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 ]
Found invariant 1 ≤ 0 for location l6
Found invariant 1 ≤ 0 for location l7
Found invariant 1 ≤ 0 for location l5
Found invariant 1 ≤ 0 for location l1
Found invariant 1 ≤ 0 for location l4
Found invariant 1 ≤ 0 for location l3
Found invariant X₉ ≤ 1 ∧ X₉ ≤ X₀ ∧ X₀+X₉ ≤ 2 ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₇ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₂ ≤ X₇ ∧ X₁ ≤ X₇ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1 for location l6
Found invariant X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ X₂ ≤ X₇ ∧ 1+X₂ ≤ X₁ for location l7
Found invariant X₉ ≤ X₀ ∧ 2 ≤ X₉ ∧ 4 ≤ X₀+X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₇ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₂ ≤ X₇ ∧ X₁ ≤ X₇ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀ for location l5
Found invariant X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₂ ≤ X₇ for location l1
Found invariant X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ X₂ ≤ X₇ ∧ 1+X₂ ≤ X₁ for location l4
Found invariant X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₇ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₂ ∧ X₂ ≤ X₇ ∧ X₁ ≤ X₇ ∧ X₁ ≤ X₂ for location l3
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 t₁₀₄: n_l1___1→l4
Cut unsatisfiable transition t₁₀₇: 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 t₉₀: 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 t₉₂: 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 t₁₀₆: 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 t₁₀₈: 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 t₉₁: 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+5 {O(n^2)}
MPRF:
n_l3___5 [X₂+1-X₁ ]
n_l6___4 [X₂+1-X₁ ]
n_l1___6 [X₂+2-X₁ ]
MPRF for transition t₉₄: 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 t₉₇: 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+18 {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
t₉₂: 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
t₉₀: 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
t₈₉: 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
t₁₀₅: 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
t₉₁: 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
t₁₀₆: 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
t₉₃: 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
t₉₄: 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
t₁₀₈: 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
t₉₅: 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
t₉₆: 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
t₉₇: 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
t₉₈: 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+28 {O(n^2)}
t₁₈: 1 {O(1)}
t₂₀: 1 {O(1)}
t₉₀: 1 {O(1)}
t₉₂: X₉+1 {O(n)}
t₂₁: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: X₉+1 {O(n)}
t₈₉: 1 {O(1)}
