Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₁ ≤ 0
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l4(X₀, X₁, X₉, X₃, X₀, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 0 < X₁
t₁₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₈, X₁₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 0 < X₁₁
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₁₁ ≤ 0
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 0 < X₄
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l7(X₀, X₁, X₂, X₁₀, X₄, X₂, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₄ ≤ 0
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₁, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l4(X₀, X₁, X₂+X₄, X₃, X₄-1, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₉: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: (X₃)² ≤ X₅
t₁₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₅ ≤ 0
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₅ < (X₃)² ∧ 0 < X₅
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l7(X₀, X₁, X₂, 2⋅X₃, X₄, 5⋅X₅+(X₄)², X₆, X₇, X₈, X₉, X₁₀, X₁₁)
Preprocessing
Eliminate variables {X₆,X₇} that do not contribute to the problem
Found invariant X₉ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁₁+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6
Found invariant X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ for location l7
Found invariant X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ for location l5
Found invariant X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ 1 ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁₁+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ for location l8
Found invariant 1 ≤ X₁₁ ∧ 1 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 0 ≤ X₁ for location l1
Found invariant X₉ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ for location l4
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₂₈: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁)
t₃₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: X₁ ≤ 0 ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 0 ≤ X₁
t₂₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l4(X₀, X₁, X₉, X₃, X₀, X₅, X₈, X₉, X₁₀, X₁₁) :|: 0 < X₁ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 0 ≤ X₁
t₃₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁)
t₃₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l1(X₈, X₁₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: 0 < X₁₁
t₃₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: X₁₁ ≤ 0
t₃₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: 0 < X₄ ∧ X₉ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁
