Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃+X₄
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃+X₄+1 ≤ X₅
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₂
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂+1 ≤ X₄
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₃-X₄)
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅+1)
t₁₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄+1, X₅)
t₁₁: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃+1, X₄, X₅)
t₂: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₁, X₅) :|: X₃ ≤ X₀
t₃: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+1 ≤ X₃
t₁₂: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₁, X₂, X₃, X₀, X₄, X₅)
Preprocessing
Found invariant X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l2
Found invariant 1+X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l6
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location l5
Found invariant 1+X₀ ≤ X₃ for location l8
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location l1
Found invariant 1+X₀ ≤ X₃ for location l10
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location l4
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃+X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃+X₄+1 ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂+1 ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₃-X₄) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅+1) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
t₁₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄+1, X₅) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
t₁₁: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃+1, X₄, X₅) :|: 1+X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₂: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₁, X₅) :|: X₃ ≤ X₀
t₃: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+1 ≤ X₃
t₁₂: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃
t₁: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₁, X₂, X₃, X₀, X₄, X₅)
MPRF for transition t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂+1 ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
l3 [X₀+1-X₃ ]
l4 [X₀+1-X₃ ]
l1 [X₀+1-X₃ ]
l5 [X₀+1-X₃ ]
l6 [X₀-X₃ ]
l7 [X₀+1-X₃ ]
l2 [X₀+1-X₃ ]
MPRF for transition t₁₁: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃+1, X₄, X₅) :|: 1+X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
l3 [X₀+1-X₃ ]
l4 [X₀+1-X₃ ]
l1 [X₀+1-X₃ ]
l5 [X₀+1-X₃ ]
l6 [X₀+1-X₃ ]
l7 [X₀+1-X₃ ]
l2 [X₀+1-X₃ ]
