Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₁₀: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₆: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₈: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₁₁: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₀)
t₄: l5(X₀, X₁, X₂, X₃) → l2(X₃+1, X₁, X₂, X₃) :|: X₃+1 < X₁
t₅: l5(X₀, X₁, X₂, X₃) → l9(X₃+1, X₁, X₂, X₃) :|: X₁ ≤ X₃+1
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₂) :|: X₂+1 < X₁
t₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1+X₂
t₁: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₁, 0, X₃)
t₁₃: l8(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃)
t₁₂: l9(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂+1, X₃)
Preprocessing
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2
Found invariant 0 ≤ X₂ for location l6
Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l5
Found invariant 0 ≤ X₂ ∧ X₁ ≤ 1+X₂ for location l8
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 0 ≤ X₂ ∧ X₁ ≤ 1+X₂ for location l10
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4
Found invariant 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location l9
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₁₀: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₈: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₁: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₀) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄: l5(X₀, X₁, X₂, X₃) → l2(X₃+1, X₁, X₂, X₃) :|: X₃+1 < X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₅: l5(X₀, X₁, X₂, X₃) → l9(X₃+1, X₁, X₂, X₃) :|: X₁ ≤ X₃+1 ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₂) :|: X₂+1 < X₁ ∧ 0 ≤ X₂
t₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1+X₂ ∧ 0 ≤ X₂
t₁: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₁, 0, X₃)
t₁₃: l8(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: 0 ≤ X₂ ∧ X₁ ≤ 1+X₂
t₁₂: l9(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂+1, X₃) :|: 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
MPRF for transition t₅: l5(X₀, X₁, X₂, X₃) → l9(X₃+1, X₁, X₂, X₃) :|: X₁ ≤ X₃+1 ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l3 [X₀+X₁-X₂-X₃ ]
l1 [X₁+1-X₂ ]
l4 [X₁+1-X₂ ]
l2 [X₁+1-X₂ ]
l5 [X₁+1-X₂ ]
l9 [X₁-X₂ ]
l6 [X₁+1-X₂ ]
MPRF for transition t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₂) :|: X₂+1 < X₁ ∧ 0 ≤ X₂ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l3 [X₁-X₂-2 ]
l1 [X₁-X₂-2 ]
l4 [X₁-X₂-2 ]
l2 [X₁-X₂-2 ]
l5 [X₁-X₂-2 ]
l9 [2⋅X₃-X₁-X₂ ]
l6 [X₁-X₂-1 ]
MPRF for transition t₁₂: l9(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂+1, X₃) :|: 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l3 [X₁+1-X₂ ]
l1 [X₁+1-X₂ ]
l4 [X₁+1-X₂ ]
l2 [X₁+1-X₂ ]
l5 [X₁+1-X₂ ]
l9 [X₁+1-X₂ ]
l6 [X₁+1-X₂ ]
MPRF for transition t₁₀: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}
MPRF:
l3 [X₁-X₀ ]
l1 [X₁-X₃-1 ]
l4 [X₁-X₃-2 ]
l2 [X₁-X₀ ]
l9 [X₁-X₃-1 ]
l6 [X₁-X₂ ]
l5 [X₁-X₃-1 ]
MPRF for transition t₆: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁⋅X₁+2⋅X₁ {O(n^2)}
MPRF:
l3 [X₁-X₃-2 ]
l1 [X₁-X₀-1 ]
l4 [X₁-X₀-1 ]
l2 [X₁-X₃-1 ]
l9 [X₁-X₃-1 ]
l6 [X₁ ]
l5 [X₁-X₃-1 ]
MPRF for transition t₈: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁⋅X₁+2⋅X₁ {O(n^2)}
MPRF:
l3 [X₁-X₃-1 ]
l1 [X₁-X₃-2 ]
l4 [X₁-X₃-2 ]
l2 [X₁-X₃-1 ]
l9 [X₁-X₃-1 ]
l6 [X₁ ]
l5 [X₁-X₃-1 ]
