Chain transitions t₁₇₁: l3→l4 and t₁₀: l4→l7 to t₁₉₀: l3→l7
Analysing control-flow refined program
Cut unsatisfiable transition t₁₁: l5→l1
Cut unsatisfiable transition t₁₆₃: l5→l4
Cut unsatisfiable transition t₁₆₄: l5→l4
Cut unsatisfiable transition t₁₆₅: l5→l4
Cut unsatisfiable transition t₁₆₆: l5→l4
Cut unsatisfiable transition t₁₆₇: l5→l2
Cut unsatisfiable transition t₁₆₈: l5→l2
Cut unsatisfiable transition t₁₇₀: l3→l2
Cut unsatisfiable transition t₁₇₁: l3→l4
Cut unsatisfiable transition t₁₇₄: l5→l7
Cut unsatisfiable transition t₁₇₅: l5→l5
Cut unsatisfiable transition t₁₇₇: l5→l5
Cut unsatisfiable transition t₁₇₈: l5→l7
Cut unsatisfiable transition t₁₇₉: l5→l5
Cut unsatisfiable transition t₁₈₀: l5→l7
Cut unsatisfiable transition t₁₈₁: l5→l5
Cut unsatisfiable transition t₁₈₂: l5→l7
Cut unsatisfiable transition t₁₈₃: l5→l5
Cut unsatisfiable transition t₁₈₅: l5→l5
Cut unsatisfiable transition t₁₈₇: l3→l5
Cut unsatisfiable transition t₁₈₉: l3→l5
Cut unsatisfiable transition t₁₉₀: l3→l7
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 l7
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l5
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l1
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 l4
MPRF for transition t₁₇₆: l7(X₀, X₁, X₂, X₃, X₄, X₅) -{2}> l5(X₀, X₁, X₂, X₃-X₀, X₄, X₅) :|: 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 t₁₈₄: l5(X₀, X₁, X₂, X₃, X₄, X₅) -{3}> l7(X₀-1, X₁, X₀, X₁, X₄, X₅) :|: 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 t₁₈₆: l5(X₀, X₁, X₂, X₃, X₄, X₅) -{3}> l7(X₀-1, X₁, X₀, X₁, X₄-X₀, X₅) :|: 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+2 {O(n)}
MPRF for transition t₁₇₃: l7(X₀, X₁, X₂, X₃, X₄, X₅) -{2}> l7(X₀, X₁, X₂, X₃-X₀, X₄, X₅) :|: 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:
4⋅X₁⋅X₁+12⋅X₁+5 {O(n^2)}
Analysing control-flow refined program
Cut unsatisfiable transition t₃: l1→l2
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_l4___3
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_l5___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_l4___5
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l1
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___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_l7___4
MPRF for transition t₄₆₄: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___5(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: 0 < X₁ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀+X₄ ≤ X₁ ∧ 1 < X₂ ∧ X₂ ≤ X₁ ∧ X₄ ≤ 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:
X₁+1 {O(n)}
MPRF for transition t₄₆₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___5(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: 0 < X₁ ∧ 1 < X₂ ∧ 1 < X₂ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
2⋅X₁ {O(n)}
MPRF for transition t₄₆₆: n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l5___2(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: 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 ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ 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:
X₁ {O(n)}
MPRF for transition t₄₆₈: n_l4___5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l7___4(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: X₀+1 ≤ X₂ ∧ 0 < X₃ ∧ 0 < X₀ ∧ 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 ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ 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:
2⋅X₁+1 {O(n)}
MPRF for transition t₄₆₉: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, X₁, X₀, 0, X₄-X₀, X₅) :|: 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 {O(n)}
MPRF for transition t₄₇₀: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: 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+1 {O(n)}
TWN: t₄₆₇: n_l4___3→n_l7___4
cycle: [t₄₆₇: n_l4___3→n_l7___4; t₄₇₁: n_l7___4→n_l4___3]