MPRF for transition t₂: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₁, X₅) :|: X₃ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
l3 [X₀-X₃ ]
l4 [X₀-X₃ ]
l1 [X₀-X₃ ]
l5 [X₀-X₃ ]
l6 [X₀-X₃ ]
l7 [X₀+1-X₃ ]
l2 [X₀-X₃ ]
MPRF for transition t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃+X₄+1 ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
MPRF:
l3 [X₂+1-X₄ ]
l4 [X₂+1-X₄ ]
l1 [X₂+1-X₄ ]
l5 [X₂-X₄ ]
l2 [X₂+1-X₄ ]
l6 [X₂-X₄ ]
l7 [X₂-X₄ ]
MPRF for transition t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
MPRF:
l3 [X₂-X₄ ]
l4 [X₂-X₄ ]
l1 [X₂-X₄ ]
l5 [X₂-X₄ ]
l2 [X₂+1-X₄ ]
l6 [X₂-X₄ ]
l7 [X₂-X₄ ]
MPRF for transition t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₃-X₄) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
MPRF:
l3 [X₂+1-X₄ ]
l4 [X₂-X₄ ]
l1 [X₂-X₄ ]
l5 [X₂-X₄ ]
l2 [X₂+1-X₄ ]
l6 [X₂-X₄ ]
l7 [X₂-X₄ ]
MPRF for transition t₁₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄+1, X₅) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
MPRF:
l3 [X₂+1-X₄ ]
l4 [X₂+1-X₄ ]
l1 [X₂+1-X₄ ]
l5 [X₂+1-X₄ ]
l2 [X₂+1-X₄ ]
l6 [X₂-X₄ ]
l7 [X₂-X₄ ]
MPRF for transition t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃+X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₀⋅X₂+2⋅X₁⋅X₂+2⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₂+5⋅X₃+X₀+X₁+2 {O(n^3)}
MPRF:
l5 [X₂+X₃+1-X₅ ]
l3 [2⋅X₂+1 ]
l4 [X₂+X₃-X₅ ]
l1 [X₂+X₃+1-X₅ ]
l6 [2⋅X₂+1 ]
l7 [2⋅X₂+1 ]
l2 [2⋅X₂+1 ]
knowledge_propagation leads to new time bound 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₀⋅X₂+2⋅X₁⋅X₂+2⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₂+5⋅X₃+X₀+X₁+2 {O(n^3)} for transition t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅+1) :|: X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
Analysing control-flow refined program
Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l2
Found invariant 1+X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l6
Found invariant X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location n_l4___4
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location n_l5___6
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location n_l1___8
Found invariant X₄ ≤ 1+X₂ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location n_l2___2
Found invariant 1+X₀ ≤ X₃ for location l8
Found invariant X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location n_l1___5
Found invariant X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location n_l3___9
Found invariant 1+X₀ ≤ X₃ for location l10