MPRF for transition t₁₁: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₀) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}
MPRF:
l3 [X₁-X₃ ]
l1 [X₁+1-X₀ ]
l4 [X₁-X₃ ]
l2 [X₁-X₃ ]
l9 [X₁-X₃ ]
l6 [X₁-X₂ ]
l5 [X₁-X₃ ]
MPRF for transition t₄: l5(X₀, X₁, X₂, X₃) → l2(X₃+1, X₁, X₂, X₃) :|: X₃+1 < X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}
MPRF:
l3 [X₁-X₀ ]
l1 [X₁-X₀ ]
l4 [X₁-X₀ ]
l2 [X₁-X₃-1 ]
l9 [X₁-X₃ ]
l6 [X₁-X₂ ]
l5 [X₁-X₃ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₅: l5→l9
Found invariant 0 ≤ X₂ for location l6
Found invariant X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___6
Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___5
Found invariant X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___7
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l3___3
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l1___2
Found invariant X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l2___9
Found invariant X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___8
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l4___1
Found invariant X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l5
Found invariant 0 ≤ X₂ ∧ X₁ ≤ 1+X₂ for location l8
Found invariant 0 ≤ X₂ ∧ X₁ ≤ 1+X₂ for location l10
Found invariant 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location l9
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l2___4
knowledge_propagation leads to new time bound X₁+1 {O(n)} for transition t₉₆: l5(X₀, X₁, X₂, X₃) → n_l2___9(X₃+1, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₃ < X₁ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₃ < X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
knowledge_propagation leads to new time bound X₁+1 {O(n)} for transition t₉₁: n_l2___9(X₀, X₁, X₂, X₃) → n_l3___8(X₀, X₁, X₂, X₀-1) :|: X₀ < X₁ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₁+1 {O(n)} for transition t₉₃: n_l3___8(X₀, X₁, X₂, X₃) → n_l1___7(X₀, X₁, X₂, X₀-1) :|: 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₁+1 {O(n)} for transition t₈₉: n_l1___7(X₀, X₁, X₂, X₃) → n_l4___6(X₀, X₁, X₂, X₀-1) :|: 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₁+1 {O(n)} for transition t₉₅: n_l4___6(X₀, X₁, X₂, X₃) → n_l5___5(X₀, X₁, X₂, X₀) :|: 1+X₀ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
MPRF for transition t₈₈: n_l1___2(X₀, X₁, X₂, X₃) → n_l4___1(X₀, X₁, X₂, X₀-1) :|: 1+X₀ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₁⋅X₁+4⋅X₁+2 {O(n^2)}
MPRF:
l5 [0 ]
l6 [0 ]
n_l4___6 [-X₀ ]
n_l2___9 [0 ]
n_l3___3 [X₁+1-X₀ ]
n_l1___2 [X₁+1-X₀ ]
n_l3___8 [-X₀ ]
n_l1___7 [-X₀ ]
n_l4___1 [X₁-X₀ ]
n_l2___4 [X₁-X₃ ]
n_l5___5 [X₁-X₀ ]
l9 [X₁-X₃ ]
MPRF for transition t₉₀: n_l2___4(X₀, X₁, X₂, X₃) → n_l3___3(X₀, X₁, X₂, X₀-1) :|: X₀ < X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₁⋅X₁+5⋅X₁+3 {O(n^2)}
MPRF:
l5 [0 ]
l6 [0 ]
n_l4___6 [-X₀ ]
n_l2___9 [0 ]
n_l3___3 [X₁-X₀-1 ]
n_l1___2 [X₁-X₀-1 ]
n_l3___8 [-X₀ ]
n_l1___7 [-X₀ ]
n_l4___1 [X₁+X₃-2⋅X₀ ]
n_l2___4 [X₁-X₀ ]
n_l5___5 [X₁-X₃-1 ]
l9 [0 ]
MPRF for transition t₉₂: n_l3___3(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁, X₂, X₀-1) :|: 1+X₀ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₁⋅X₁+5⋅X₁+3 {O(n^2)}
MPRF:
l5 [0 ]
l6 [0 ]
n_l4___6 [-X₀ ]
n_l2___9 [0 ]
n_l3___3 [X₁-X₀ ]
n_l1___2 [X₁-X₀-1 ]
n_l3___8 [-X₀ ]
n_l1___7 [-X₀ ]
n_l4___1 [X₁-X₀-1 ]
n_l2___4 [X₁-X₀ ]
n_l5___5 [X₁-X₀-1 ]
l9 [0 ]
