Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₁ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₂ < X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₉, X₈, X₇, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 < X₀
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₀ ≤ 1
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀-1, X₁, X₂+X₀-1, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
Preprocessing
Eliminate variables {X₃,X₄,X₅,X₆} that do not contribute to the problem
Found invariant X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1 for location l6
Found invariant X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₂ ≤ X₁ for location l7
Found invariant 2 ≤ X₉ ∧ 4 ≤ X₀+X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀ for location l5
Found invariant X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ for location l1
Found invariant X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₂ ≤ X₁ for location l4
Found invariant X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₇, X₈, X₉
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₈: l0(X₀, X₁, X₂, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₇, X₈, X₉)
t₁₉: l1(X₀, X₁, X₂, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂
t₂₀: l1(X₀, X₁, X₂, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₂ < X₁ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂
t₂₁: l2(X₀, X₁, X₂, X₇, X₈, X₉) → l1(X₉, X₈, X₇, X₇, X₈, X₉)
t₂₂: l3(X₀, X₁, X₂, X₇, X₈, X₉) → l5(X₀, X₁, X₂, X₇, X₈, X₉) :|: 1 < X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂
t₂₃: l3(X₀, X₁, X₂, X₇, X₈, X₉) → l6(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₀ ≤ 1 ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂
t₂₄: l4(X₀, X₁, X₂, X₇, X₈, X₉) → l7(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₂ ≤ X₁
t₂₅: l5(X₀, X₁, X₂, X₇, X₈, X₉) → l1(X₀-1, X₁, X₂+X₀-1, X₇, X₈, X₉) :|: 2 ≤ X₉ ∧ 4 ≤ X₀+X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀
t₂₆: l6(X₀, X₁, X₂, X₇, X₈, X₉) → l1(X₀, X₁+1, X₂, X₇, X₈, X₉) :|: X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1
MPRF for transition t₂₂: l3(X₀, X₁, X₂, X₇, X₈, X₉) → l5(X₀, X₁, X₂, X₇, X₈, X₉) :|: 1 < X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₉+1 {O(n)}
MPRF:
l3 [X₀-1 ]
l5 [X₀-2 ]
l6 [X₀-1 ]
l1 [X₀-1 ]
MPRF for transition t₂₅: l5(X₀, X₁, X₂, X₇, X₈, X₉) → l1(X₀-1, X₁, X₂+X₀-1, X₇, X₈, X₉) :|: 2 ≤ X₉ ∧ 4 ≤ X₀+X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₉+1 {O(n)}
MPRF:
l3 [X₀-1 ]
l5 [X₀-1 ]
l6 [X₀-1 ]
l1 [X₀-1 ]
MPRF for transition t₁₉: l1(X₀, X₁, X₂, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ of depth 1:
new bound:
X₉⋅X₉⋅X₉+4⋅X₉⋅X₉+X₇⋅X₉+X₈⋅X₉+2⋅X₇+2⋅X₈+3⋅X₉+1 {O(n^3)}
MPRF:
l3 [X₂-X₁ ]
l5 [X₀+X₂-X₈ ]
l6 [X₂-X₁ ]
l1 [X₂+1-X₁ ]
MPRF for transition t₂₃: l3(X₀, X₁, X₂, X₇, X₈, X₉) → l6(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₀ ≤ 1 ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ of depth 1:
new bound:
X₉⋅X₉⋅X₉+4⋅X₉⋅X₉+X₇⋅X₉+X₈⋅X₉+2⋅X₇+2⋅X₈+3⋅X₉+1 {O(n^3)}
MPRF:
l3 [X₂+1-X₁ ]
l5 [X₀+X₂-X₈ ]
l6 [X₂-X₁ ]
l1 [X₂+1-X₁ ]
MPRF for transition t₂₆: l6(X₀, X₁, X₂, X₇, X₈, X₉) → l1(X₀, X₁+1, X₂, X₇, X₈, X₉) :|: X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1 of depth 1:
new bound:
X₉⋅X₉⋅X₉+4⋅X₉⋅X₉+X₇⋅X₉+X₈⋅X₉+2⋅X₇+2⋅X₈+3⋅X₉+1 {O(n^3)}
