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) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, 0, X₂, X₃, X₄) :|: X₀ < X₄
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₁, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₁
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₀
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₇: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁, X₂, X₃, X₄)
t₆: l6(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁+1, X₂, X₃, X₄)
Preprocessing
Eliminate variables {X₃} that do not contribute to the problem
Found invariant 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ for location l7
Found invariant 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location l5
Found invariant X₂ ≤ X₀ for location l1
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ for location l4
Found invariant 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₇: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₁₈: l1(X₀, X₁, X₂, X₃) → l3(X₀, 0, X₂, X₃) :|: X₀ < X₃ ∧ X₂ ≤ X₀
t₁₉: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀
t₂₀: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₂₁: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ < X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
t₂₂: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
t₂₃: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀
t₂₄: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁
t₂₅: l6(X₀, X₁, X₂, X₃) → l3(X₀, X₁+1, X₂, X₃) :|: 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
MPRF for transition t₁₈: l1(X₀, X₁, X₂, X₃) → l3(X₀, 0, X₂, X₃) :|: X₀ < X₃ ∧ X₂ ≤ X₀ of depth 1:
new bound:
X₂+X₃ {O(n)}
MPRF for transition t₂₁: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ < X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₂+X₃ {O(n)}
MPRF for transition t₂₄: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
X₂+X₃ {O(n)}
MPRF for transition t₂₂: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:
new bound:
2⋅X₂⋅X₂+3⋅X₂⋅X₃+X₃⋅X₃+2⋅X₂+X₃+1 {O(n^2)}
MPRF for transition t₂₅: l6(X₀, X₁, X₂, X₃) → l3(X₀, X₁+1, X₂, X₃) :|: 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
2⋅X₂⋅X₂+3⋅X₂⋅X₃+X₃⋅X₃+2⋅X₂+X₃+1 {O(n^2)}
Chain transitions t₂₄: l5→l1 and t₁₉: l1→l4 to t₅₃: l5→l4
Chain transitions t₂₀: l2→l1 and t₁₉: l1→l4 to t₅₄: l2→l4
Chain transitions t₂₀: l2→l1 and t₁₈: l1→l3 to t₅₅: l2→l3
Chain transitions t₂₄: l5→l1 and t₁₈: l1→l3 to t₅₆: l5→l3
Chain transitions t₂₅: l6→l3 and t₂₂: l3→l6 to t₅₇: l6→l6
Chain transitions t₅₆: l5→l3 and t₂₂: l3→l6 to t₅₈: l5→l6
Chain transitions t₅₆: l5→l3 and t₂₁: l3→l5 to t₅₉: l5→l5
Chain transitions t₂₅: l6→l3 and t₂₁: l3→l5 to t₆₀: l6→l5
Chain transitions t₅₅: l2→l3 and t₂₁: l3→l5 to t₆₁: l2→l5
Chain transitions t₅₅: l2→l3 and t₂₂: l3→l6 to t₆₂: l2→l6
Analysing control-flow refined program
Found invariant 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ for location l7
Found invariant 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location l5
Found invariant X₂ ≤ X₀ for location l1
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ for location l4
Found invariant 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ for location l3
MPRF for transition t₅₈: l5(X₀, X₁, X₂, X₃) -{3}> l6(1+X₀, 0, X₂, X₃) :|: 1+X₀ < X₃ ∧ 0 ≤ 1+X₀ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ 0 ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
2⋅X₂+2⋅X₃ {O(n)}