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 t₄₆₇: n_l4___3→n_l7___4 of 4⋅X₃+6⋅X₀+8 {O(n)}
relevant size-bounds w.r.t. t₄₆₈:
X₀: X₁ {O(n)}
X₃: 3⋅X₁ {O(n)}
Runtime-bound of t₄₆₈: 2⋅X₁+1 {O(n)}
Results in: 36⋅X₁⋅X₁+34⋅X₁+8 {O(n^2)}
TWN: t₄₇₁: n_l7___4→n_l4___3
TWN - Lifting for t₄₇₁: n_l7___4→n_l4___3 of 4⋅X₃+6⋅X₀+8 {O(n)}
relevant size-bounds w.r.t. t₄₆₈:
X₀: X₁ {O(n)}
X₃: 3⋅X₁ {O(n)}
Runtime-bound of t₄₆₈: 2⋅X₁+1 {O(n)}
Results in: 36⋅X₁⋅X₁+34⋅X₁+8 {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, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l6, n_l1___1, n_l4___3, n_l4___5, n_l5___2, n_l7___4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₄₆₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___5(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: 0 < X₁ ∧ 1 < X₂ ∧ 1 < X₂ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ < 0
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₅
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 0 ∧ 0 ≤ X₅
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₁, X₃, X₁, X₅) :|: 1 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, nondef.0) :|: X₁ ≤ 1
t₄₉₁: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, 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
t₄₆₄: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___5(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: 0 < X₁ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀+X₄ ≤ X₁ ∧ 1 < X₂ ∧ X₂ ≤ X₁ ∧ X₄ ≤ 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
t₄₆₆: n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l5___2(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: 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 ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ 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
t₄₆₇: n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l7___4(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: 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 ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ 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
t₄₆₈: n_l4___5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l7___4(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: X₀+1 ≤ X₂ ∧ 0 < X₃ ∧ 0 < X₀ ∧ 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 ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ 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
t₄₇₀: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: 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
t₄₆₉: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, X₁, X₀, 0, X₄-X₀, X₅) :|: 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
t₄₇₁: n_l7___4(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___3(X₀, X₁, X₀+1, X₃-X₀, X₄, X₅) :|: 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:
72⋅X₁⋅X₁+76⋅X₁+19 {O(n^2)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l6, n_l1___1, n_l4___3, n_l4___5, n_l5___2, n_l7___4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₄₆₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___5(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: 0 < X₁ ∧ 1 < X₂ ∧ 1 < X₂ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ < 0
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₅
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 0 ∧ 0 ≤ X₅
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₁, X₃, X₁, X₅) :|: 1 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, nondef.0) :|: X₁ ≤ 1
t₄₉₁: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, 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
t₄₆₄: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___5(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: 0 < X₁ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀+X₄ ≤ X₁ ∧ 1 < X₂ ∧ X₂ ≤ X₁ ∧ X₄ ≤ 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