MPRF:
l3 [X₂+1-X₁ ]
l5 [X₀+X₂-X₈ ]
l6 [X₂+1-X₁ ]
l1 [X₂+1-X₁ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₈₀: n_l1___1→l4
Cut unsatisfiable transition t₈₃: n_l3___5→l5
Found invariant X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ 1+X₂ ∧ X₀ ≤ 1 for location n_l1___6
Found invariant 2 ≤ X₉ ∧ 3 ≤ X₀+X₉ ∧ 1+X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ 1+X₇ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l6___2
Found invariant X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1 for location n_l6___4
Found invariant 2 ≤ X₉ ∧ 3 ≤ X₀+X₉ ∧ 1+X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ 1+X₇ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀ for location n_l3___3
Found invariant X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1 for location n_l3___5
Found invariant X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₂ ≤ X₁ for location l7
Found invariant X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₇ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂ ∧ X₂ ≤ X₇ ∧ X₁ ≤ X₇ ∧ X₁ ≤ X₂ for location n_l3___8
Found invariant 2 ≤ X₉ ∧ 4 ≤ X₀+X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀ for location l5
Found invariant X₉ ≤ 1 ∧ X₉ ≤ X₀ ∧ X₀+X₉ ≤ 2 ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₇ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂ ∧ X₂ ≤ X₇ ∧ X₁ ≤ X₇ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1 for location n_l6___7
Found invariant X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂ for location l1
Found invariant X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₂ ≤ X₁ for location l4
Found invariant 2 ≤ X₉ ∧ 3 ≤ X₀+X₉ ∧ 1+X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₁ ≤ 1+X₈ ∧ 1+X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___1
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₆₆: l1(X₀, X₁, X₂, X₇, X₈, X₉) → n_l3___8(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₇ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₉ ∧ X₀ ≤ X₉ ∧ X₉ ≤ X₀ ∧ X₂ ≤ X₇ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₈ ∧ X₈ ≤ X₁ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂
knowledge_propagation leads to new time bound X₉+1 {O(n)} for transition t₆₈: l1(X₀, X₁, X₂, X₇, X₈, X₉) → n_l3___3(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₁ ≤ X₂ ∧ X₇ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₉ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₀+X₇ ≤ X₂ ∧ X₀+X₁ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂
knowledge_propagation leads to new time bound X₉+1 {O(n)} for transition t₈₂: n_l3___3(X₀, X₁, X₂, X₇, X₈, X₉) → l5(X₀, X₁, X₂, X₇, X₈, X₉) :|: 1 < X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₉ ∧ 3 ≤ X₀+X₉ ∧ 1+X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ 1+X₇ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₈₄: n_l3___8(X₀, X₁, X₂, X₇, X₈, X₉) → l5(X₀, X₁, X₂, X₇, X₈, X₉) :|: 1 < X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₇ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂ ∧ X₂ ≤ X₇ ∧ X₁ ≤ X₇ ∧ X₁ ≤ X₂
MPRF for transition t₆₇: n_l1___6(X₀, X₁, X₂, X₇, X₈, X₉) → n_l3___5(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₀ ≤ 1 ∧ X₇ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₉ ∧ X₇ ≤ X₂ ∧ X₀ ≤ X₉ ∧ 1+X₈ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ X₀ ≤ 1 ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ 1+X₂ ∧ X₀ ≤ 1 of depth 1:
new bound:
2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+3 {O(n^2)}
MPRF:
n_l3___5 [X₂-X₁ ]
n_l6___4 [X₂-X₁ ]
n_l1___6 [X₂+1-X₁ ]
MPRF for transition t₇₀: n_l3___5(X₀, X₁, X₂, X₇, X₈, X₉) → n_l6___4(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₀ ≤ 1 ∧ X₇ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₁ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ 1 ∧ X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1 of depth 1:
new bound:
2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+4 {O(n^2)}
MPRF:
n_l3___5 [X₂+1-X₁ ]
n_l6___4 [X₂-X₁ ]
n_l1___6 [X₂+1-X₁ ]
MPRF for transition t₇₃: n_l6___4(X₀, X₁, X₂, X₇, X₈, X₉) → n_l1___6(X₀, X₁+1, X₂, X₇, X₈, X₉) :|: X₀ ≤ 1 ∧ X₇ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₁ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ 1 ∧ X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1 of depth 1:
new bound:
2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+4 {O(n^2)}
MPRF:
n_l3___5 [X₂+1-X₁ ]
n_l6___4 [X₂+1-X₁ ]
n_l1___6 [X₂+1-X₁ ]
CFR: Improvement to new bound with the following program:
new bound:
6⋅X₉⋅X₉+15⋅X₉+6⋅X₇+6⋅X₈+16 {O(n^2)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₇, X₈, X₉
Temp_Vars:
Locations: l0, l1, l2, l4, l5, l7, n_l1___1, n_l1___6, n_l3___3, n_l3___5, n_l3___8, n_l6___2, n_l6___4, n_l6___7
Transitions:
t₁₈: l0(X₀, X₁, X₂, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₇, X₈, X₉)
t₂₀: l1(X₀, X₁, X₂, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₂ < X₁ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂
t₆₈: l1(X₀, X₁, X₂, X₇, X₈, X₉) → n_l3___3(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₁ ≤ X₂ ∧ X₇ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₉ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₀+X₇ ≤ X₂ ∧ X₀+X₁ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂
t₆₆: l1(X₀, X₁, X₂, X₇, X₈, X₉) → n_l3___8(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₇ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₉ ∧ X₀ ≤ X₉ ∧ X₉ ≤ X₀ ∧ X₂ ≤ X₇ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₈ ∧ X₈ ≤ X₁ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂
t₂₁: l2(X₀, X₁, X₂, X₇, X₈, X₉) → l1(X₉, X₈, X₇, X₇, X₈, X₉)
t₂₄: l4(X₀, X₁, X₂, X₇, X₈, X₉) → l7(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₂ ≤ X₁
t₂₅: l5(X₀, X₁, X₂, X₇, X₈, X₉) → l1(X₀-1, X₁, X₂+X₀-1, X₇, X₈, X₉) :|: 2 ≤ X₉ ∧ 4 ≤ X₀+X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₉ ∧ 4 ≤ X₀+X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀
t₆₅: n_l1___1(X₀, X₁, X₂, X₇, X₈, X₉) → n_l3___5(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₀ ≤ 1 ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₇ ≤ X₂ ∧ X₀ ≤ X₉ ∧ 1+X₈ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ X₀ ≤ 1 ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ 2 ≤ X₉ ∧ 3 ≤ X₀+X₉ ∧ 1+X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₁ ≤ 1+X₈ ∧ 1+X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₈₁: n_l1___6(X₀, X₁, X₂, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₂ < X₁ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ 1+X₂ ∧ X₀ ≤ 1