Found invariant X₄ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ for location n_l3___1
Found invariant X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ for location n_l4___7
Found invariant 1+X₃ ≤ X₅ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location n_l5___3
knowledge_propagation leads to new time bound X₀+X₁+1 {O(n)} for transition t₁₀₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l3___9(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
knowledge_propagation leads to new time bound X₀+X₁+1 {O(n)} for transition t₁₀₄: n_l3___9(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___8(X₀, X₁, X₂, X₃, X₄, X₃-X₄) :|: X₁ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂
MPRF for transition t₉₈: n_l1___5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l5___3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 1+X₃+X₄ ≤ X₅ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₀+2⋅X₀⋅X₂+2⋅X₀⋅X₃+2⋅X₁⋅X₁+2⋅X₁⋅X₂+2⋅X₁⋅X₃+4⋅X₀⋅X₁+2⋅X₂+3⋅X₃+5⋅X₀+5⋅X₁+3 {O(n^2)}
MPRF:
n_l3___9 [X₀+X₂+1-X₃ ]
l7 [X₀+X₂+1-X₃ ]
l2 [X₀+X₂+1-X₃ ]
l6 [X₀+X₂-X₃ ]
n_l3___1 [X₀+2⋅X₂+1-X₃-X₄ ]
n_l1___8 [X₀+2⋅X₂+1-X₃-X₄ ]
n_l4___4 [X₀+2⋅X₂+1-X₃-X₄ ]
n_l4___7 [X₀+2⋅X₂+1-X₃-X₄ ]
n_l1___5 [X₀+2⋅X₂+1-X₃-X₄ ]
n_l5___3 [X₀+2⋅X₂-X₃-X₄ ]
n_l5___6 [X₀+2⋅X₂-X₃-X₄ ]
n_l2___2 [X₀+2⋅X₂+1-X₃-X₄ ]
MPRF for transition t₉₉: n_l1___8(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₄+X₅ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₅ ≤ X₃+X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₀+2⋅X₀⋅X₂+2⋅X₁⋅X₁+2⋅X₁⋅X₂+4⋅X₀⋅X₁+X₀⋅X₃+X₁⋅X₃+2⋅X₂+5⋅X₀+5⋅X₁+X₃+3 {O(n^2)}
MPRF:
n_l3___9 [X₀+1-X₃ ]
l7 [X₀+1-X₃ ]
l2 [X₀+1-X₃ ]
l6 [X₀-X₃ ]
n_l3___1 [X₀+X₂+1-X₃-X₄ ]
n_l1___8 [X₀+X₂+1-X₃-X₄ ]
n_l4___4 [X₀+X₂-X₃-X₄ ]
n_l4___7 [X₀+X₂-X₃-X₄ ]
n_l1___5 [X₀+X₂-X₃-X₄ ]
n_l5___3 [X₀+X₂-X₃-X₄ ]
n_l5___6 [X₀+X₂-X₃-X₄ ]
n_l2___2 [X₀+X₂+1-X₃-X₄ ]
MPRF for transition t₁₀₀: n_l1___8(X₀, X₁, X₂, X₃, X₄, X₅) → n_l5___6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₄+X₅ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 1+X₃+X₄ ≤ X₅ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₂+X₀+X₁+2 {O(n^2)}
MPRF:
n_l3___9 [-2⋅X₂-1 ]
l7 [-2⋅X₂-1 ]
l2 [-2⋅X₂-1 ]
l6 [-2⋅X₂-1 ]
n_l3___1 [1-2⋅X₄ ]
n_l1___8 [1-2⋅X₄ ]
n_l4___4 [1-2⋅X₄ ]
n_l4___7 [1-2⋅X₄ ]
n_l1___5 [1-2⋅X₄ ]
n_l5___3 [-2⋅X₄-1 ]
n_l5___6 [-2⋅X₄-1 ]
n_l2___2 [1-2⋅X₄ ]
MPRF for transition t₁₀₂: n_l2___2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l3___1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ 1+X₂ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₄ ≤ 1+X₂ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+2 {O(n^2)}