MPRF for transition t₅₉: l5(X₀, X₁, X₂, X₃) -{3}> l5(1+X₀, 0, X₂, X₃) :|: 1+X₀ < X₃ ∧ 1+X₀ < 0 ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ 0 ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
2⋅X₂ {O(n)}
MPRF for transition t₆₀: l6(X₀, X₁, X₂, X₃) -{2}> l5(X₀, 1+X₁, X₂, X₃) :|: X₀ < X₁+1 ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
2⋅X₂+2⋅X₃+1 {O(n)}
MPRF for transition t₅₇: l6(X₀, X₁, X₂, X₃) -{2}> l6(X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₂⋅X₃+6⋅X₃⋅X₃+5⋅X₃ {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Found invariant 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l6___3
Found invariant 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___1
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ for location l7
Found invariant 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location l5
Found invariant 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l3___2
Found invariant X₂ ≤ X₀ for location l1
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ for location l4
Found invariant 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l3
knowledge_propagation leads to new time bound X₂+X₃ {O(n)} for transition t₁₄₉: l3(X₀, X₁, X₂, X₃) → n_l6___3(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁
knowledge_propagation leads to new time bound X₂+X₃ {O(n)} for transition t₁₅₁: n_l6___3(X₀, X₁, X₂, X₃) → n_l3___2(X₀, X₁+1, X₂, X₃) :|: X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
MPRF for transition t₁₄₈: n_l3___2(X₀, X₁, X₂, X₃) → n_l6___1(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
2⋅X₂⋅X₂+2⋅X₃⋅X₃+4⋅X₂⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}
MPRF for transition t₁₅₀: n_l6___1(X₀, X₁, X₂, X₃) → n_l3___2(X₀, X₁+1, X₂, X₃) :|: 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂⋅X₃+X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}
MPRF for transition t₁₅₅: n_l3___2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ < X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₂+X₃ {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:2⋅X₃⋅X₃+4⋅X₂⋅X₂+6⋅X₂⋅X₃+5⋅X₃+7⋅X₂+6 {O(n^2)}
t₁₇: 1 {O(1)}
t₁₈: X₂+X₃ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₂+X₃ {O(n)}
t₂₂: 2⋅X₂⋅X₂+3⋅X₂⋅X₃+X₃⋅X₃+2⋅X₂+X₃+1 {O(n^2)}
t₂₃: 1 {O(1)}
t₂₄: X₂+X₃ {O(n)}
t₂₅: 2⋅X₂⋅X₂+3⋅X₂⋅X₃+X₃⋅X₃+2⋅X₂+X₃+1 {O(n^2)}
Costbounds
Overall costbound: 2⋅X₃⋅X₃+4⋅X₂⋅X₂+6⋅X₂⋅X₃+5⋅X₃+7⋅X₂+6 {O(n^2)}
t₁₇: 1 {O(1)}
t₁₈: X₂+X₃ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₂+X₃ {O(n)}
t₂₂: 2⋅X₂⋅X₂+3⋅X₂⋅X₃+X₃⋅X₃+2⋅X₂+X₃+1 {O(n^2)}
t₂₃: 1 {O(1)}
t₂₄: X₂+X₃ {O(n)}
t₂₅: 2⋅X₂⋅X₂+3⋅X₂⋅X₃+X₃⋅X₃+2⋅X₂+X₃+1 {O(n^2)}
Sizebounds
t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₈, X₀: 2⋅X₂+X₃ {O(n)}
t₁₈, X₁: 0 {O(1)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₉, X₀: 3⋅X₂+X₃ {O(n)}
t₁₉, X₁: 2⋅X₂⋅X₂+3⋅X₂⋅X₃+X₃⋅X₃+2⋅X₂+X₁+X₃+1 {O(n^2)}
t₁₉, X₂: 2⋅X₂ {O(n)}
t₁₉, X₃: 2⋅X₃ {O(n)}
t₂₀, X₀: X₂ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₁, X₀: 2⋅X₂+X₃ {O(n)}
t₂₁, X₁: 2⋅X₂⋅X₂+3⋅X₂⋅X₃+X₃⋅X₃+2⋅X₂+X₃+1 {O(n^2)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₂, X₀: 2⋅X₂+X₃ {O(n)}
t₂₂, X₁: 2⋅X₂⋅X₂+3⋅X₂⋅X₃+X₃⋅X₃+2⋅X₂+X₃+1 {O(n^2)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₃, X₀: 3⋅X₂+X₃ {O(n)}
t₂₃, X₁: 2⋅X₂⋅X₂+3⋅X₂⋅X₃+X₃⋅X₃+2⋅X₂+X₁+X₃+1 {O(n^2)}
t₂₃, X₂: 2⋅X₂ {O(n)}
t₂₃, X₃: 2⋅X₃ {O(n)}
t₂₄, X₀: 2⋅X₂+X₃ {O(n)}
t₂₄, X₁: 2⋅X₂⋅X₂+3⋅X₂⋅X₃+X₃⋅X₃+2⋅X₂+X₃+1 {O(n^2)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₅, X₀: 2⋅X₂+X₃ {O(n)}
t₂₅, X₁: 2⋅X₂⋅X₂+3⋅X₂⋅X₃+X₃⋅X₃+2⋅X₂+X₃+1 {O(n^2)}
t₂₅, X₂: X₂ {O(n)}
t₂₅, X₃: X₃ {O(n)}