Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: X₂ < 1
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: 1 < X₂
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ < 0
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₅
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 0 ∧ 0 ≤ X₅
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₁, X₃, X₁, X₅) :|: 1 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, nondef.0) :|: X₁ ≤ 1
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₀
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₃
t₁₁: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: X₃ < 0
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: 0 < X₃
t₁₃: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄-X₀, X₅) :|: X₃ ≤ 0 ∧ 0 ≤ X₃
t₁₄: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃-X₀, X₄, X₅)
Preprocessing
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l7
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 l5
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ for location l1
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l4
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: X₂ < 1 ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ < 0
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₅
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 0 ∧ 0 ≤ X₅
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₁, X₃, X₁, X₅) :|: 1 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, nondef.0) :|: X₁ ≤ 1
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₀ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₁: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: X₃ < 0 ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: 0 < X₃ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₁₃: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄-X₀, X₅) :|: 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: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃-X₀, X₄, X₅) :|: 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, X₅) → l4(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l5 [X₀-1 ]
l1 [X₂-1 ]
l7 [X₂-2 ]
l4 [X₂-2 ]
MPRF for transition t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: 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:
l5 [X₂-2 ]
l1 [X₂-2 ]
l7 [2⋅X₀-X₂ ]
l4 [2⋅X₀-X₂ ]
MPRF for transition t₁₃: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄-X₀, X₅) :|: 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:
l5 [X₀ ]
l1 [X₂-1 ]
l7 [X₀ ]
l4 [X₀ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₃: l1→l2
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_l4___3
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_l5___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_l4___5
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l1
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___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_l7___4
MPRF for transition t₁₃₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___5(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 0 < X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
n_l4___5 [X₀-1 ]
n_l1___1 [X₀-1 ]
n_l5___2 [2⋅X₀-X₂ ]
l1 [X₂-1 ]
n_l7___4 [X₀-1 ]
n_l4___3 [X₀-1 ]
MPRF for transition t₁₃₂: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___5(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: X₂ ≤ X₁ ∧ X₄ ≤ 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_l4___5 [X₂-2 ]
n_l1___1 [X₀-1 ]
n_l5___2 [X₂-2 ]
l1 [X₂-1 ]
n_l7___4 [X₀-1 ]
n_l4___3 [X₂-2 ]
MPRF for transition t₁₃₄: n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l5___2(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 < X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ 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_l4___5 [X₀ ]
n_l1___1 [X₀-1 ]
n_l5___2 [X₀-1 ]
l1 [X₂-1 ]
n_l7___4 [X₀ ]
n_l4___3 [X₀ ]
MPRF for transition t₁₃₆: n_l4___5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l7___4(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 < X₃ ∧ 0 < X₀ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ 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+1 {O(n)}
MPRF:
n_l4___5 [X₀ ]
n_l1___1 [X₀-1 ]
n_l5___2 [X₀-1 ]
l1 [X₂-1 ]
n_l7___4 [X₀-1 ]
n_l4___3 [X₀-1 ]
MPRF for transition t₁₃₇: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, X₁, X₀, 0, X₄-X₀, X₅) :|: 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_l4___5 [X₂-1 ]
n_l1___1 [X₀-1 ]
n_l5___2 [X₀ ]
l1 [X₂-1 ]
n_l7___4 [X₂-1 ]
n_l4___3 [X₂-1 ]
MPRF for transition t₁₃₈: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: 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_l4___5 [X₂-1 ]
n_l1___1 [X₂-1 ]
n_l5___2 [X₀ ]
l1 [X₂-1 ]
n_l7___4 [X₂-1 ]
n_l4___3 [X₀ ]
MPRF for transition t₁₃₅: n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l7___4(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 < X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ 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:
l1 [X₁ ]
n_l1___1 [X₁ ]
n_l5___2 [X₃ ]
n_l4___5 [X₃ ]
n_l7___4 [X₃ ]
n_l4___3 [X₃+1 ]
MPRF for transition t₁₃₉: n_l7___4(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___3(X₀, X₁, X₀+1, X₃-X₀, X₄, X₅) :|: 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:
3⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
MPRF:
l1 [X₁+1 ]
n_l1___1 [X₀+X₁ ]
n_l5___2 [X₀+X₃ ]
n_l4___5 [X₃+1 ]
n_l7___4 [X₃+1 ]
n_l4___3 [X₀+X₃ ]
CFR: Improvement to new bound with the following program:
new bound:
5⋅X₁⋅X₁+14⋅X₁+8 {O(n^2)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l6, n_l1___1, n_l4___3, n_l4___5, n_l5___2, n_l7___4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₃₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___5(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 0 < X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 < X₂ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ < 0
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₅
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 0 ∧ 0 ≤ X₅
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₁, X₃, X₁, X₅) :|: 1 < X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, nondef.0) :|: X₁ ≤ 1
t₁₅₉: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, 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
t₁₃₂: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___5(X₂-1, X₁, X₂, X₁, X₄, X₅) :|: X₂ ≤ X₁ ∧ X₄ ≤ 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
t₁₃₄: n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l5___2(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 < X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ 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
t₁₃₅: n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l7___4(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 < X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ 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
t₁₃₆: n_l4___5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l7___4(X₀, X₁, X₀+1, X₃, X₄, X₅) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 < X₃ ∧ 0 < X₀ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ 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
t₁₃₈: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₀, X₃, X₄, X₅) :|: 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
t₁₃₇: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀, X₁, X₀, 0, X₄-X₀, X₅) :|: 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
t₁₃₉: n_l7___4(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___3(X₀, X₁, X₀+1, X₃-X₀, X₄, X₅) :|: 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:5⋅X₁⋅X₁+14⋅X₁+15 {O(n^2)}
t₀: 1 {O(1)}
t₁₃₃: X₁+1 {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₁₃₂: X₁+1 {O(n)}
t₁₅₉: 1 {O(1)}
t₁₃₄: X₁+1 {O(n)}
t₁₃₅: 2⋅X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₃₆: X₁+1 {O(n)}
t₁₃₇: X₁+1 {O(n)}
t₁₃₈: X₁+1 {O(n)}
t₁₃₉: 3⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
Costbounds
Overall costbound: 5⋅X₁⋅X₁+14⋅X₁+15 {O(n^2)}
t₀: 1 {O(1)}
t₁₃₃: X₁+1 {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₁₃₂: X₁+1 {O(n)}
t₁₅₉: 1 {O(1)}
t₁₃₄: X₁+1 {O(n)}
t₁₃₅: 2⋅X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₃₆: X₁+1 {O(n)}
t₁₃₇: X₁+1 {O(n)}
t₁₃₈: X₁+1 {O(n)}
t₁₃₉: 3⋅X₁⋅X₁+5⋅X₁+2 {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)}
t₀, X₅: X₅ {O(n)}
t₁₃₃, X₀: X₁ {O(n)}
t₁₃₃, X₁: X₁ {O(n)}
t₁₃₃, X₂: 2⋅X₁ {O(n)}
t₁₃₃, X₃: 2⋅X₁ {O(n)}
t₁₃₃, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₃₃, X₅: X₅ {O(n)}
t₆, X₀: X₀+1 {O(n)}
t₆, X₁: 2⋅X₁ {O(n)}
t₆, X₂: X₂+1 {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₁⋅X₁+3⋅X₁+X₄ {O(n^2)}
t₇, X₀: X₀+1 {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}
t₇, X₂: X₂+1 {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₁⋅X₁+3⋅X₁+X₄ {O(n^2)}
t₈, X₀: X₀+1 {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: X₂+1 {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₁⋅X₁+3⋅X₁+X₄ {O(n^2)}
t₈, X₅: 0 {O(1)}
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)}
t₂, X₅: X₅ {O(n)}
t₁₃₂, X₀: X₁ {O(n)}
t₁₃₂, X₁: X₁ {O(n)}
t₁₃₂, X₂: X₁ {O(n)}
t₁₃₂, X₃: X₁ {O(n)}
t₁₃₂, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₃₂, X₅: X₅ {O(n)}
t₁₅₉, X₀: 1 {O(1)}
t₁₅₉, X₁: X₁ {O(n)}
t₁₅₉, X₂: 1 {O(1)}
t₁₅₉, X₃: 0 {O(1)}
t₁₅₉, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₅₉, X₅: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₃₄, X₀: X₁ {O(n)}
t₁₃₄, X₁: X₁ {O(n)}
t₁₃₄, X₂: X₁+1 {O(n)}
t₁₃₄, X₃: 3⋅X₁ {O(n)}
t₁₃₄, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₃₄, X₅: X₅ {O(n)}
t₁₃₅, X₀: X₁ {O(n)}
t₁₃₅, X₁: X₁ {O(n)}
t₁₃₅, X₂: X₁+1 {O(n)}
t₁₃₅, X₃: 3⋅X₁ {O(n)}
t₁₃₅, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₃₅, X₅: X₅ {O(n)}
t₁₃₆, X₀: X₁ {O(n)}
t₁₃₆, X₁: X₁ {O(n)}
t₁₃₆, X₂: 2⋅X₁+2 {O(n)}
t₁₃₆, X₃: 3⋅X₁ {O(n)}
t₁₃₆, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₃₆, X₅: X₅ {O(n)}
t₁₃₇, X₀: X₁ {O(n)}
t₁₃₇, X₁: X₁ {O(n)}
t₁₃₇, X₂: X₁ {O(n)}
t₁₃₇, X₃: 0 {O(1)}
t₁₃₇, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₃₇, X₅: X₅ {O(n)}
t₁₃₈, X₀: X₁ {O(n)}
t₁₃₈, X₁: X₁ {O(n)}
t₁₃₈, X₂: X₁ {O(n)}
t₁₃₈, X₃: 3⋅X₁ {O(n)}
t₁₃₈, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₃₈, X₅: X₅ {O(n)}
t₁₃₉, X₀: X₁ {O(n)}
t₁₃₉, X₁: X₁ {O(n)}
t₁₃₉, X₂: 2⋅X₁+2 {O(n)}
t₁₃₉, X₃: 3⋅X₁ {O(n)}
t₁₃₉, X₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₁₃₉, X₅: X₅ {O(n)}