t₃₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l7(X₀, X₁, X₂, X₁₀, X₄, X₂, X₈, X₉, X₁₀, X₁₁) :|: X₄ ≤ 0 ∧ X₉ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁
t₃₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l1(X₁, X₁-1, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁
t₃₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l4(X₀, X₁, X₂+X₄, X₃, X₄-1, X₅, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁₁+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₉: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: (X₃)² ≤ X₅ ∧ X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁
t₄₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: X₅ ≤ 0 ∧ X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁
t₃₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: X₅ < (X₃)² ∧ 0 < X₅ ∧ X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁
t₄₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l7(X₀, X₁, X₂, 2⋅X₃, X₄, 5⋅X₅+(X₄)², X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ 1 ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁₁+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁
MPRF for transition t₂₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l4(X₀, X₁, X₉, X₃, X₀, X₅, X₈, X₉, X₁₀, X₁₁) :|: 0 < X₁ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₁₁+1 {O(n)}
MPRF:
l1 [X₁+1 ]
l6 [X₁ ]
l4 [X₁ ]
l5 [X₁ ]
l8 [X₁ ]
l7 [X₁ ]
MPRF for transition t₃₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l7(X₀, X₁, X₂, X₁₀, X₄, X₂, X₈, X₉, X₁₀, X₁₁) :|: X₄ ≤ 0 ∧ X₉ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁₁ {O(n)}
MPRF:
l1 [X₁ ]
l6 [X₁ ]
l4 [X₁ ]
l5 [X₁-1 ]
l8 [X₁-1 ]
l7 [X₁-1 ]
MPRF for transition t₃₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l1(X₁, X₁-1, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ of depth 1:
new bound:
2⋅X₁₁ {O(n)}
MPRF:
l1 [X₁+X₁₁ ]
l6 [X₁+X₁₁ ]
l4 [X₁+X₁₁ ]
l5 [X₁+X₁₁ ]
l8 [X₁+X₁₁ ]
l7 [X₁+X₁₁ ]
MPRF for transition t₃₉: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: (X₃)² ≤ X₅ ∧ X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁₁ {O(n)}
MPRF:
l1 [X₁ ]
l6 [X₁ ]
l4 [X₁ ]
l5 [X₁-1 ]
l8 [X₁ ]
l7 [X₁ ]
MPRF for transition t₄₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: X₅ ≤ 0 ∧ X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁₁ {O(n)}
MPRF:
l1 [X₁ ]
l6 [X₁ ]
l4 [X₁ ]
l5 [X₁-1 ]
l8 [X₁ ]
l7 [X₁ ]
MPRF for transition t₃₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: 0 < X₄ ∧ X₉ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ of depth 1:
new bound:
2⋅X₁₁⋅X₁₁+X₈ {O(n^2)}
MPRF:
l5 [X₁ ]
l1 [X₀ ]
l6 [X₄-1 ]
l4 [X₄ ]
l8 [X₄ ]
l7 [X₄ ]
MPRF for transition t₃₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l4(X₀, X₁, X₂+X₄, X₃, X₄-1, X₅, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁₁+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