t₆₇: n_l1___6(X₀, X₁, X₂, X₇, X₈, X₉) → n_l3___5(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₀ ≤ 1 ∧ X₇ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₉ ∧ X₇ ≤ X₂ ∧ X₀ ≤ X₉ ∧ 1+X₈ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ X₀ ≤ 1 ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ 1+X₂ ∧ X₀ ≤ 1
t₈₂: n_l3___3(X₀, X₁, X₂, X₇, X₈, X₉) → l5(X₀, X₁, X₂, X₇, X₈, X₉) :|: 1 < X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₉ ∧ 3 ≤ X₀+X₉ ∧ 1+X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ 1+X₇ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀
t₆₉: n_l3___3(X₀, X₁, X₂, X₇, X₈, X₉) → n_l6___2(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₀+X₇ ≤ X₂ ∧ 1+X₀ ≤ X₉ ∧ X₀+X₁ ≤ X₂ ∧ X₈ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ 1 ∧ 2 ≤ X₉ ∧ 3 ≤ X₀+X₉ ∧ 1+X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ 1+X₇ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀
t₇₀: n_l3___5(X₀, X₁, X₂, X₇, X₈, X₉) → n_l6___4(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₀ ≤ 1 ∧ X₇ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₁ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ 1 ∧ X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1
t₈₄: n_l3___8(X₀, X₁, X₂, X₇, X₈, X₉) → l5(X₀, X₁, X₂, X₇, X₈, X₉) :|: 1 < X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₇ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂ ∧ X₂ ≤ X₇ ∧ X₁ ≤ X₇ ∧ X₁ ≤ X₂
t₇₁: n_l3___8(X₀, X₁, X₂, X₇, X₈, X₉) → n_l6___7(X₀, X₁, X₂, X₇, X₈, X₉) :|: X₁ ≤ X₇ ∧ X₂ ≤ X₇ ∧ X₇ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₉ ≤ X₀ ∧ X₁ ≤ X₈ ∧ X₈ ≤ X₁ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ 1 ∧ X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₇ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂ ∧ X₂ ≤ X₇ ∧ X₁ ≤ X₇ ∧ X₁ ≤ X₂
t₇₂: n_l6___2(X₀, X₁, X₂, X₇, X₈, X₉) → n_l1___1(X₀, X₁+1, X₂, X₇, X₈, X₉) :|: 1+X₇ ≤ X₂ ∧ 2 ≤ X₉ ∧ 1+X₁ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ 1 ∧ 2 ≤ X₉ ∧ 3 ≤ X₀+X₉ ∧ 1+X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ 1+X₇ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₇₃: n_l6___4(X₀, X₁, X₂, X₇, X₈, X₉) → n_l1___6(X₀, X₁+1, X₂, X₇, X₈, X₉) :|: X₀ ≤ 1 ∧ X₇ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₁ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ 1 ∧ X₀ ≤ X₉ ∧ 1+X₈ ≤ X₂ ∧ 1+X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1
t₇₄: n_l6___7(X₀, X₁, X₂, X₇, X₈, X₉) → n_l1___6(X₀, X₁+1, X₂, X₇, X₈, X₉) :|: X₀ ≤ 1 ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₈ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₉ ∧ X₉ ≤ X₀ ∧ X₂ ≤ X₇ ∧ X₇ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₉ ∧ X₀ ≤ 1 ∧ X₉ ≤ 1 ∧ X₉ ≤ X₀ ∧ X₀+X₉ ≤ 2 ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₇ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₈ ∧ X₇ ≤ X₂ ∧ X₂ ≤ X₇ ∧ X₁ ≤ X₇ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1
All Bounds
Timebounds
Overall timebound:6⋅X₉⋅X₉+15⋅X₉+6⋅X₇+6⋅X₈+26 {O(n^2)}
t₁₈: 1 {O(1)}
t₂₀: 1 {O(1)}
t₆₆: 1 {O(1)}
t₆₈: X₉+1 {O(n)}
t₂₁: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: X₉+1 {O(n)}
t₆₅: 1 {O(1)}
t₆₇: 2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+3 {O(n^2)}
t₈₁: 1 {O(1)}
t₆₉: 1 {O(1)}
t₈₂: X₉+1 {O(n)}
t₇₀: 2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+4 {O(n^2)}
t₇₁: 1 {O(1)}
t₈₄: 1 {O(1)}
t₇₂: 1 {O(1)}