t₉₁: 2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+5 {O(n^2)}
t₁₀₅: 1 {O(1)}
t₉₃: 1 {O(1)}
t₁₀₆: X₉+1 {O(n)}
t₉₄: 2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+4 {O(n^2)}
t₉₅: 1 {O(1)}
t₁₀₈: 1 {O(1)}
t₉₆: 1 {O(1)}
t₉₇: 2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+4 {O(n^2)}
t₉₈: 1 {O(1)}
Costbounds
Overall costbound: 6⋅X₉⋅X₉+15⋅X₉+6⋅X₇+6⋅X₈+28 {O(n^2)}
t₁₈: 1 {O(1)}
t₂₀: 1 {O(1)}
t₉₀: 1 {O(1)}
t₉₂: X₉+1 {O(n)}
t₂₁: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: X₉+1 {O(n)}
t₈₉: 1 {O(1)}
t₉₁: 2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+5 {O(n^2)}
t₁₀₅: 1 {O(1)}
t₉₃: 1 {O(1)}
t₁₀₆: X₉+1 {O(n)}
t₉₄: 2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+4 {O(n^2)}
t₉₅: 1 {O(1)}
t₁₀₈: 1 {O(1)}
t₉₆: 1 {O(1)}
t₉₇: 2⋅X₉⋅X₉+2⋅X₇+2⋅X₈+4⋅X₉+4 {O(n^2)}
t₉₈: 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)}
t₉₀, X₀: X₉ {O(n)}
t₉₀, X₁: X₈ {O(n)}
t₉₀, X₂: X₇ {O(n)}
t₉₀, X₇: X₇ {O(n)}
t₉₀, X₈: X₈ {O(n)}
t₉₀, X₉: X₉ {O(n)}
t₉₂, X₀: X₉ {O(n)}
t₉₂, X₁: X₈ {O(n)}
t₉₂, X₂: 2⋅X₉⋅X₉+4⋅X₉+X₇ {O(n^2)}
t₉₂, X₇: X₇ {O(n)}
t₉₂, X₈: X₈ {O(n)}
t₉₂, 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)}
t₈₉, X₀: 1 {O(1)}
t₈₉, X₁: X₈+1 {O(n)}
t₈₉, X₂: 2⋅X₉⋅X₉+4⋅X₉+X₇ {O(n^2)}
t₈₉, X₇: X₇ {O(n)}
t₈₉, X₈: X₈ {O(n)}
t₈₉, X₉: X₉ {O(n)}
t₉₁, X₀: X₉+1 {O(n)}
t₉₁, X₁: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₈+4⋅X₉+6 {O(n^2)}
t₉₁, X₂: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₉ {O(n^2)}
t₉₁, X₇: 2⋅X₇ {O(n)}
t₉₁, X₈: 2⋅X₈ {O(n)}
t₉₁, X₉: 2⋅X₉ {O(n)}
t₁₀₅, X₀: 2⋅X₉+1 {O(n)}
t₁₀₅, X₁: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₉+5⋅X₈+7 {O(n^2)}
t₁₀₅, X₂: 2⋅X₉⋅X₉+3⋅X₇+4⋅X₉ {O(n^2)}
t₁₀₅, X₇: 3⋅X₇ {O(n)}
t₁₀₅, X₈: 3⋅X₈ {O(n)}
t₁₀₅, X₉: 3⋅X₉ {O(n)}
t₉₃, X₀: 1 {O(1)}
t₉₃, X₁: X₈ {O(n)}
t₉₃, X₂: 2⋅X₉⋅X₉+4⋅X₉+X₇ {O(n^2)}
t₉₃, X₇: X₇ {O(n)}
t₉₃, X₈: X₈ {O(n)}
t₉₃, X₉: X₉ {O(n)}
t₁₀₆, X₀: X₉ {O(n)}
t₁₀₆, X₁: X₈ {O(n)}
t₁₀₆, X₂: 2⋅X₉⋅X₉+4⋅X₉+X₇ {O(n^2)}
t₁₀₆, X₇: X₇ {O(n)}
t₁₀₆, X₈: X₈ {O(n)}
t₁₀₆, X₉: X₉ {O(n)}
t₉₄, X₀: X₉+1 {O(n)}
t₉₄, X₁: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₈+4⋅X₉+6 {O(n^2)}
t₉₄, X₂: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₉ {O(n^2)}
t₉₄, X₇: 2⋅X₇ {O(n)}
t₉₄, X₈: 2⋅X₈ {O(n)}
t₉₄, X₉: 2⋅X₉ {O(n)}
t₉₅, X₀: X₉ {O(n)}
t₉₅, X₁: X₈ {O(n)}
t₉₅, X₂: X₇ {O(n)}
t₉₅, X₇: X₇ {O(n)}
t₉₅, X₈: X₈ {O(n)}
t₉₅, X₉: X₉ {O(n)}
t₁₀₈, X₀: X₉ {O(n)}
t₁₀₈, X₁: X₈ {O(n)}
t₁₀₈, X₂: X₇ {O(n)}
t₁₀₈, X₇: X₇ {O(n)}
t₁₀₈, X₈: X₈ {O(n)}
t₁₀₈, X₉: X₉ {O(n)}
t₉₆, X₀: 1 {O(1)}
t₉₆, X₁: X₈+1 {O(n)}
t₉₆, X₂: 2⋅X₉⋅X₉+4⋅X₉+X₇ {O(n^2)}
t₉₆, X₇: X₇ {O(n)}
t₉₆, X₈: X₈ {O(n)}
t₉₆, X₉: X₉ {O(n)}
t₉₇, X₀: X₉+1 {O(n)}
t₉₇, X₁: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₈+4⋅X₉+6 {O(n^2)}
t₉₇, X₂: 2⋅X₉⋅X₉+2⋅X₇+4⋅X₉ {O(n^2)}
t₉₇, X₇: 2⋅X₇ {O(n)}
t₉₇, X₈: 2⋅X₈ {O(n)}
t₉₇, X₉: 2⋅X₉ {O(n)}
t₉₈, X₀: X₉ {O(n)}
t₉₈, X₁: X₈+1 {O(n)}
t₉₈, X₂: X₇ {O(n)}
t₉₈, X₇: X₇ {O(n)}
t₉₈, X₈: X₈ {O(n)}
t₉₈, X₉: X₉ {O(n)}