4⋅X₁₁⋅X₁₁+X₁₁+X₈ {O(n^2)}
MPRF:
l5 [X₁+X₁₁ ]
l1 [X₀+X₁₁ ]
l6 [X₁+X₄ ]
l4 [X₁+X₄ ]
l8 [X₄ ]
l7 [X₄ ]
Analysing control-flow refined program
Found invariant X₉ ≤ X₂ ∧ X₂ ≤ X₉ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁₁+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___3
Found invariant 1+X₉ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁₁+X₄ ∧ 2 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 3 ≤ X₀+X₁₁ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l6___1
Found invariant X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ 1 ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁₁+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁₁+X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ for location n_l8___1
Found invariant X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁₁+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁₀ ∧ X₁₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁₁+X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ for location n_l8___3
Found invariant 1+X₉ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₁₁+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___2
Found invariant X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁₀ ∧ X₁₀ ≤ X₃ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ for location l7
Found invariant X₉ ≤ X₂ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁₁+X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ for location n_l7___2
Found invariant X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ for location l5
Found invariant 1 ≤ X₁₁ ∧ 1 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 0 ≤ X₁ for location l1
Found invariant X₉ ≤ X₂ ∧ X₂ ≤ X₉ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ for location l4
knowledge_propagation leads to new time bound X₁₁+1 {O(n)} for transition t₉₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → n_l6___3(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: X₁ ≤ X₁₁ ∧ X₉ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₉ ≤ X₂ ∧ 0 < X₄ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₁₁ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁
knowledge_propagation leads to new time bound X₁₁+1 {O(n)} for transition t₉₈: n_l6___3(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → n_l4___2(X₀, X₁, X₂+X₄, X₃, X₄-1, X₅, X₈, X₉, X₁₀, X₁₁) :|: X₁ ≤ X₁₁ ∧ X₉ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₀ ∧ 0 < X₄ ∧ 1 ≤ X₁ ∧ X₉ ≤ X₂ ∧ 1 ≤ X₄ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₁₁ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁₁+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₁₁₄: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → n_l8___3(X₀, X₁, X₂, X₃, X₄, Arg5_P, X₈, Arg9_P, X₁₀, Arg11_P) :|: X₄ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁₀ ∧ X₁₀ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₉ ≤ X₂ ∧ X₁ ≤ X₁₁ ∧ X₄ ≤ 0 ∧ X₃ ≤ X₁₀ ∧ X₁₀ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₉ ≤ X₂ ∧ X₁ ≤ X₁₁ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₁₁ ∧ X₉ ≤ X₂ ∧ X₄ ≤ 0 ∧ X₄ ≤ 0 ∧ X₂ ≤ Arg5_P ∧ Arg9_P ≤ X₂ ∧ X₁ ≤ Arg11_P ∧ 0 < Arg5_P ∧ 1 ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₉ ≤ Arg9_P ∧ Arg9_P ≤ X₉ ∧ X₅ ≤ Arg5_P ∧ Arg5_P ≤ X₅ ∧ X₁₁ ≤ Arg11_P ∧ Arg11_P ≤ X₁₁ ∧ X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁₀ ∧ X₁₀ ≤ X₃ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁₁ {O(n)}
MPRF:
l4 [X₁ ]
l1 [X₁ ]
l7 [X₁ ]
n_l6___1 [X₁ ]
n_l6___3 [X₁ ]
n_l4___2 [X₁ ]
l5 [X₁-1 ]
n_l8___1 [X₁-1 ]
n_l8___3 [X₁-1 ]
n_l7___2 [X₁-1 ]
MPRF for transition t₉₅: n_l4___2(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → n_l6___1(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: X₁ ≤ X₁₁ ∧ X₉ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₁₁ ∧ 1+X₄+X₉ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₉ ≤ X₂ ∧ 0 < X₄ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₁₁ ∧ 1+X₉ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₁₁+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
3⋅X₁₁⋅X₁₁+X₁₁⋅X₈+4⋅X₁₁+X₈+1 {O(n^2)}
MPRF:
l4 [0 ]
n_l6___3 [0 ]
l1 [0 ]
l7 [0 ]
n_l6___1 [X₄ ]
n_l4___2 [X₄+1 ]
l5 [0 ]
n_l8___1 [0 ]
n_l8___3 [0 ]
n_l7___2 [0 ]
MPRF for transition t₁₀₂: n_l4___2(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l7(X₀, X₁, X₂, X₁₀, X₄, X₂, X₈, X₉, X₁₀, X₁₁) :|: X₄ ≤ 0 ∧ X₉ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ ∧ 1+X₉ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₁₁+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁₁ {O(n)}
MPRF:
l4 [X₁ ]
l1 [X₁ ]
l7 [X₁-1 ]
n_l6___1 [X₁ ]
n_l6___3 [X₁ ]
n_l4___2 [X₁ ]
l5 [X₁-1 ]
n_l8___1 [X₁-1 ]
n_l8___3 [X₁-1 ]
n_l7___2 [X₁-1 ]
MPRF for transition t₉₇: n_l6___1(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → n_l4___2(X₀, X₁, X₂+X₄, X₃, X₄-1, X₅, X₈, X₉, X₁₀, X₁₁) :|: X₁ ≤ X₁₁ ∧ 1+X₄+X₉ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 < X₄ ∧ 1 ≤ X₁ ∧ X₉ ≤ X₂ ∧ 1 ≤ X₄ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₁₁ ∧ 1+X₉ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁₁+X₄ ∧ 2 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 3 ≤ X₀+X₁₁ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
3⋅X₁₁⋅X₁₁+X₁₁⋅X₈+3⋅X₁₁+X₈ {O(n^2)}
MPRF:
l4 [0 ]
n_l6___3 [0 ]
l1 [0 ]
l7 [0 ]
n_l6___1 [X₄ ]
n_l4___2 [X₄ ]
l5 [0 ]
n_l8___1 [0 ]
n_l8___3 [0 ]
n_l7___2 [0 ]
