Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅)
t₅: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l13(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: l13(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, 0, X₂, X₃, X₄, X₅)
t₁₀: l14(X₀, X₁, X₂, X₃, X₄, X₅) → l15(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂+1 < X₅
t₁₁: l14(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 1+X₂
t₁₂: l15(X₀, X₁, X₂, X₃, X₄, X₅) → l14(X₀, X₁, X₂+1, X₃, X₄, X₅)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₀, X₂, X₃, X₄, X₅) :|: X₅ ≤ 1+X₂ ∧ X₀+1 < X₅
t₁₆: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂+1 < X₅
t₁₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 1+X₀
t₁₃: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₁+1, X₁, X₂, X₃, X₄, X₅)
t₁₄: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l14(X₀, X₁, 0, X₃, X₄, X₅)
t₁₈: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l16(X₀, X₁, X₂, X₃, X₄, X₅)
Preprocessing
Eliminate variables {X₃,X₄} that do not contribute to the problem
Found invariant X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l6
Found invariant 2 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l15
Found invariant X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l7
Found invariant X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 0 ≤ X₁ for location l8
Found invariant X₅ ≤ 1+X₂ ∧ X₅ ≤ 2+X₁ ∧ X₅ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l16
Found invariant X₅ ≤ 1+X₂ ∧ X₅ ≤ 2+X₁ ∧ X₅ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l9
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l14
Cut unsatisfiable transition t₅₁: l5→l9
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₅
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₃₈: l0(X₀, X₁, X₂, X₅) → l2(X₀, X₁, X₂, X₅)
t₃₉: l1(X₀, X₁, X₂, X₅) → l4(X₀, X₁, X₂, X₅)
t₄₀: l10(X₀, X₁, X₂, X₅) → l11(X₀, X₁, X₂, X₅)
t₄₁: l11(X₀, X₁, X₂, X₅) → l12(X₀, X₁, X₂, X₅)
t₄₂: l12(X₀, X₁, X₂, X₅) → l13(X₀, X₁, X₂, X₅)
t₄₃: l13(X₀, X₁, X₂, X₅) → l8(X₀, 0, X₂, X₅)
t₄₄: l14(X₀, X₁, X₂, X₅) → l15(X₀, X₁, X₂, X₅) :|: X₂+1 < X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₄₅: l14(X₀, X₁, X₂, X₅) → l6(X₀, X₁, X₂, X₅) :|: X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₄₆: l15(X₀, X₁, X₂, X₅) → l14(X₀, X₁, X₂+1, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₄₇: l2(X₀, X₁, X₂, X₅) → l3(X₀, X₁, X₂, X₅)
t₄₈: l3(X₀, X₁, X₂, X₅) → l1(X₀, X₁, X₂, X₅)
t₄₉: l4(X₀, X₁, X₂, X₅) → l10(X₀, X₁, X₂, X₅)
t₅₀: l5(X₀, X₁, X₂, X₅) → l8(X₀, X₀, X₂, X₅) :|: X₅ ≤ 1+X₂ ∧ X₀+1 < X₅ ∧ X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀
t₅₂: l5(X₀, X₁, X₂, X₅) → l9(X₀, X₁, X₂, X₅) :|: X₅ ≤ 1+X₀ ∧ X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀
t₅₃: l6(X₀, X₁, X₂, X₅) → l7(X₁+1, X₁, X₂, X₅) :|: X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₅₄: l7(X₀, X₁, X₂, X₅) → l5(X₀, X₁, X₂, X₅) :|: X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀
t₅₅: l8(X₀, X₁, X₂, X₅) → l14(X₀, X₁, 0, X₅) :|: 0 ≤ X₁