t₇₃: 2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+4 {O(n^2)}
t₇₄: 1 {O(1)}
Costbounds
Overall costbound: 6⋅X₉⋅X₉+15⋅X₉+6⋅X₇+6⋅X₈+26 {O(n^2)}
t₁₈: 1 {O(1)}
t₂₀: 1 {O(1)}
t₆₆: 1 {O(1)}
t₆₈: X₉+1 {O(n)}
t₂₁: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: X₉+1 {O(n)}
t₆₅: 1 {O(1)}
t₆₇: 2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+3 {O(n^2)}
t₈₁: 1 {O(1)}
t₆₉: 1 {O(1)}
t₈₂: X₉+1 {O(n)}
t₇₀: 2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+4 {O(n^2)}
t₇₁: 1 {O(1)}
t₈₄: 1 {O(1)}
t₇₂: 1 {O(1)}
t₇₃: 2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+4 {O(n^2)}
t₇₄: 1 {O(1)}
Sizebounds
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₇: X₇ {O(n)}
t₁₈, X₈: X₈ {O(n)}
t₁₈, X₉: X₉ {O(n)}
t₂₀, X₀: X₉ {O(n)}
t₂₀, X₁: X₈ {O(n)}
t₂₀, X₂: X₇ {O(n)}
t₂₀, X₇: X₇ {O(n)}
t₂₀, X₈: X₈ {O(n)}
t₂₀, X₉: X₉ {O(n)}
t₆₆, X₀: X₉ {O(n)}
t₆₆, X₁: X₈ {O(n)}
t₆₆, X₂: X₇ {O(n)}
t₆₆, X₇: X₇ {O(n)}
t₆₆, X₈: X₈ {O(n)}
t₆₆, X₉: X₉ {O(n)}
t₆₈, X₀: X₉ {O(n)}
t₆₈, X₁: X₈ {O(n)}
t₆₈, X₂: 2⋅X₉⋅X₉+4⋅X₉+X₇ {O(n^2)}
t₆₈, X₇: X₇ {O(n)}
t₆₈, X₈: X₈ {O(n)}
t₆₈, X₉: X₉ {O(n)}
t₂₁, X₀: X₉ {O(n)}
t₂₁, X₁: X₈ {O(n)}
t₂₁, X₂: X₇ {O(n)}
t₂₁, X₇: X₇ {O(n)}
t₂₁, X₈: X₈ {O(n)}
t₂₁, X₉: X₉ {O(n)}
t₂₄, X₀: 2⋅X₉ {O(n)}
t₂₄, X₁: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₉+6⋅X₈+7 {O(n^2)}
t₂₄, X₂: X₉⋅X₉+2⋅X₇+2⋅X₉ {O(n^2)}
t₂₄, X₇: 4⋅X₇ {O(n)}
t₂₄, X₈: 4⋅X₈ {O(n)}
t₂₄, X₉: 4⋅X₉ {O(n)}
t₂₅, X₀: X₉ {O(n)}
t₂₅, X₁: X₈ {O(n)}
t₂₅, X₂: X₉⋅X₉+2⋅X₉+X₇ {O(n^2)}
t₂₅, X₇: X₇ {O(n)}
t₂₅, X₈: X₈ {O(n)}
t₂₅, X₉: X₉ {O(n)}
t₆₅, X₀: 1 {O(1)}
t₆₅, X₁: X₈+1 {O(n)}
t₆₅, X₂: 2⋅X₉⋅X₉+4⋅X₉+X₇ {O(n^2)}
t₆₅, X₇: X₇ {O(n)}
t₆₅, X₈: X₈ {O(n)}
t₆₅, X₉: X₉ {O(n)}
t₆₇, X₀: X₉+1 {O(n)}
t₆₇, X₁: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₈+4⋅X₉+6 {O(n^2)}
t₆₇, X₂: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₉ {O(n^2)}
t₆₇, X₇: 2⋅X₇ {O(n)}
t₆₇, X₈: 2⋅X₈ {O(n)}
t₆₇, X₉: 2⋅X₉ {O(n)}
t₈₁, X₀: 2⋅X₉+1 {O(n)}
t₈₁, X₁: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₉+5⋅X₈+7 {O(n^2)}
t₈₁, X₂: 2⋅X₉⋅X₉+3⋅X₇+4⋅X₉ {O(n^2)}
t₈₁, X₇: 3⋅X₇ {O(n)}
t₈₁, X₈: 3⋅X₈ {O(n)}
t₈₁, X₉: 3⋅X₉ {O(n)}
t₆₉, X₀: 1 {O(1)}
t₆₉, X₁: X₈ {O(n)}
t₆₉, X₂: 2⋅X₉⋅X₉+4⋅X₉+X₇ {O(n^2)}
t₆₉, X₇: X₇ {O(n)}
t₆₉, X₈: X₈ {O(n)}
t₆₉, X₉: X₉ {O(n)}
t₈₂, X₀: X₉ {O(n)}
t₈₂, X₁: X₈ {O(n)}
t₈₂, X₂: 2⋅X₉⋅X₉+4⋅X₉+X₇ {O(n^2)}
t₈₂, X₇: X₇ {O(n)}
t₈₂, X₈: X₈ {O(n)}
t₈₂, X₉: X₉ {O(n)}
t₇₀, X₀: X₉+1 {O(n)}
t₇₀, X₁: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₈+4⋅X₉+6 {O(n^2)}
t₇₀, X₂: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₉ {O(n^2)}
t₇₀, X₇: 2⋅X₇ {O(n)}
t₇₀, X₈: 2⋅X₈ {O(n)}
t₇₀, X₉: 2⋅X₉ {O(n)}
t₇₁, X₀: X₉ {O(n)}
t₇₁, X₁: X₈ {O(n)}
t₇₁, X₂: X₇ {O(n)}
t₇₁, X₇: X₇ {O(n)}
t₇₁, X₈: X₈ {O(n)}
t₇₁, X₉: X₉ {O(n)}
t₈₄, X₀: X₉ {O(n)}
t₈₄, X₁: X₈ {O(n)}
t₈₄, X₂: X₇ {O(n)}
t₈₄, X₇: X₇ {O(n)}
t₈₄, X₈: X₈ {O(n)}
t₈₄, X₉: X₉ {O(n)}
t₇₂, X₀: 1 {O(1)}
t₇₂, X₁: X₈+1 {O(n)}
t₇₂, X₂: 2⋅X₉⋅X₉+4⋅X₉+X₇ {O(n^2)}
t₇₂, X₇: X₇ {O(n)}
t₇₂, X₈: X₈ {O(n)}
t₇₂, X₉: X₉ {O(n)}
t₇₃, X₀: X₉+1 {O(n)}
t₇₃, X₁: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₈+4⋅X₉+6 {O(n^2)}
t₇₃, X₂: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₉ {O(n^2)}
t₇₃, X₇: 2⋅X₇ {O(n)}
t₇₃, X₈: 2⋅X₈ {O(n)}
t₇₃, X₉: 2⋅X₉ {O(n)}
t₇₄, X₀: X₉ {O(n)}
t₇₄, X₁: X₈+1 {O(n)}
t₇₄, X₂: X₇ {O(n)}
t₇₄, X₇: X₇ {O(n)}
t₇₄, X₈: X₈ {O(n)}
t₇₄, X₉: X₉ {O(n)}