Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀
t₉: l2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀-X₃-1, X₂, X₃, 2⋅X₃+100)
t₇: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄
t₈: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄-1)
Preprocessing
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 0 ≤ X₃ ∧ X₀ ≤ X₂ for location l1
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ 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
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂
t₉: l2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀-X₃-1, X₂, X₃, 2⋅X₃+100) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₇: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄-1) :|: 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
l4 [X₀ ]
l1 [X₀+1 ]
l6 [X₀ ]
l5 [X₀ ]
MPRF for transition t₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀-X₃-1, X₂, X₃, 2⋅X₃+100) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l4 [X₀ ]
l1 [X₀ ]
l6 [X₀-1 ]
l5 [X₀-1 ]
MPRF for transition t₇: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l4 [X₀ ]
l1 [X₀ ]
l6 [X₀ ]
l5 [X₀ ]
MPRF for transition t₆: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₂⋅X₂+2⋅X₂⋅X₃+100⋅X₂+2⋅X₃+98 {O(n^2)}
MPRF:
l1 [2⋅X₀+2⋅X₃+98 ]
l4 [2⋅X₀+2⋅X₃+98 ]
l6 [2⋅X₁+2⋅X₃+X₄-1 ]
l5 [2⋅X₁+2⋅X₃+X₄ ]
MPRF for transition t₈: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄-1) :|: 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
4⋅X₂⋅X₂+100⋅X₂+96 {O(n^2)}
MPRF:
l1 [2⋅X₀+2⋅X₂+96 ]
l4 [2⋅X₀+2⋅X₂+96 ]
l6 [2⋅X₁+2⋅X₂+X₄-2 ]
l5 [2⋅X₁+2⋅X₂+X₄-2 ]
Analysing control-flow refined program
Cut unsatisfiable transition t₇: l5→l1
Cut unsatisfiable transition t₇₆: n_l5___4→l1
Found invariant 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___3
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___1
Found invariant 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___5
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___2
Found invariant 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___4
Found invariant 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 0 ≤ X₃ ∧ X₀ ≤ X₂ for location l1
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l4
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₆₈: l5(X₀, X₁, X₂, X₃, X₄) → n_l6___5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 < X₄ ∧ 1 ≤ X₄ ∧ 100+2⋅X₃ ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ X₀ ≤ 1+X₁+X₃ ∧ 1+X₁+X₃ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₇₁: n_l6___5(X₀, X₁, X₂, X₃, X₄) → n_l5___4(X₀, X₁, X₂, X₃, X₄-1) :|: X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ X₄ ≤ 98+2⋅X₀ ∧ 2⋅X₀+98 ≤ 2⋅X₁+X₄ ∧ 2⋅X₁+X₄ ≤ 98+2⋅X₀ ∧ 2⋅X₃+100 ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₆₇: n_l5___4(X₀, X₁, X₂, X₃, X₄) → n_l6___3(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 < X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₇₀: n_l6___3(X₀, X₁, X₂, X₃, X₄) → n_l5___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₆₆: n_l5___2(X₀, X₁, X₂, X₃, X₄) → n_l6___1(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
98⋅X₂+1 {O(n)}
MPRF:
l4 [98⋅X₀+1 ]
l5 [99⋅X₁+97⋅X₃+X₄-X₀ ]
l1 [98⋅X₀+1 ]
n_l6___1 [96⋅X₀+2⋅X₁+X₄-96 ]
n_l6___3 [96⋅X₀+2⋅X₁+X₄-96 ]
n_l5___2 [96⋅X₀+2⋅X₁+X₄-95 ]
n_l6___5 [96⋅X₀+2⋅X₁+X₄-97 ]
n_l5___4 [96⋅X₀+2⋅X₁+X₄-96 ]
MPRF for transition t₇₅: n_l5___2(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
99⋅X₂+99⋅X₃ {O(n)}
MPRF:
l4 [99⋅X₀+99⋅X₃ ]
l5 [99⋅X₀+99⋅X₃ ]
l1 [99⋅X₀+99⋅X₃ ]
n_l6___1 [99⋅X₁+99⋅X₃+1 ]
n_l6___3 [99⋅X₁+99⋅X₃+X₄ ]
n_l5___2 [99⋅X₁+99⋅X₃+1 ]
n_l6___5 [97⋅X₀+2⋅X₁+99⋅X₃+X₄-98 ]
n_l5___4 [97⋅X₀+2⋅X₁+99⋅X₃+X₄-97 ]
MPRF for transition t₆₉: n_l6___1(X₀, X₁, X₂, X₃, X₄) → n_l5___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 < X₄ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
98⋅X₂+98⋅X₃+97 {O(n)}
MPRF:
l4 [98⋅X₀+98⋅X₃+97 ]