MPRF:
n_l3___9 [1 ]
l7 [1 ]
l2 [1 ]
l6 [1 ]
n_l3___1 [X₂+1-X₄ ]
n_l1___8 [X₂+1-X₄ ]
n_l4___4 [X₂+1-X₄ ]
n_l4___7 [X₂+1-X₄ ]
n_l1___5 [X₂+1-X₄ ]
n_l5___3 [X₂+1-X₄ ]
n_l5___6 [X₂+1-X₄ ]
n_l2___2 [X₂+2-X₄ ]
MPRF for transition t₁₁₈: n_l2___2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂+1 ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ 1+X₂ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
l7 [X₀+1-X₃ ]
l2 [X₀+1-X₃ ]
l6 [X₀-X₃ ]
n_l3___1 [X₀+1-X₃ ]
n_l3___9 [X₀+1-X₃ ]
n_l1___8 [X₀+1-X₃ ]
n_l4___4 [X₀+1-X₃ ]
n_l4___7 [X₀+1-X₃ ]
n_l1___5 [X₀+1-X₃ ]
n_l5___3 [X₀+1-X₃ ]
n_l5___6 [X₀+1-X₃ ]
n_l2___2 [X₀+1-X₃ ]
MPRF for transition t₁₀₃: n_l3___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___8(X₀, X₁, X₂, X₃, X₄, X₃-X₄) :|: X₄ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 1+X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₀+2⋅X₀⋅X₂+2⋅X₁⋅X₁+2⋅X₁⋅X₂+4⋅X₀⋅X₁+X₀⋅X₃+X₁⋅X₃+2⋅X₂+4⋅X₀+4⋅X₁+X₃+2 {O(n^2)}
MPRF:
n_l3___9 [X₀+1-X₃ ]
l7 [X₀+1-X₃ ]
l2 [X₀+1-X₃ ]
l6 [X₀-X₃ ]
n_l3___1 [X₀+X₂+1-X₃-X₄ ]
n_l1___8 [X₀+X₂-X₃-X₄ ]
n_l4___4 [X₀+X₂-X₃-X₄ ]
n_l4___7 [X₀+X₂-X₃-X₄ ]
n_l1___5 [X₀+X₂-X₃-X₄ ]
n_l5___3 [X₀+X₂-X₃-X₄ ]
n_l5___6 [X₀+X₂-X₃-X₄ ]
n_l2___2 [X₀+X₂+1-X₃-X₄ ]
MPRF for transition t₁₀₆: n_l4___7(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___5(X₀, X₁, X₂, X₃, X₄, X₅+1) :|: X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₄ ∧ X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₀+2⋅X₀⋅X₂+2⋅X₀⋅X₃+2⋅X₁⋅X₁+2⋅X₁⋅X₂+2⋅X₁⋅X₃+4⋅X₀⋅X₁+2⋅X₂+3⋅X₃+5⋅X₀+5⋅X₁+3 {O(n^2)}
MPRF:
n_l3___9 [X₀+X₂+1-X₃ ]
l7 [X₀+X₂+1-X₃ ]
l2 [X₀+X₂+1-X₃ ]
l6 [X₀+X₂-X₃ ]
n_l3___1 [X₀+2⋅X₂+1-X₃-X₄ ]
n_l1___8 [X₀+2⋅X₂+1-X₃-X₄ ]
n_l4___4 [X₀+2⋅X₂-X₃-X₄ ]
n_l4___7 [X₀+2⋅X₂+1-2⋅X₄-X₅ ]
n_l1___5 [X₀+2⋅X₂-X₃-X₄ ]
n_l5___3 [X₀+2⋅X₂-X₃-X₄ ]
n_l5___6 [X₀+2⋅X₂-X₃-X₄ ]
n_l2___2 [X₀+2⋅X₂+1-X₃-X₄ ]
MPRF for transition t₁₀₇: n_l5___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l2___2(X₀, X₁, X₂, X₃, X₄+1, X₅) :|: 1+X₃+X₄ ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₅ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₀+2⋅X₀⋅X₂+2⋅X₀⋅X₃+2⋅X₁⋅X₁+2⋅X₁⋅X₂+2⋅X₁⋅X₃+4⋅X₀⋅X₁+2⋅X₂+3⋅X₃+5⋅X₀+5⋅X₁+3 {O(n^2)}
MPRF:
n_l3___9 [X₀+X₂+1-X₃ ]
l7 [X₀+X₂+1-X₃ ]
l2 [X₀+X₂+1-X₃ ]
l6 [X₀+X₂-X₃ ]
n_l3___1 [X₀+2⋅X₂+1-X₃-X₄ ]
n_l1___8 [X₀+2⋅X₂+1-X₃-X₄ ]
n_l4___4 [X₀+2⋅X₂+1-X₃-X₄ ]
n_l4___7 [X₀+2⋅X₂+1-X₃-X₄ ]
n_l1___5 [X₀+2⋅X₂+1-X₃-X₄ ]
n_l5___3 [X₀+2⋅X₂+1-X₃-X₄ ]
n_l5___6 [X₀+2⋅X₂-X₃-X₄ ]