t₅₆: l9(X₀, X₁, X₂, X₅) → l16(X₀, X₁, X₂, X₅) :|: X₅ ≤ 1+X₂ ∧ X₅ ≤ 2+X₁ ∧ X₅ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀
MPRF for transition t₅₀: l5(X₀, X₁, X₂, X₅) → l8(X₀, X₀, X₂, X₅) :|: X₅ ≤ 1+X₂ ∧ X₀+1 < X₅ ∧ X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₅+1 {O(n)}
MPRF:
l15 [X₅+1-X₁ ]
l6 [X₅+1-X₁ ]
l7 [X₀+X₅-2⋅X₁ ]
l5 [X₅+2-X₀ ]
l8 [X₅+1-X₁ ]
l14 [X₅+1-X₁ ]
knowledge_propagation leads to new time bound X₅+2 {O(n)} for transition t₅₅: l8(X₀, X₁, X₂, X₅) → l14(X₀, X₁, 0, X₅) :|: 0 ≤ X₁
MPRF for transition t₄₄: l14(X₀, X₁, X₂, X₅) → l15(X₀, X₁, X₂, X₅) :|: X₂+1 < X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₅⋅X₅+2⋅X₅ {O(n^2)}
MPRF:
l15 [X₅-X₂-1 ]
l14 [X₅-X₂ ]
l8 [X₅-X₂ ]
l6 [X₅-X₂ ]
l7 [X₅-X₂ ]
l5 [X₅-X₂ ]
MPRF for transition t₄₅: l14(X₀, X₁, X₂, X₅) → l6(X₀, X₁, X₂, X₅) :|: X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₅+2 {O(n)}
MPRF:
l15 [1 ]
l14 [1 ]
l8 [1-X₁ ]
l6 [0 ]
l7 [0 ]
l5 [1-X₀ ]
MPRF for transition t₄₆: l15(X₀, X₁, X₂, X₅) → l14(X₀, X₁, X₂+1, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₅⋅X₅+2⋅X₅ {O(n^2)}
MPRF:
l15 [X₅-X₂ ]
l14 [X₅-X₂ ]
l8 [X₅-X₂ ]
l6 [X₅-X₂ ]
l7 [X₅-X₂ ]
l5 [X₅-X₂ ]
MPRF for transition t₅₃: l6(X₀, X₁, X₂, X₅) → l7(X₁+1, X₁, X₂, X₅) :|: X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
2⋅X₅+4 {O(n)}
MPRF:
l15 [2 ]
l14 [2 ]
l8 [1 ]
l6 [2 ]
l7 [1 ]
l5 [X₁+2-X₀ ]
MPRF for transition t₅₄: l7(X₀, X₁, X₂, X₅) → l5(X₀, X₁, X₂, X₅) :|: X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₅+2 {O(n)}
MPRF:
l15 [1 ]
l14 [1 ]
l8 [0 ]
l6 [1 ]
l7 [1 ]
l5 [0 ]
Analysing control-flow refined program
Found invariant 2 ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location n_l14___2
Found invariant X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l6
Found invariant 2 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location n_l15___3
Found invariant X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l7
Found invariant X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 0 ≤ X₁ for location l8
Found invariant 3 ≤ X₅ ∧ 4 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location n_l15___1
Found invariant X₅ ≤ 1+X₂ ∧ X₅ ≤ 2+X₁ ∧ X₅ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l16
Found invariant X₅ ≤ 1+X₂ ∧ X₅ ≤ 2+X₁ ∧ X₅ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ for location l9
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l14
knowledge_propagation leads to new time bound X₅+2 {O(n)} for transition t₁₂₈: l14(X₀, X₁, X₂, X₅) → n_l15___3(X₀, X₁, X₂, X₅) :|: 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ < X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
knowledge_propagation leads to new time bound X₅+2 {O(n)} for transition t₁₃₀: n_l15___3(X₀, X₁, X₂, X₅) → n_l14___2(X₀, X₁, X₂+1, X₅) :|: 1 < X₅ ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
MPRF for transition t₁₂₇: n_l14___2(X₀, X₁, X₂, X₅) → n_l15___1(X₀, X₁, X₂, X₅) :|: 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ < X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₅⋅X₅+4⋅X₅+4 {O(n^2)}
MPRF:
n_l15___3 [0 ]
l7 [0 ]
