Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₂-1, X₁, X₂, X₁, X₄) :|: X₂ < 1
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₂-1, X₁, X₂, X₁, X₄) :|: 1 < X₂
t₉: l2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₁, X₃, X₁) :|: 0 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 0
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 0 ≤ X₄
t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀
t₁₀: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄-X₀) :|: X₃ ≤ 0 ∧ 0 ≤ X₃
t₁₄: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: X₃ < 0
t₁₅: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: 0 < X₃
t₁₂: l8(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃-X₀, X₄)
Preprocessing
Found invariant X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l6
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l5
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l8
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l4
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₂-1, X₁, X₂, X₁, X₄) :|: X₂ < 1 ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₂-1, X₁, X₂, X₁, X₄) :|: 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₉: l2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₁, X₃, X₁) :|: 0 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 0 ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₀ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₀: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄-X₀) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₄: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: X₃ < 0 ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₅: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: 0 < X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₂: l8(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃-X₀, X₄) :|: X₄ ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
MPRF for transition t₅: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₂-1, X₁, X₂, X₁, X₄) :|: 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l6 [X₀-1 ]
l1 [X₂-1 ]
l8 [X₂-2 ]
l5 [X₂-2 ]
MPRF for transition t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄-X₀) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l6 [X₀ ]
l1 [X₂-1 ]
l8 [X₀ ]
l5 [X₀ ]
MPRF for transition t₁₅: l6(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₀, X₃, X₄) :|: 0 < X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
l6 [X₀-1 ]
l1 [X₂-2 ]
l8 [2⋅X₀-X₂ ]
l5 [2⋅X₀-X₂ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₃₉₉: l1→n_l5___10
Cut unsatisfiable transition t₄₃₃: n_l1___3→l4
Cut unreachable locations [n_l5___10; n_l5___7; n_l8___5; n_l8___8] from the program graph
Found invariant X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l6___6
Found invariant X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___1
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l8___2
Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___9
Found invariant 1+X₄ ≤ X₁ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___4
Found invariant X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l1___3
Found invariant X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l4
MPRF for transition t₄₀₁: n_l1___3(X₀, X₁, X₂, X₃, X₄) → n_l5___9(X₂-1, X₁, X₂, X₁, X₄) :|: X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 < X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
n_l5___9 [X₂+1 ]
n_l1___3 [X₀+2 ]
n_l6___6 [X₂+1 ]
n_l1___4 [X₂+1 ]
n_l8___2 [X₀+2 ]
n_l5___1 [2⋅X₂-X₀ ]
MPRF for transition t₄₀₂: n_l1___4(X₀, X₁, X₂, X₃, X₄) → n_l5___9(X₂-1, X₁, X₂, X₁, X₄) :|: X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 < X₁ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀+X₄ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 < X₂ ∧ 1+X₄ ≤ X₁ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
n_l5___9 [X₀-1 ]
n_l1___3 [X₀-1 ]
n_l6___6 [X₀-1 ]
n_l1___4 [X₀-1 ]
n_l8___2 [X₀-1 ]
n_l5___1 [X₀-1 ]