MPRF for transition t₁₂₁: n_l7___2(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) :|: (X₃)² ≤ X₅ ∧ X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ ∧ X₉ ≤ X₂ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁₁+X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁₁ {O(n)}
MPRF:
l4 [X₁ ]
l1 [X₁ ]
l7 [X₁ ]
n_l6___1 [X₁ ]
n_l6___3 [X₁ ]
n_l4___2 [X₁ ]
l5 [X₁-1 ]
n_l8___1 [X₁ ]
n_l8___3 [X₁ ]
n_l7___2 [X₁ ]
MPRF for transition t₁₁₆: n_l8___3(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉, X₁₀, X₁₁) → n_l7___2(X₀, X₁, X₂, 2⋅X₃, Arg4_P, NoDet0, X₈, Arg9_P, X₁₀, Arg11_P) :|: X₄ ≤ 0 ∧ X₉ ≤ X₂ ∧ X₁ ≤ X₁₁ ∧ 0 < X₂ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁₀ ∧ X₁₀ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ Arg4_P ≤ 0 ∧ X₂ ≤ X₅ ∧ Arg9_P ≤ X₂ ∧ X₁ ≤ Arg11_P ∧ 1 ≤ X₅ ∧ 1 ≤ X₁ ∧ Arg4_P ≤ X₀ ∧ X₉ ≤ Arg9_P ∧ Arg9_P ≤ X₉ ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ X₁₁ ≤ Arg11_P ∧ Arg11_P ≤ X₁₁ ∧ X₉ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁₁+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁₁ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁₀ ∧ X₁₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁₁+X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₁+X₁₁ ∧ X₁ ≤ X₁₁ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁₁ {O(n)}
MPRF:
l4 [X₁ ]
l1 [X₁ ]
l7 [X₁ ]
n_l6___1 [X₁ ]
n_l6___3 [X₁ ]
n_l4___2 [X₁ ]
l5 [X₁-1 ]
n_l8___1 [X₁-1 ]
n_l8___3 [X₁ ]
n_l7___2 [X₁-1 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₂₈: 1 {O(1)}
t₂₉: X₁₁+1 {O(n)}
t₃₀: 1 {O(1)}
t₃₁: 1 {O(1)}
t₃₂: 1 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: 2⋅X₁₁⋅X₁₁+X₈ {O(n^2)}
t₃₅: X₁₁ {O(n)}
t₃₆: 2⋅X₁₁ {O(n)}
t₃₇: 4⋅X₁₁⋅X₁₁+X₁₁+X₈ {O(n^2)}
t₃₈: inf {Infinity}
t₃₉: X₁₁ {O(n)}
t₄₀: X₁₁ {O(n)}
t₄₁: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
t₂₈: 1 {O(1)}
t₂₉: X₁₁+1 {O(n)}
t₃₀: 1 {O(1)}
t₃₁: 1 {O(1)}
t₃₂: 1 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: 2⋅X₁₁⋅X₁₁+X₈ {O(n^2)}
t₃₅: X₁₁ {O(n)}
t₃₆: 2⋅X₁₁ {O(n)}
t₃₇: 4⋅X₁₁⋅X₁₁+X₁₁+X₈ {O(n^2)}
t₃₈: inf {Infinity}
t₃₉: X₁₁ {O(n)}
t₄₀: X₁₁ {O(n)}
t₄₁: inf {Infinity}
Sizebounds
t₂₈, X₀: X₀ {O(n)}
t₂₈, X₁: X₁ {O(n)}
t₂₈, X₂: X₂ {O(n)}
t₂₈, X₃: X₃ {O(n)}
t₂₈, X₄: X₄ {O(n)}
t₂₈, X₅: X₅ {O(n)}
t₂₈, X₈: X₈ {O(n)}
t₂₈, X₉: X₉ {O(n)}
t₂₈, X₁₀: X₁₀ {O(n)}
t₂₈, X₁₁: X₁₁ {O(n)}
t₂₉, X₀: 2⋅X₁₁+X₈ {O(n)}
t₂₉, X₁: X₁₁ {O(n)}
t₂₉, X₂: 2⋅X₉ {O(n)}
t₂₉, X₄: 2⋅X₁₁+X₈ {O(n)}
t₂₉, X₈: X₈ {O(n)}
t₂₉, X₉: X₉ {O(n)}
t₂₉, X₁₀: X₁₀ {O(n)}
t₂₉, X₁₁: X₁₁ {O(n)}
t₃₀, X₀: 2⋅X₁₁ {O(n)}
t₃₀, X₁: 0 {O(1)}
t₃₀, X₂: 16⋅X₁₁⋅X₁₁⋅X₈+32⋅X₁₁⋅X₁₁⋅X₁₁+12⋅X₁₁⋅X₈+4⋅X₈⋅X₈+8⋅X₁₁⋅X₁₁+16⋅X₉+4⋅X₈+8⋅X₁₁ {O(n^3)}
t₃₀, X₄: 16⋅X₁₁+8⋅X₈ {O(n)}
t₃₀, X₈: X₈ {O(n)}
t₃₀, X₉: X₉ {O(n)}
t₃₀, X₁₀: X₁₀ {O(n)}