l5 [0 ]
l8 [0 ]
l14 [0 ]
l6 [0 ]
n_l15___1 [X₅-X₂-2 ]
n_l14___2 [X₅-X₂-1 ]
MPRF for transition t₁₃₄: n_l14___2(X₀, X₁, X₂, X₅) → l6(X₀, X₁, X₂, X₅) :|: X₅ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
3⋅X₅+8 {O(n)}
MPRF:
n_l15___3 [6-2⋅X₅ ]
l7 [0 ]
l5 [0 ]
l8 [6-2⋅X₅ ]
l14 [6-2⋅X₅ ]
l6 [0 ]
n_l15___1 [1 ]
n_l14___2 [1 ]
MPRF for transition t₁₂₉: n_l15___1(X₀, X₁, X₂, X₅) → n_l14___2(X₀, X₁, X₂+1, X₅) :|: 1+X₂ < X₅ ∧ 1 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 2+X₂ ≤ X₅ ∧ 3 ≤ X₅ ∧ 4 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
2⋅X₅⋅X₅+7⋅X₅+4 {O(n^2)}
MPRF:
n_l15___3 [X₅ ]
l7 [X₅ ]
l5 [X₅ ]
l8 [X₅ ]
l14 [X₅ ]
l6 [X₅ ]
n_l15___1 [2⋅X₅-X₂-1 ]
n_l14___2 [2⋅X₅-X₂-1 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:2⋅X₅⋅X₅+10⋅X₅+22 {O(n^2)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}
t₄₁: 1 {O(1)}
t₄₂: 1 {O(1)}
t₄₃: 1 {O(1)}
t₄₄: X₅⋅X₅+2⋅X₅ {O(n^2)}
t₄₅: X₅+2 {O(n)}
t₄₆: X₅⋅X₅+2⋅X₅ {O(n^2)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
t₄₉: 1 {O(1)}
t₅₀: X₅+1 {O(n)}
t₅₂: 1 {O(1)}
t₅₃: 2⋅X₅+4 {O(n)}
t₅₄: X₅+2 {O(n)}
t₅₅: X₅+2 {O(n)}
t₅₆: 1 {O(1)}
Costbounds
Overall costbound: 2⋅X₅⋅X₅+10⋅X₅+22 {O(n^2)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}
t₄₁: 1 {O(1)}
t₄₂: 1 {O(1)}
t₄₃: 1 {O(1)}
t₄₄: X₅⋅X₅+2⋅X₅ {O(n^2)}
t₄₅: X₅+2 {O(n)}
t₄₆: X₅⋅X₅+2⋅X₅ {O(n^2)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
t₄₉: 1 {O(1)}
t₅₀: X₅+1 {O(n)}
t₅₂: 1 {O(1)}
t₅₃: 2⋅X₅+4 {O(n)}
t₅₄: X₅+2 {O(n)}
t₅₅: X₅+2 {O(n)}
t₅₆: 1 {O(1)}
Sizebounds
t₃₈, X₀: X₀ {O(n)}
t₃₈, X₁: X₁ {O(n)}
t₃₈, X₂: X₂ {O(n)}
t₃₈, X₅: X₅ {O(n)}
t₃₉, X₀: X₀ {O(n)}
t₃₉, X₁: X₁ {O(n)}
t₃₉, X₂: X₂ {O(n)}
t₃₉, X₅: X₅ {O(n)}
t₄₀, X₀: X₀ {O(n)}
t₄₀, X₁: X₁ {O(n)}
t₄₀, X₂: X₂ {O(n)}
t₄₀, X₅: X₅ {O(n)}
t₄₁, X₀: X₀ {O(n)}
t₄₁, X₁: X₁ {O(n)}
t₄₁, X₂: X₂ {O(n)}
t₄₁, X₅: X₅ {O(n)}
t₄₂, X₀: X₀ {O(n)}
t₄₂, X₁: X₁ {O(n)}
t₄₂, X₂: X₂ {O(n)}
t₄₂, X₅: X₅ {O(n)}
t₄₃, X₀: X₀ {O(n)}
t₄₃, X₁: 0 {O(1)}
t₄₃, X₂: X₂ {O(n)}
t₄₃, X₅: X₅ {O(n)}
t₄₄, X₀: 2⋅X₅+X₀+4 {O(n)}
t₄₄, X₁: 2⋅X₅+4 {O(n)}
t₄₄, X₂: X₅⋅X₅+2⋅X₅ {O(n^2)}
t₄₄, X₅: X₅ {O(n)}
t₄₅, X₀: 2⋅X₀+4⋅X₅+8 {O(n)}
t₄₅, X₁: 2⋅X₅+4 {O(n)}
t₄₅, X₂: X₅⋅X₅+2⋅X₅ {O(n^2)}
t₄₅, X₅: X₅ {O(n)}
t₄₆, X₀: 2⋅X₅+X₀+4 {O(n)}
t₄₆, X₁: 2⋅X₅+4 {O(n)}
t₄₆, X₂: X₅⋅X₅+2⋅X₅ {O(n^2)}
t₄₆, X₅: X₅ {O(n)}
t₄₇, X₀: X₀ {O(n)}
t₄₇, X₁: X₁ {O(n)}
t₄₇, X₂: X₂ {O(n)}
t₄₇, X₅: X₅ {O(n)}
t₄₈, X₀: X₀ {O(n)}
t₄₈, X₁: X₁ {O(n)}
t₄₈, X₂: X₂ {O(n)}
t₄₈, X₅: X₅ {O(n)}
t₄₉, X₀: X₀ {O(n)}
t₄₉, X₁: X₁ {O(n)}
t₄₉, X₂: X₂ {O(n)}
t₄₉, X₅: X₅ {O(n)}
t₅₀, X₀: 2⋅X₅+4 {O(n)}
t₅₀, X₁: 2⋅X₅+4 {O(n)}
t₅₀, X₂: X₅⋅X₅+2⋅X₅ {O(n^2)}
t₅₀, X₅: X₅ {O(n)}
t₅₂, X₀: 2⋅X₅+4 {O(n)}
t₅₂, X₁: 2⋅X₅+4 {O(n)}
t₅₂, X₂: X₅⋅X₅+2⋅X₅ {O(n^2)}
t₅₂, X₅: X₅ {O(n)}
t₅₃, X₀: 2⋅X₅+4 {O(n)}
t₅₃, X₁: 2⋅X₅+4 {O(n)}
t₅₃, X₂: X₅⋅X₅+2⋅X₅ {O(n^2)}
t₅₃, X₅: X₅ {O(n)}
t₅₄, X₀: 2⋅X₅+4 {O(n)}
t₅₄, X₁: 2⋅X₅+4 {O(n)}
t₅₄, X₂: X₅⋅X₅+2⋅X₅ {O(n^2)}
t₅₄, X₅: X₅ {O(n)}
t₅₅, X₀: 2⋅X₅+X₀+4 {O(n)}
t₅₅, X₁: 2⋅X₅+4 {O(n)}
t₅₅, X₂: 0 {O(1)}
t₅₅, X₅: X₅ {O(n)}
t₅₆, X₀: 2⋅X₅+4 {O(n)}
t₅₆, X₁: 2⋅X₅+4 {O(n)}
t₅₆, X₂: X₅⋅X₅+2⋅X₅ {O(n^2)}
t₅₆, X₅: X₅ {O(n)}