t₄₆₆: n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l5___2(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: 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 ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ 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
t₄₆₇: n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l7___4(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: 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 ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ 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
t₄₆₈: n_l4___5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l7___4(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: X₀+1 ≤ X₂ ∧ 0 < X₃ ∧ 0 < X₀ ∧ 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 ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ 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
t₄₇₀: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: 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
t₄₆₉: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, X₁, X₀, 0, X₄-X₀, X₅) :|: 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
t₄₇₁: n_l7___4(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___3(X₀, X₁, X₀+1, X₃-X₀, X₄, X₅) :|: 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:72⋅X₁⋅X₁+76⋅X₁+26 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₄₆₄: X₁+1 {O(n)}
t₄₆₅: 2⋅X₁ {O(n)}
t₄₆₆: X₁ {O(n)}
t₄₆₇: 36⋅X₁⋅X₁+34⋅X₁+8 {O(n^2)}
t₄₆₈: 2⋅X₁+1 {O(n)}
t₄₆₉: X₁ {O(n)}
t₄₇₀: X₁+1 {O(n)}
t₄₇₁: 36⋅X₁⋅X₁+34⋅X₁+8 {O(n^2)}
t₄₉₁: 1 {O(1)}
Costbounds
Overall costbound: 72⋅X₁⋅X₁+76⋅X₁+26 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₄₆₄: X₁+1 {O(n)}
t₄₆₅: 2⋅X₁ {O(n)}
t₄₆₆: X₁ {O(n)}
t₄₆₇: 36⋅X₁⋅X₁+34⋅X₁+8 {O(n^2)}
t₄₆₈: 2⋅X₁+1 {O(n)}
t₄₆₉: X₁ {O(n)}
t₄₇₀: X₁+1 {O(n)}
t₄₇₁: 36⋅X₁⋅X₁+34⋅X₁+8 {O(n^2)}
t₄₉₁: 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)}
t₀, X₅: X₅ {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)}
t₂, X₅: X₅ {O(n)}
t₆, X₀: X₀+1 {O(n)}
t₆, X₁: 2⋅X₁ {O(n)}
t₆, X₂: X₂+1 {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₁⋅X₁+2⋅X₁+X₄ {O(n^2)}
t₇, X₀: X₀+1 {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}
t₇, X₂: X₂+1 {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₁⋅X₁+2⋅X₁+X₄ {O(n^2)}
t₈, X₀: X₀+1 {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: X₂+1 {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₁⋅X₁+2⋅X₁+X₄ {O(n^2)}
t₈, X₅: 0 {O(1)}
t₄₆₄, X₀: X₁ {O(n)}
t₄₆₄, X₁: X₁ {O(n)}
t₄₆₄, X₂: X₁ {O(n)}
t₄₆₄, X₃: X₁ {O(n)}
t₄₆₄, X₄: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₄₆₄, X₅: X₅ {O(n)}
t₄₆₅, X₀: X₁ {O(n)}
t₄₆₅, X₁: X₁ {O(n)}
t₄₆₅, X₂: 2⋅X₁ {O(n)}
t₄₆₅, X₃: 2⋅X₁ {O(n)}
t₄₆₅, X₄: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₄₆₅, X₅: X₅ {O(n)}
t₄₆₆, X₀: X₁ {O(n)}
t₄₆₆, X₁: X₁ {O(n)}
t₄₆₆, X₂: X₁+1 {O(n)}
t₄₆₆, X₃: 3⋅X₁ {O(n)}
t₄₆₆, X₄: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₄₆₆, X₅: X₅ {O(n)}
t₄₆₇, X₀: X₁ {O(n)}
t₄₆₇, X₁: X₁ {O(n)}
t₄₆₇, X₂: X₁+1 {O(n)}
t₄₆₇, X₃: 3⋅X₁ {O(n)}
t₄₆₇, X₄: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₄₆₇, X₅: X₅ {O(n)}
t₄₆₈, X₀: X₁ {O(n)}
t₄₆₈, X₁: X₁ {O(n)}
t₄₆₈, X₂: 2⋅X₁+2 {O(n)}
t₄₆₈, X₃: 3⋅X₁ {O(n)}
t₄₆₈, X₄: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₄₆₈, X₅: X₅ {O(n)}
t₄₆₉, X₀: X₁ {O(n)}
t₄₆₉, X₁: X₁ {O(n)}
t₄₆₉, X₂: X₁ {O(n)}
t₄₆₉, X₃: 0 {O(1)}
t₄₆₉, X₄: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₄₆₉, X₅: X₅ {O(n)}
t₄₇₀, X₀: X₁ {O(n)}
t₄₇₀, X₁: X₁ {O(n)}
t₄₇₀, X₂: X₁ {O(n)}
t₄₇₀, X₃: 3⋅X₁ {O(n)}
t₄₇₀, X₄: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₄₇₀, X₅: X₅ {O(n)}
t₄₇₁, X₀: X₁ {O(n)}
t₄₇₁, X₁: X₁ {O(n)}
t₄₇₁, X₂: 2⋅X₁+2 {O(n)}
t₄₇₁, X₃: 3⋅X₁ {O(n)}
t₄₇₁, X₄: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₄₇₁, X₅: X₅ {O(n)}
t₄₉₁, X₀: 1 {O(1)}
t₄₉₁, X₁: X₁ {O(n)}
t₄₉₁, X₂: 1 {O(1)}
t₄₉₁, X₃: 0 {O(1)}
t₄₉₁, X₄: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₄₉₁, X₅: X₁⋅X₁+2⋅X₁ {O(n^2)}