t₃₀, X₁₁: X₁₁ {O(n)}
t₃₁, X₀: 2⋅X₁₁+X₀ {O(n)}
t₃₁, X₁: X₁ {O(n)}
t₃₁, X₂: 16⋅X₁₁⋅X₁₁⋅X₈+32⋅X₁₁⋅X₁₁⋅X₁₁+12⋅X₁₁⋅X₈+4⋅X₈⋅X₈+8⋅X₁₁⋅X₁₁+16⋅X₉+4⋅X₈+8⋅X₁₁+X₂ {O(n^3)}
t₃₁, X₄: 16⋅X₁₁+8⋅X₈+X₄ {O(n)}
t₃₁, X₈: 2⋅X₈ {O(n)}
t₃₁, X₉: 2⋅X₉ {O(n)}
t₃₁, X₁₀: 2⋅X₁₀ {O(n)}
t₃₁, X₁₁: 2⋅X₁₁ {O(n)}
t₃₂, X₀: X₈ {O(n)}
t₃₂, X₁: X₁₁ {O(n)}
t₃₂, X₂: X₂ {O(n)}
t₃₂, X₃: X₃ {O(n)}
t₃₂, X₄: X₄ {O(n)}
t₃₂, X₅: X₅ {O(n)}
t₃₂, X₈: X₈ {O(n)}
t₃₂, X₉: X₉ {O(n)}
t₃₂, X₁₀: X₁₀ {O(n)}
t₃₂, X₁₁: X₁₁ {O(n)}
t₃₃, X₀: X₀ {O(n)}
t₃₃, X₁: X₁ {O(n)}
t₃₃, X₂: X₂ {O(n)}
t₃₃, X₃: X₃ {O(n)}
t₃₃, X₄: X₄ {O(n)}
t₃₃, X₅: X₅ {O(n)}
t₃₃, X₈: X₈ {O(n)}
t₃₃, X₉: X₉ {O(n)}
t₃₃, X₁₀: X₁₀ {O(n)}
t₃₃, X₁₁: X₁₁ {O(n)}
t₃₄, X₀: 2⋅X₁₁+X₈ {O(n)}
t₃₄, X₁: X₁₁ {O(n)}
t₃₄, X₂: 4⋅X₁₁⋅X₁₁⋅X₈+8⋅X₁₁⋅X₁₁⋅X₁₁+2⋅X₁₁⋅X₁₁+3⋅X₁₁⋅X₈+X₈⋅X₈+2⋅X₁₁+2⋅X₉+X₈ {O(n^3)}
t₃₄, X₄: 2⋅X₁₁+X₈ {O(n)}
t₃₄, X₈: X₈ {O(n)}
t₃₄, X₉: X₉ {O(n)}
t₃₄, X₁₀: X₁₀ {O(n)}
t₃₄, X₁₁: X₁₁ {O(n)}
t₃₅, X₀: 2⋅X₈+4⋅X₁₁ {O(n)}
t₃₅, X₁: X₁₁ {O(n)}
t₃₅, X₂: 4⋅X₁₁⋅X₁₁⋅X₈+8⋅X₁₁⋅X₁₁⋅X₁₁+2⋅X₁₁⋅X₁₁+3⋅X₁₁⋅X₈+X₈⋅X₈+2⋅X₁₁+4⋅X₉+X₈ {O(n^3)}
t₃₅, X₃: 2⋅X₁₀ {O(n)}
t₃₅, X₄: 2⋅X₈+4⋅X₁₁ {O(n)}
t₃₅, X₅: 4⋅X₁₁⋅X₁₁⋅X₈+8⋅X₁₁⋅X₁₁⋅X₁₁+2⋅X₁₁⋅X₁₁+3⋅X₁₁⋅X₈+X₈⋅X₈+2⋅X₁₁+4⋅X₉+X₈ {O(n^3)}
t₃₅, X₈: X₈ {O(n)}
t₃₅, X₉: X₉ {O(n)}
t₃₅, X₁₀: X₁₀ {O(n)}
t₃₅, X₁₁: X₁₁ {O(n)}
t₃₆, X₀: 2⋅X₁₁ {O(n)}
t₃₆, X₁: X₁₁ {O(n)}
t₃₆, X₂: 16⋅X₁₁⋅X₁₁⋅X₈+32⋅X₁₁⋅X₁₁⋅X₁₁+12⋅X₁₁⋅X₈+4⋅X₈⋅X₈+8⋅X₁₁⋅X₁₁+16⋅X₉+4⋅X₈+8⋅X₁₁ {O(n^3)}
t₃₆, X₄: 16⋅X₁₁+8⋅X₈ {O(n)}
t₃₆, X₈: X₈ {O(n)}
t₃₆, X₉: X₉ {O(n)}
t₃₆, X₁₀: X₁₀ {O(n)}
t₃₆, X₁₁: X₁₁ {O(n)}
t₃₇, X₀: 2⋅X₁₁+X₈ {O(n)}
t₃₇, X₁: X₁₁ {O(n)}
t₃₇, X₂: 4⋅X₁₁⋅X₁₁⋅X₈+8⋅X₁₁⋅X₁₁⋅X₁₁+2⋅X₁₁⋅X₁₁+3⋅X₁₁⋅X₈+X₈⋅X₈+2⋅X₁₁+2⋅X₉+X₈ {O(n^3)}
t₃₇, X₄: 2⋅X₁₁+X₈ {O(n)}
t₃₇, X₈: X₈ {O(n)}
t₃₇, X₉: X₉ {O(n)}
t₃₇, X₁₀: X₁₀ {O(n)}
t₃₇, X₁₁: X₁₁ {O(n)}
t₃₈, X₀: 2⋅X₈+4⋅X₁₁ {O(n)}
t₃₈, X₁: X₁₁ {O(n)}
t₃₈, X₂: 4⋅X₁₁⋅X₁₁⋅X₈+8⋅X₁₁⋅X₁₁⋅X₁₁+2⋅X₁₁⋅X₁₁+3⋅X₁₁⋅X₈+X₈⋅X₈+2⋅X₁₁+4⋅X₉+X₈ {O(n^3)}
t₃₈, X₄: 2⋅X₈+4⋅X₁₁ {O(n)}
t₃₈, X₈: X₈ {O(n)}
t₃₈, X₉: X₉ {O(n)}
t₃₈, X₁₀: X₁₀ {O(n)}
t₃₈, X₁₁: X₁₁ {O(n)}
t₃₉, X₀: 4⋅X₈+8⋅X₁₁ {O(n)}
t₃₉, X₁: X₁₁ {O(n)}
t₃₉, X₂: 16⋅X₁₁⋅X₁₁⋅X₁₁+8⋅X₁₁⋅X₁₁⋅X₈+2⋅X₈⋅X₈+4⋅X₁₁⋅X₁₁+6⋅X₁₁⋅X₈+2⋅X₈+4⋅X₁₁+8⋅X₉ {O(n^3)}
t₃₉, X₄: 4⋅X₈+8⋅X₁₁ {O(n)}
t₃₉, X₈: X₈ {O(n)}
t₃₉, X₉: X₉ {O(n)}
t₃₉, X₁₀: X₁₀ {O(n)}
t₃₉, X₁₁: X₁₁ {O(n)}
t₄₀, X₀: 4⋅X₈+8⋅X₁₁ {O(n)}
t₄₀, X₁: X₁₁ {O(n)}
t₄₀, X₂: 16⋅X₁₁⋅X₁₁⋅X₁₁+8⋅X₁₁⋅X₁₁⋅X₈+2⋅X₈⋅X₈+4⋅X₁₁⋅X₁₁+6⋅X₁₁⋅X₈+2⋅X₈+4⋅X₁₁+8⋅X₉ {O(n^3)}
t₄₀, X₄: 4⋅X₈+8⋅X₁₁ {O(n)}
t₄₀, X₈: X₈ {O(n)}
t₄₀, X₉: X₉ {O(n)}
t₄₀, X₁₀: X₁₀ {O(n)}
t₄₀, X₁₁: X₁₁ {O(n)}
t₄₁, X₀: 2⋅X₈+4⋅X₁₁ {O(n)}
t₄₁, X₁: X₁₁ {O(n)}
t₄₁, X₂: 4⋅X₁₁⋅X₁₁⋅X₈+8⋅X₁₁⋅X₁₁⋅X₁₁+2⋅X₁₁⋅X₁₁+3⋅X₁₁⋅X₈+X₈⋅X₈+2⋅X₁₁+4⋅X₉+X₈ {O(n^3)}
t₄₁, X₄: 2⋅X₈+4⋅X₁₁ {O(n)}
t₄₁, X₈: X₈ {O(n)}
t₄₁, X₉: X₉ {O(n)}
t₄₁, X₁₀: X₁₀ {O(n)}
t₄₁, X₁₁: X₁₁ {O(n)}