Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 0 ∧ X₂ < 0
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 0 ∧ 0 < X₂
t₁₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂ ∧ X₂ < 0
t₁₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂ ∧ 0 < X₂
t₁₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₁-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₁₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₁-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₁₅: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁-1, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
t₁₆: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀-1, X₁-1, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₂
t₁₇: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₁-1, X₁-1, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, nondef.0, X₃, X₄, X₅, X₆)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ < X₅
t₃: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(2⋅X₅, 2⋅X₅, X₂, X₃, X₄, X₅, X₆)
t₁₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₅
t₂: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < 0
Preprocessing
Cut unsatisfiable transition t₁₀: l1→l4
Cut unsatisfiable transition t₁₁: l1→l4
Cut unsatisfiable transition t₁₃: l1→l4
Cut unsatisfiable transition t₁₄: l1→l4
Cut unsatisfiable transition t₁₅: l1→l4
Cut unsatisfiable transition t₁₆: l1→l4
Eliminate variables {X₃,X₄,X₆} that do not contribute to the problem
Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ for location l2
Found invariant 0 ≤ X₅ for location l5
Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ for location l1
Found invariant 0 ≤ X₅ for location l4
Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₃₇: l0(X₀, X₁, X₂, X₅) → l7(X₀, X₁, X₂, X₅)
t₃₈: l1(X₀, X₁, X₂, X₅) → l4(X₀-1, X₁, X₂, X₅) :|: X₂ < 0 ∧ X₂ < 0 ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₃₉: l1(X₀, X₁, X₂, X₅) → l4(X₀-1, X₁, X₂, X₅) :|: 0 < X₂ ∧ 0 < X₂ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₄₀: l1(X₀, X₁, X₂, X₅) → l4(X₁-1, X₁-1, X₂, X₅) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₄₁: l2(X₀, X₁, X₂, X₅) → l3(X₀, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₄₂: l3(X₀, X₁, X₂, X₅) → l1(X₀, X₁, nondef.0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₄₃: l4(X₀, X₁, X₂, X₅) → l2(X₀, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅
t₄₄: l4(X₀, X₁, X₂, X₅) → l6(X₀, X₁, X₂, X₅) :|: X₀ < X₅ ∧ 0 ≤ X₅
t₄₅: l5(X₀, X₁, X₂, X₅) → l4(2⋅X₅, 2⋅X₅, X₂, X₅) :|: 0 ≤ X₅
t₄₆: l6(X₀, X₁, X₂, X₅) → l8(X₀, X₁, X₂, X₅)
t₄₇: l7(X₀, X₁, X₂, X₅) → l5(X₀, X₁, X₂, X₅) :|: 0 ≤ X₅
t₄₈: l7(X₀, X₁, X₂, X₅) → l6(X₀, X₁, X₂, X₅) :|: X₅ < 0
Analysing control-flow refined program
Cut unsatisfiable transition t₄₄: l4→l6
Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ for location n_l2___6
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___9
Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ for location n_l1___4
Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ for location n_l3___5
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___11
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l2___3
Found invariant 0 ≤ X₅ for location l5
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l3___2
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l4
Found invariant X₅ ≤ 1+X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₀+X₅ ∧ 0 ≤ 1+X₀ for location n_l4___8
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___1
Found invariant X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l3___10
Found invariant 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l4___7
MPRF for transition t₄₄₇: n_l1___1(X₀, X₁, X₂, X₅) → n_l4___7(X₁-1, X₁-1, 0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₅+2 {O(n)}
MPRF:
n_l3___2 [X₁+1 ]
n_l1___1 [X₀+1 ]
n_l3___5 [X₁ ]
n_l1___4 [X₁ ]
n_l4___7 [X₀+1 ]
n_l2___3 [X₀+1 ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]
MPRF for transition t₄₄₈: n_l1___1(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₂ < 0 ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₅+2 {O(n)}
MPRF:
n_l3___2 [X₀+1 ]
n_l1___1 [X₀+1 ]
n_l3___5 [X₁ ]
n_l1___4 [X₁ ]
n_l4___7 [X₀+1 ]
n_l2___3 [X₁+1 ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]
MPRF for transition t₄₄₉: n_l1___1(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 < X₂ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₅+2 {O(n)}
MPRF:
n_l3___2 [X₀+1 ]
n_l1___1 [X₀+1 ]
n_l3___5 [X₁ ]