n_l2___2 [X₀+2⋅X₂+1-X₃-X₄ ]
MPRF for transition t₁₀₈: n_l5___6(X₀, X₁, X₂, X₃, X₄, X₅) → n_l2___2(X₀, X₁, X₂, X₃, X₄+1, X₅) :|: 1+2⋅X₄ ≤ 0 ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₄+X₅ ≤ X₀ ∧ X₃ ≤ X₄+X₅ ∧ X₄+X₅ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:
new bound:
2⋅X₀⋅X₀+2⋅X₁⋅X₁+4⋅X₀⋅X₁+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₂+6⋅X₀+6⋅X₁+4 {O(n^2)}
MPRF:
n_l3___9 [X₀+1-2⋅X₂-X₃ ]
l7 [X₀+1-2⋅X₂-X₃ ]
l2 [X₀+1-2⋅X₂-X₃ ]
l6 [X₀-2⋅X₂-X₃ ]
n_l3___1 [X₀+2-X₃-2⋅X₄ ]
n_l1___8 [X₀+2-X₃-2⋅X₄ ]
n_l4___4 [X₀-X₃-2⋅X₄ ]
n_l4___7 [X₀-X₃-2⋅X₄ ]
n_l1___5 [X₀-X₃-2⋅X₄ ]
n_l5___3 [X₀-X₃-2⋅X₄ ]
n_l5___6 [X₀+2-X₃-2⋅X₄ ]
n_l2___2 [X₀+2-X₃-2⋅X₄ ]
MPRF for transition t₉₇: n_l1___5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₅ ≤ X₃+X₄ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ of depth 1:
new bound:
4⋅X₀⋅X₀⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₀⋅X₃⋅X₃+4⋅X₁⋅X₁⋅X₃+4⋅X₁⋅X₂⋅X₃+4⋅X₁⋅X₃⋅X₃+8⋅X₀⋅X₁⋅X₃+10⋅X₀⋅X₃+10⋅X₁⋅X₃+4⋅X₂⋅X₃+6⋅X₃⋅X₃+8⋅X₃ {O(n^3)}
MPRF:
l7 [2⋅X₂ ]
l2 [2⋅X₂ ]
n_l5___3 [X₂+X₃-X₅ ]
l6 [2⋅X₂ ]
n_l3___1 [2⋅X₂ ]
n_l3___9 [2⋅X₂ ]
n_l1___8 [2⋅X₂ ]
n_l4___4 [X₂+X₃-X₅ ]
n_l4___7 [X₂+X₃-X₅ ]
n_l1___5 [X₂+X₃+1-X₅ ]
n_l5___6 [2⋅X₂ ]
n_l2___2 [2⋅X₂ ]
MPRF for transition t₁₀₅: n_l4___4(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___5(X₀, X₁, X₂, X₃, X₄, X₅+1) :|: X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₅ ≤ X₃+X₄ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ of depth 1:
new bound:
12⋅X₀⋅X₀⋅X₁+12⋅X₀⋅X₁⋅X₁+16⋅X₀⋅X₁⋅X₃+4⋅X₀⋅X₀⋅X₀+4⋅X₀⋅X₀⋅X₂+4⋅X₀⋅X₂⋅X₃+4⋅X₀⋅X₃⋅X₃+4⋅X₁⋅X₁⋅X₁+4⋅X₁⋅X₁⋅X₂+4⋅X₁⋅X₂⋅X₃+4⋅X₁⋅X₃⋅X₃+8⋅X₀⋅X₀⋅X₃+8⋅X₀⋅X₁⋅X₂+8⋅X₁⋅X₁⋅X₃+12⋅X₀⋅X₀+12⋅X₁⋅X₁+18⋅X₀⋅X₃+18⋅X₁⋅X₃+24⋅X₀⋅X₁+4⋅X₂⋅X₃+6⋅X₀⋅X₂+6⋅X₁⋅X₂+6⋅X₃⋅X₃+11⋅X₃+12⋅X₀+12⋅X₁+2⋅X₂+4 {O(n^3)}
MPRF:
l7 [X₀+2⋅X₂+1-X₃ ]
l2 [X₀+2⋅X₂-X₃ ]
n_l5___3 [X₀+X₄-X₅ ]
l6 [X₀+2⋅X₂-X₃ ]
n_l3___1 [X₀+2⋅X₂-X₃ ]
n_l3___9 [X₀+2⋅X₂-X₃ ]
n_l1___8 [X₀+2⋅X₂-X₃ ]
n_l4___4 [X₀+X₄+1-X₅ ]
n_l4___7 [X₀+X₄-X₅ ]
n_l1___5 [X₀+X₄+1-X₅ ]
n_l5___6 [X₀+2⋅X₂-X₃ ]
n_l2___2 [X₀+2⋅X₂-X₃ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₀⋅X₃⋅X₃+4⋅X₁⋅X₃⋅X₃+8⋅X₀⋅X₂⋅X₃+8⋅X₁⋅X₂⋅X₃+10⋅X₀⋅X₃+10⋅X₁⋅X₃+12⋅X₀⋅X₂+12⋅X₁⋅X₂+4⋅X₃⋅X₃+8⋅X₂⋅X₃+12⋅X₂+14⋅X₃+9⋅X₀+9⋅X₁+15 {O(n^3)}
t₀: 1 {O(1)}
t₇: 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₀⋅X₂+2⋅X₁⋅X₂+2⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₂+5⋅X₃+X₀+X₁+2 {O(n^3)}
t₈: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₄: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₅: X₀+X₁+1 {O(n)}