MPRF for transition t₄₀₃: n_l5___1(X₀, X₁, X₂, X₃, X₄) → n_l6___6(X₀, X₁, X₀+1, X₃, X₄) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 < X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₃ < X₀ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
n_l5___9 [X₂-1 ]
n_l1___3 [X₂-1 ]
n_l6___6 [X₀-1 ]
n_l1___4 [X₂-1 ]
n_l8___2 [X₂-1 ]
n_l5___1 [X₂-1 ]
MPRF for transition t₄₀₈: n_l5___9(X₀, X₁, X₂, X₃, X₄) → n_l8___2(X₀, X₁, X₀+1, X₃, X₄) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 < X₀ ∧ 0 < X₃ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
n_l5___9 [X₀ ]
n_l1___3 [X₀-1 ]
n_l6___6 [X₀-1 ]
n_l1___4 [X₀-1 ]
n_l8___2 [X₂-2 ]
n_l5___1 [X₀-1 ]
MPRF for transition t₄₀₉: n_l6___6(X₀, X₁, X₂, X₃, X₄) → n_l1___3(X₀, X₁, X₀, X₃, X₄) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 < X₃ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
n_l5___9 [X₂-1 ]
n_l1___3 [X₀-1 ]
n_l6___6 [X₀ ]
n_l1___4 [X₀-1 ]
n_l8___2 [X₂-1 ]
n_l5___1 [X₂-1 ]
MPRF for transition t₄₁₀: n_l6___6(X₀, X₁, X₂, X₃, X₄) → n_l1___4(X₀, X₁, X₀, 0, X₄-X₀) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
n_l5___9 [X₂-1 ]
n_l1___3 [X₀-1 ]
n_l6___6 [X₀ ]
n_l1___4 [X₀-1 ]
n_l8___2 [X₀ ]
n_l5___1 [X₀ ]
Found invariant X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l6___6
Found invariant X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___1
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l8___2
Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___9
Found invariant 1+X₄ ≤ X₁ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___4
Found invariant X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l1___3
Found invariant X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l4
Found invariant X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l6___6
Found invariant X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___1
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l8___2
Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___9
Found invariant 1+X₄ ≤ X₁ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___4
Found invariant X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l1___3
Found invariant X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l4
MPRF for transition t₄₀₄: n_l5___1(X₀, X₁, X₂, X₃, X₄) → n_l8___2(X₀, X₁, X₀+1, X₃, X₄) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 < X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₁⋅X₁+3⋅X₁ {O(n^2)}
MPRF:
n_l1___3 [X₁ ]
n_l1___4 [X₁ ]
n_l6___6 [0 ]
n_l5___9 [X₃ ]
n_l8___2 [X₃ ]
n_l5___1 [X₃+1 ]
MPRF for transition t₄₁₁: n_l8___2(X₀, X₁, X₂, X₃, X₄) → n_l5___1(X₀, X₁, X₀+1, X₃-X₀, X₄) :|: X₄ ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ X₂ ≤ X₁ ∧ 1 < X₂ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
5⋅X₁⋅X₁+7⋅X₁ {O(n^2)}
MPRF:
n_l1___3 [X₀+2⋅X₁ ]
n_l1___4 [2⋅X₁ ]
n_l6___6 [X₀+X₁+X₃-1 ]
n_l5___9 [X₁+X₃ ]
n_l8___2 [X₁+X₃ ]
n_l5___1 [X₀+X₁+X₃-1 ]
CFR: Improvement to new bound with the following program:
new bound:
7⋅X₁⋅X₁+16⋅X₁+5 {O(n^2)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l7, n_l1___3, n_l1___4, n_l5___1, n_l5___9, n_l6___6, n_l8___2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₄₀₀: l1(X₀, X₁, X₂, X₃, X₄) → n_l5___9(X₂-1, X₁, X₂, X₁, X₄) :|: X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 < X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₉: l2(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₁, X₃, X₁) :|: 0 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 0 ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₄₀₁: n_l1___3(X₀, X₁, X₂, X₃, X₄) → n_l5___9(X₂-1, X₁, X₂, X₁, X₄) :|: X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 < X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₄₃₄: n_l1___4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₀₂: n_l1___4(X₀, X₁, X₂, X₃, X₄) → n_l5___9(X₂-1, X₁, X₂, X₁, X₄) :|: X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 < X₁ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀+X₄ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 < X₂ ∧ 1+X₄ ≤ X₁ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₀₃: n_l5___1(X₀, X₁, X₂, X₃, X₄) → n_l6___6(X₀, X₁, X₀+1, X₃, X₄) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 < X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₃ < X₀ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₀₄: n_l5___1(X₀, X₁, X₂, X₃, X₄) → n_l8___2(X₀, X₁, X₀+1, X₃, X₄) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 < X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₀₈: n_l5___9(X₀, X₁, X₂, X₃, X₄) → n_l8___2(X₀, X₁, X₀+1, X₃, X₄) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 < X₀ ∧ 0 < X₃ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₀₉: n_l6___6(X₀, X₁, X₂, X₃, X₄) → n_l1___3(X₀, X₁, X₀, X₃, X₄) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 < X₃ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₁₀: n_l6___6(X₀, X₁, X₂, X₃, X₄) → n_l1___4(X₀, X₁, X₀, 0, X₄-X₀) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₃ < X₀ ∧ 0 ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₁₁: n_l8___2(X₀, X₁, X₂, X₃, X₄) → n_l5___1(X₀, X₁, X₀+1, X₃-X₀, X₄) :|: X₄ ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ X₂ ≤ X₁ ∧ 1 < X₂ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:7⋅X₁⋅X₁+16⋅X₁+15 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄₀₀: 1 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₄₀₁: X₁+1 {O(n)}
t₄₀₂: X₁+1 {O(n)}
t₄₃₄: 1 {O(1)}
t₄₀₃: X₁+1 {O(n)}
t₄₀₄: 2⋅X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₀₈: X₁ {O(n)}
t₄₀₉: X₁+1 {O(n)}
t₄₁₀: X₁+1 {O(n)}
t₄₁₁: 5⋅X₁⋅X₁+7⋅X₁ {O(n^2)}
Costbounds
Overall costbound: 7⋅X₁⋅X₁+16⋅X₁+15 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄₀₀: 1 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₄₀₁: X₁+1 {O(n)}
t₄₀₂: X₁+1 {O(n)}
t₄₃₄: 1 {O(1)}
t₄₀₃: X₁+1 {O(n)}
t₄₀₄: 2⋅X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₀₈: X₁ {O(n)}
t₄₀₉: X₁+1 {O(n)}
t₄₁₀: X₁+1 {O(n)}
t₄₁₁: 5⋅X₁⋅X₁+7⋅X₁ {O(n^2)}
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)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: 1 {O(1)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₁ {O(n)}
t₄₀₀, X₀: X₁ {O(n)}
t₄₀₀, X₁: X₁ {O(n)}
t₄₀₀, X₂: X₁ {O(n)}
t₄₀₀, X₃: X₁ {O(n)}
t₄₀₀, X₄: X₁ {O(n)}
t₉, X₀: 2⋅X₀+3 {O(n)}
t₉, X₁: 5⋅X₁ {O(n)}
t₉, X₂: X₂+3 {O(n)}
t₉, X₃: 2⋅X₃ {O(n)}
t₉, X₄: 2⋅X₁⋅X₁+7⋅X₁+X₄ {O(n^2)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₁ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₁ {O(n)}
t₆, X₀: 1 {O(1)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 1 {O(1)}
t₆, X₃: 0 {O(1)}
t₆, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₇, X₀: X₀+1 {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}
t₇, X₂: 1 {O(1)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₁⋅X₁+4⋅X₁ {O(n^2)}
t₈, X₀: 1 {O(1)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 1 {O(1)}
t₈, X₃: 0 {O(1)}
t₈, X₄: 0 {O(1)}
t₄₀₁, X₀: X₁ {O(n)}
t₄₀₁, X₁: X₁ {O(n)}
t₄₀₁, X₂: X₁ {O(n)}
t₄₀₁, X₃: X₁ {O(n)}
t₄₀₁, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₀₂, X₀: X₁ {O(n)}
t₄₀₂, X₁: X₁ {O(n)}
t₄₀₂, X₂: X₁ {O(n)}
t₄₀₂, X₃: X₁ {O(n)}
t₄₀₂, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₃₄, X₀: 1 {O(1)}
t₄₃₄, X₁: X₁ {O(n)}
t₄₃₄, X₂: 1 {O(1)}
t₄₃₄, X₃: 0 {O(1)}
t₄₃₄, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₀₃, X₀: X₁ {O(n)}
t₄₀₃, X₁: X₁ {O(n)}
t₄₀₃, X₂: X₁+1 {O(n)}
t₄₀₃, X₃: 3⋅X₁ {O(n)}
t₄₀₃, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₀₄, X₀: X₁ {O(n)}
t₄₀₄, X₁: X₁ {O(n)}
t₄₀₄, X₂: X₁+1 {O(n)}
t₄₀₄, X₃: 3⋅X₁ {O(n)}
t₄₀₄, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₀₈, X₀: X₁ {O(n)}
t₄₀₈, X₁: X₁ {O(n)}
t₄₀₈, X₂: 3⋅X₁+3 {O(n)}
t₄₀₈, X₃: 3⋅X₁ {O(n)}
t₄₀₈, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₀₉, X₀: X₁ {O(n)}
t₄₀₉, X₁: X₁ {O(n)}
t₄₀₉, X₂: X₁ {O(n)}
t₄₀₉, X₃: 3⋅X₁ {O(n)}
t₄₀₉, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₁₀, X₀: X₁ {O(n)}
t₄₁₀, X₁: X₁ {O(n)}
t₄₁₀, X₂: X₁ {O(n)}
t₄₁₀, X₃: 0 {O(1)}
t₄₁₀, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₄₁₁, X₀: X₁ {O(n)}
t₄₁₁, X₁: X₁ {O(n)}
t₄₁₁, X₂: 2⋅X₁+2 {O(n)}
t₄₁₁, X₃: 3⋅X₁ {O(n)}
t₄₁₁, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}