l5 [96⋅X₀+2⋅X₁+100⋅X₃+99 ]
l1 [98⋅X₀+98⋅X₃+97 ]
n_l6___1 [98⋅X₁+98⋅X₃+X₄+97 ]
n_l6___3 [96⋅X₀+2⋅X₁+98⋅X₃+X₄ ]
n_l5___2 [98⋅X₁+98⋅X₃+X₄+97 ]
n_l6___5 [96⋅X₀+2⋅X₁+98⋅X₃+X₄-1 ]
n_l5___4 [96⋅X₀+2⋅X₁+98⋅X₃+X₄ ]
CFR: Improvement to new bound with the following program:
new bound:
197⋅X₃+301⋅X₂+99 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l7, n_l5___2, n_l5___4, n_l6___1, n_l6___3, n_l6___5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂
t₉: l2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₃ < 0
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀-X₃-1, X₂, X₃, 2⋅X₃+100) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₆₈: l5(X₀, X₁, X₂, X₃, X₄) → n_l6___5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 < X₄ ∧ 1 ≤ X₄ ∧ 100+2⋅X₃ ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ X₀ ≤ 1+X₁+X₃ ∧ 1+X₁+X₃ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇₅: n_l5___2(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆₆: n_l5___2(X₀, X₁, X₂, X₃, X₄) → n_l6___1(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆₇: n_l5___4(X₀, X₁, X₂, X₃, X₄) → n_l6___3(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 < X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 < X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆₉: n_l6___1(X₀, X₁, X₂, X₃, X₄) → n_l5___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 0 < X₄ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇₀: n_l6___3(X₀, X₁, X₂, X₃, X₄) → n_l5___2(X₀, X₁, X₂, X₃, X₄-1) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 99 ≤ X₄ ∧ 99 ≤ X₃+X₄ ∧ 99+X₃ ≤ X₄ ∧ 100 ≤ X₂+X₄ ∧ 99 ≤ X₁+X₄ ∧ 100 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇₁: n_l6___5(X₀, X₁, X₂, X₃, X₄) → n_l5___4(X₀, X₁, X₂, X₃, X₄-1) :|: X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ X₄ ≤ 98+2⋅X₀ ∧ 2⋅X₀+98 ≤ 2⋅X₁+X₄ ∧ 2⋅X₁+X₄ ≤ 98+2⋅X₀ ∧ 2⋅X₃+100 ≤ X₄ ∧ X₄ ≤ 100+2⋅X₃ ∧ 0 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 100 ≤ X₄ ∧ 100 ≤ X₃+X₄ ∧ 100+X₃ ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ 100 ≤ X₁+X₄ ∧ 101 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:197⋅X₃+301⋅X₂+104 {O(n)}
t₀: 1 {O(1)}
t₃: X₂+1 {O(n)}
t₄: 1 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: X₂ {O(n)}
t₆₈: X₂ {O(n)}
t₆₆: 98⋅X₂+1 {O(n)}
t₇₅: 99⋅X₂+99⋅X₃ {O(n)}
t₆₇: X₂ {O(n)}
t₆₉: 98⋅X₂+98⋅X₃+97 {O(n)}
t₇₀: X₂ {O(n)}
t₇₁: X₂ {O(n)}
Costbounds
Overall costbound: 197⋅X₃+301⋅X₂+104 {O(n)}
t₀: 1 {O(1)}
t₃: X₂+1 {O(n)}
t₄: 1 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: X₂ {O(n)}
t₆₈: X₂ {O(n)}
t₆₆: 98⋅X₂+1 {O(n)}
t₇₅: 99⋅X₂+99⋅X₃ {O(n)}
t₆₇: X₂ {O(n)}
t₆₉: 98⋅X₂+98⋅X₃+97 {O(n)}
t₇₀: X₂ {O(n)}
t₇₁: X₂ {O(n)}
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)}
t₃, X₀: X₂ {O(n)}
t₃, X₁: X₁+X₂ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₄, X₀: 2⋅X₂ {O(n)}
t₄, X₁: X₁+X₂ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₉, X₀: 2⋅X₂+X₀ {O(n)}
t₉, X₁: 2⋅X₁+X₂ {O(n)}
t₉, X₂: 3⋅X₂ {O(n)}
t₉, X₃: 3⋅X₃ {O(n)}
t₉, X₄: 2⋅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: X₂ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₅, X₀: X₂ {O(n)}
t₅, X₁: X₂ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: 2⋅X₃+100 {O(n)}
t₆₈, X₀: X₂ {O(n)}
t₆₈, X₁: X₂ {O(n)}
t₆₈, X₂: X₂ {O(n)}
t₆₈, X₃: X₃ {O(n)}
t₆₈, X₄: 2⋅X₃+100 {O(n)}
t₆₆, X₀: X₂ {O(n)}
t₆₆, X₁: X₂ {O(n)}
t₆₆, X₂: X₂ {O(n)}
t₆₆, X₃: X₃ {O(n)}
t₆₆, X₄: 2⋅X₃+100 {O(n)}
t₇₅, X₀: X₂ {O(n)}
t₇₅, X₁: X₂ {O(n)}
t₇₅, X₂: X₂ {O(n)}
t₇₅, X₃: X₃ {O(n)}
t₇₅, X₄: 0 {O(1)}
t₆₇, X₀: X₂ {O(n)}
t₆₇, X₁: X₂ {O(n)}
t₆₇, X₂: X₂ {O(n)}
t₆₇, X₃: X₃ {O(n)}
t₆₇, X₄: 2⋅X₃+100 {O(n)}
t₆₉, X₀: X₂ {O(n)}
t₆₉, X₁: X₂ {O(n)}
t₆₉, X₂: X₂ {O(n)}
t₆₉, X₃: X₃ {O(n)}
t₆₉, X₄: 2⋅X₃+100 {O(n)}
t₇₀, X₀: X₂ {O(n)}
t₇₀, X₁: X₂ {O(n)}
t₇₀, X₂: X₂ {O(n)}
t₇₀, X₃: X₃ {O(n)}
t₇₀, X₄: 2⋅X₃+100 {O(n)}
t₇₁, X₀: X₂ {O(n)}
t₇₁, X₁: X₂ {O(n)}
t₇₁, X₂: X₂ {O(n)}
t₇₁, X₃: X₃ {O(n)}
t₇₁, X₄: 2⋅X₃+100 {O(n)}