t₆: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₉: 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₀⋅X₂+2⋅X₁⋅X₂+2⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₂+5⋅X₃+X₀+X₁+2 {O(n^3)}
t₁₀: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₁₁: X₀+X₁+1 {O(n)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₀⋅X₃⋅X₃+4⋅X₁⋅X₃⋅X₃+8⋅X₀⋅X₂⋅X₃+8⋅X₁⋅X₂⋅X₃+10⋅X₀⋅X₃+10⋅X₁⋅X₃+12⋅X₀⋅X₂+12⋅X₁⋅X₂+4⋅X₃⋅X₃+8⋅X₂⋅X₃+12⋅X₂+14⋅X₃+9⋅X₀+9⋅X₁+15 {O(n^3)}
t₀: 1 {O(1)}
t₇: 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₀⋅X₂+2⋅X₁⋅X₂+2⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₂+5⋅X₃+X₀+X₁+2 {O(n^3)}
t₈: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₄: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₅: X₀+X₁+1 {O(n)}
t₆: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₉: 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₀⋅X₂+2⋅X₁⋅X₂+2⋅X₃⋅X₃+3⋅X₀⋅X₃+3⋅X₁⋅X₃+4⋅X₂⋅X₃+2⋅X₂+5⋅X₃+X₀+X₁+2 {O(n^3)}
t₁₀: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₁₁: X₀+X₁+1 {O(n)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁: 1 {O(1)}
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)}
t₀, X₅: X₅ {O(n)}
t₇, X₀: X₁ {O(n)}
t₇, X₁: X₂ {O(n)}
t₇, X₂: X₃ {O(n)}
t₇, X₃: 2⋅X₀+X₁+1 {O(n)}
t₇, X₄: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+4⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₇, X₅: 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₃⋅X₃+4⋅X₀⋅X₂+4⋅X₀⋅X₃+4⋅X₁⋅X₂+4⋅X₁⋅X₃+4⋅X₂⋅X₃+3⋅X₁+4⋅X₀+6⋅X₂+6⋅X₃+4 {O(n^3)}
t₈, X₀: X₁ {O(n)}
t₈, X₁: X₂ {O(n)}
t₈, X₂: X₃ {O(n)}
t₈, X₃: 2⋅X₀+X₁+1 {O(n)}
t₈, X₄: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+4⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₈, X₅: 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₃⋅X₃+4⋅X₂⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+6⋅X₀⋅X₂+6⋅X₁⋅X₂+10⋅X₂+5⋅X₁+7⋅X₀+7⋅X₃+6 {O(n^3)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₂ {O(n)}
t₄, X₂: X₃ {O(n)}
t₄, X₃: 2⋅X₀+X₁+1 {O(n)}
t₄, X₄: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+4⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₄, X₅: 4⋅X₀⋅X₃⋅X₃+4⋅X₁⋅X₃⋅X₃+8⋅X₀⋅X₂⋅X₃+8⋅X₁⋅X₂⋅X₃+10⋅X₀⋅X₃+10⋅X₁⋅X₃+12⋅X₀⋅X₂+12⋅X₁⋅X₂+4⋅X₃⋅X₃+8⋅X₂⋅X₃+10⋅X₁+14⋅X₀+14⋅X₃+20⋅X₂+X₅+12 {O(n^3)}
t₅, X₀: X₁ {O(n)}
t₅, X₁: X₂ {O(n)}
t₅, X₂: X₃ {O(n)}
t₅, X₃: 2⋅X₀+X₁+1 {O(n)}
t₅, X₄: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+6⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₅, X₅: 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₃⋅X₃+4⋅X₂⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+6⋅X₀⋅X₂+6⋅X₁⋅X₂+10⋅X₂+5⋅X₁+7⋅X₀+7⋅X₃+X₅+6 {O(n^3)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: X₂ {O(n)}