MPRF for transition t₉₄: n_l4___1(X₀, X₁, X₂, X₃) → n_l5___5(X₀, X₁, X₂, X₀) :|: 1+X₀ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₁⋅X₁+4⋅X₁+2 {O(n^2)}
MPRF:
l5 [0 ]
l6 [0 ]
n_l4___6 [-X₀ ]
n_l2___9 [0 ]
n_l3___3 [X₁+1-X₀ ]
n_l1___2 [X₁+1-X₀ ]
n_l3___8 [0 ]
n_l1___7 [0 ]
n_l4___1 [X₁+1-X₀ ]
n_l2___4 [X₁-X₃ ]
n_l5___5 [X₁-X₀ ]
l9 [0 ]
MPRF for transition t₉₇: n_l5___5(X₀, X₁, X₂, X₃) → n_l2___4(X₃+1, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₃ < X₁ ∧ X₂ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₁⋅X₁+4⋅X₁+2 {O(n^2)}
MPRF:
l5 [0 ]
l6 [0 ]
n_l4___6 [-X₀ ]
n_l2___9 [0 ]
n_l3___3 [X₁-X₀ ]
n_l1___2 [X₁-X₀ ]
n_l3___8 [0 ]
n_l1___7 [0 ]
n_l4___1 [X₁-X₀ ]
n_l2___4 [X₁-X₃-1 ]
n_l5___5 [X₁-X₃ ]
l9 [X₁-X₃ ]
MPRF for transition t₁₀₄: n_l5___5(X₀, X₁, X₂, X₃) → l9(X₃+1, X₁, X₂, X₃) :|: X₁ ≤ X₃+1 ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
l5 [X₁+2-X₃ ]
l6 [X₁+2-X₂ ]
n_l2___9 [X₁+2-X₂ ]
n_l3___3 [X₁+2-X₂ ]
n_l1___2 [X₁+2-X₂ ]
n_l3___8 [2⋅X₀+X₁-3⋅X₂ ]
n_l1___7 [2⋅X₀+X₁-3⋅X₂ ]
n_l4___1 [X₁+2-X₂ ]
n_l4___6 [2⋅X₀+X₁-3⋅X₂ ]
n_l2___4 [X₁+2-X₂ ]
n_l5___5 [X₁+2-X₂ ]
l9 [X₁+1-X₂ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:8⋅X₁⋅X₁+19⋅X₁+10 {O(n^2)}
t₀: 1 {O(1)}
t₁₀: 2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}
t₆: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₈: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₁₁: 2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}
t₄: 2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}
t₅: X₁+1 {O(n)}
t₂: X₁+1 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₂: X₁+1 {O(n)}
Costbounds
Overall costbound: 8⋅X₁⋅X₁+19⋅X₁+10 {O(n^2)}
t₀: 1 {O(1)}
t₁₀: 2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}
t₆: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₈: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₁₁: 2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}
t₄: 2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}
t₅: X₁+1 {O(n)}
t₂: X₁+1 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₂: X₁+1 {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁₀, X₀: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₁+1 {O(n)}
t₁₀, X₃: 2⋅X₁⋅X₁+6⋅X₁+3 {O(n^2)}
t₆, X₀: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₁+1 {O(n)}
t₆, X₃: 2⋅X₁⋅X₁+6⋅X₁+3 {O(n^2)}
t₈, X₀: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₁+1 {O(n)}
t₈, X₃: 2⋅X₁⋅X₁+6⋅X₁+3 {O(n^2)}
t₁₁, X₀: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₁+1 {O(n)}
t₁₁, X₃: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₄, X₀: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₁+1 {O(n)}
t₄, X₃: 2⋅X₁⋅X₁+6⋅X₁+3 {O(n^2)}
t₅, X₀: 2⋅X₁⋅X₁+5⋅X₁+3 {O(n^2)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₁+1 {O(n)}
t₅, X₃: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₂, X₀: 2⋅X₁⋅X₁+5⋅X₁+X₀+3 {O(n^2)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₁+1 {O(n)}
t₂, X₃: X₁+1 {O(n)}
t₃, X₀: 2⋅X₁⋅X₁+5⋅X₁+X₀+3 {O(n^2)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: X₁+1 {O(n)}
t₃, X₃: 2⋅X₁⋅X₁+5⋅X₁+X₃+2 {O(n^2)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 0 {O(1)}
t₁, X₃: X₃ {O(n)}
t₁₃, X₀: 2⋅X₁⋅X₁+5⋅X₁+X₀+3 {O(n^2)}
t₁₃, X₁: 2⋅X₁ {O(n)}
t₁₃, X₂: X₁+1 {O(n)}
t₁₃, X₃: 2⋅X₁⋅X₁+5⋅X₁+X₃+2 {O(n^2)}
t₁₂, X₀: 2⋅X₁⋅X₁+5⋅X₁+3 {O(n^2)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₁+1 {O(n)}
t₁₂, X₃: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}