t₆, X₂: X₃ {O(n)}
t₆, X₃: 2⋅X₀+X₁+1 {O(n)}
t₆, X₄: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+4⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₆, X₅: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₁+3⋅X₀+4⋅X₂+X₃+2 {O(n^2)}
t₉, X₀: X₁ {O(n)}
t₉, X₁: X₂ {O(n)}
t₉, X₂: X₃ {O(n)}
t₉, X₃: 2⋅X₀+X₁+1 {O(n)}
t₉, X₄: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+4⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₉, X₅: 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₃⋅X₃+4⋅X₀⋅X₂+4⋅X₀⋅X₃+4⋅X₁⋅X₂+4⋅X₁⋅X₃+4⋅X₂⋅X₃+3⋅X₁+4⋅X₀+6⋅X₂+6⋅X₃+4 {O(n^3)}
t₁₀, X₀: X₁ {O(n)}
t₁₀, X₁: X₂ {O(n)}
t₁₀, X₂: X₃ {O(n)}
t₁₀, X₃: 2⋅X₀+X₁+1 {O(n)}
t₁₀, X₄: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+4⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₁₀, X₅: 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₃⋅X₃+4⋅X₂⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+6⋅X₀⋅X₂+6⋅X₁⋅X₂+10⋅X₂+5⋅X₁+7⋅X₀+7⋅X₃+6 {O(n^3)}
t₁₁, X₀: X₁ {O(n)}
t₁₁, X₁: X₂ {O(n)}
t₁₁, X₂: X₃ {O(n)}
t₁₁, X₃: 2⋅X₀+X₁+1 {O(n)}
t₁₁, X₄: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+6⋅X₂+X₀+X₁+X₃+1 {O(n^2)}
t₁₁, X₅: 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₃⋅X₃+4⋅X₂⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+6⋅X₀⋅X₂+6⋅X₁⋅X₂+10⋅X₂+5⋅X₁+7⋅X₀+7⋅X₃+X₅+6 {O(n^3)}
t₂, X₀: X₁ {O(n)}
t₂, X₁: X₂ {O(n)}
t₂, X₂: X₃ {O(n)}
t₂, X₃: 2⋅X₀+X₁+1 {O(n)}
t₂, X₄: 2⋅X₂ {O(n)}
t₂, X₅: 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₃⋅X₃+4⋅X₂⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+6⋅X₀⋅X₂+6⋅X₁⋅X₂+10⋅X₂+5⋅X₁+7⋅X₀+7⋅X₃+X₅+6 {O(n^3)}
t₃, X₀: 2⋅X₁ {O(n)}
t₃, X₁: 2⋅X₂ {O(n)}
t₃, X₂: 2⋅X₃ {O(n)}
t₃, X₃: 3⋅X₀+X₁+1 {O(n)}
t₃, X₄: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+6⋅X₂+X₀+X₁+X₃+X₄+1 {O(n^2)}
t₃, X₅: 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₃⋅X₃+4⋅X₂⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+6⋅X₀⋅X₂+6⋅X₁⋅X₂+10⋅X₂+2⋅X₅+5⋅X₁+7⋅X₀+7⋅X₃+6 {O(n^3)}
t₁₂, X₀: 2⋅X₁ {O(n)}
t₁₂, X₁: 2⋅X₂ {O(n)}
t₁₂, X₂: 2⋅X₃ {O(n)}
t₁₂, X₃: 3⋅X₀+X₁+1 {O(n)}
t₁₂, X₄: 2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+6⋅X₂+X₀+X₁+X₃+X₄+1 {O(n^2)}
t₁₂, X₅: 2⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₃⋅X₃+4⋅X₀⋅X₂⋅X₃+4⋅X₁⋅X₂⋅X₃+2⋅X₃⋅X₃+4⋅X₂⋅X₃+5⋅X₀⋅X₃+5⋅X₁⋅X₃+6⋅X₀⋅X₂+6⋅X₁⋅X₂+10⋅X₂+2⋅X₅+5⋅X₁+7⋅X₀+7⋅X₃+6 {O(n^3)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₃ {O(n)}
t₁, X₃: X₀ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}