n_l1___4 [X₁ ]
n_l4___7 [X₀+1 ]
n_l2___3 [X₁+1 ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]
MPRF for transition t₄₅₇: n_l2___3(X₀, X₁, X₂, X₅) → n_l3___2(X₀, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₅+2 {O(n)}
MPRF:
n_l3___2 [X₀ ]
n_l1___1 [X₀ ]
n_l3___5 [X₁ ]
n_l1___4 [X₁ ]
n_l4___7 [X₁+1 ]
n_l2___3 [X₁+1 ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]
MPRF for transition t₄₆₀: n_l3___2(X₀, X₁, X₂, X₅) → n_l1___1(X₀, X₁, NoDet0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
6⋅X₅+2 {O(n)}
MPRF:
n_l3___2 [X₁+1 ]
n_l1___1 [X₀ ]
n_l3___5 [X₁ ]
n_l1___4 [X₁ ]
n_l4___7 [X₁+1 ]
n_l2___3 [X₀+1 ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]
MPRF for transition t₄₆₃: n_l4___7(X₀, X₁, X₂, X₅) → n_l2___3(X₀, X₁, X₂, X₅) :|: 0 ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:
new bound:
6⋅X₅+2 {O(n)}
MPRF:
n_l3___2 [X₁ ]
n_l1___1 [X₀ ]
n_l3___5 [X₁ ]
n_l1___4 [X₁ ]
n_l4___7 [X₀+1 ]
n_l2___3 [X₀ ]
n_l4___8 [X₁ ]
n_l2___6 [X₁ ]
MPRF for transition t₄₅₀: n_l1___4(X₀, X₁, X₂, X₅) → n_l4___7(X₁-1, X₁-1, 0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
12⋅X₅+8 {O(n)}
MPRF:
n_l4___7 [1 ]
n_l2___3 [2 ]
n_l3___2 [2 ]
n_l1___1 [2 ]
n_l3___5 [2 ]
n_l1___4 [2 ]
n_l4___8 [2 ]
n_l2___6 [2 ]
MPRF for transition t₄₅₁: n_l1___4(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₂ < 0 ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
120⋅X₅⋅X₅+128⋅X₅+32 {O(n^2)}
MPRF:
n_l4___7 [1 ]
n_l2___3 [X₀+1 ]
n_l3___2 [X₀+1 ]
n_l1___1 [X₀+1 ]
n_l3___5 [X₀+1 ]
n_l1___4 [X₀+1 ]
n_l4___8 [X₀+1 ]
n_l2___6 [X₀+1 ]
MPRF for transition t₄₅₂: n_l1___4(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 < X₂ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
120⋅X₅⋅X₅+128⋅X₅+32 {O(n^2)}
MPRF:
n_l4___7 [1 ]
n_l2___3 [X₀+1 ]
n_l3___2 [X₀+1 ]
n_l1___1 [X₀+1 ]
n_l3___5 [X₀+1 ]
n_l1___4 [X₀+1 ]
n_l4___8 [X₀+1 ]
n_l2___6 [X₀+1 ]
MPRF for transition t₄₅₈: n_l2___6(X₀, X₁, X₂, X₅) → n_l3___5(X₀, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
120⋅X₅⋅X₅+128⋅X₅+34 {O(n^2)}
MPRF:
n_l4___7 [X₁+1-X₀ ]
n_l2___3 [X₀+1 ]
n_l3___2 [X₀+1 ]
n_l1___1 [X₀+1 ]
n_l3___5 [X₀+1 ]
n_l1___4 [X₀+1 ]
n_l4___8 [X₀+2 ]
n_l2___6 [X₀+2 ]
MPRF for transition t₄₆₁: n_l3___5(X₀, X₁, X₂, X₅) → n_l1___4(X₀, X₁, NoDet0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀ of depth 1:
new bound:
120⋅X₅⋅X₅+128⋅X₅+34 {O(n^2)}
MPRF:
n_l4___7 [1 ]
n_l2___3 [X₀+1 ]
n_l3___2 [X₀+1 ]
n_l1___1 [X₁+1 ]
n_l3___5 [X₀+2 ]
n_l1___4 [X₀+1 ]
n_l4___8 [X₀+2 ]
n_l2___6 [X₀+2 ]
MPRF for transition t₄₆₄: n_l4___8(X₀, X₁, X₂, X₅) → n_l2___6(X₀, X₁, X₂, X₅) :|: 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ 1+X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₀+X₅ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
120⋅X₅⋅X₅+128⋅X₅+34 {O(n^2)}
MPRF:
n_l4___7 [1 ]
n_l2___3 [X₀+1 ]
n_l3___2 [X₀+1 ]
n_l1___1 [X₁+1 ]
n_l3___5 [X₀+1 ]
n_l1___4 [X₀+1 ]
n_l4___8 [X₀+2 ]
n_l2___6 [X₀+1 ]
CFR: Improvement to new bound with the following program:
new bound:
600⋅X₅⋅X₅+688⋅X₅+186 {O(n^2)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₅
Temp_Vars: NoDet0
Locations: l0, l4, l5, l6, l7, l8, n_l1___1, n_l1___4, n_l1___9, n_l2___11, n_l2___3, n_l2___6, n_l3___10, n_l3___2, n_l3___5, n_l4___7, n_l4___8
Transitions:
t₃₇: l0(X₀, X₁, X₂, X₅) → l7(X₀, X₁, X₂, X₅)
t₄₆₂: l4(X₀, X₁, X₂, X₅) → n_l2___11(X₀, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₁ ≤ 2⋅X₅ ∧ 2⋅X₅ ≤ X₁ ∧ X₀ ≤ 2⋅X₅ ∧ 2⋅X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₄₅: l5(X₀, X₁, X₂, X₅) → l4(2⋅X₅, 2⋅X₅, X₂, X₅) :|: 0 ≤ X₅ ∧ 0 ≤ X₅
t₄₆: l6(X₀, X₁, X₂, X₅) → l8(X₀, X₁, X₂, X₅)
t₄₇: l7(X₀, X₁, X₂, X₅) → l5(X₀, X₁, X₂, X₅) :|: 0 ≤ X₅
t₄₈: l7(X₀, X₁, X₂, X₅) → l6(X₀, X₁, X₂, X₅) :|: X₅ < 0
t₄₄₇: n_l1___1(X₀, X₁, X₂, X₅) → n_l4___7(X₁-1, X₁-1, 0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄₄₈: n_l1___1(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₂ < 0 ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄₄₉: n_l1___1(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 < X₂ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄₅₀: n_l1___4(X₀, X₁, X₂, X₅) → n_l4___7(X₁-1, X₁-1, 0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₄₅₁: n_l1___4(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₂ < 0 ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₄₅₂: n_l1___4(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 < X₂ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₄₅₃: n_l1___9(X₀, X₁, X₂, X₅) → n_l4___7(X₁-1, X₁-1, 0, X₅) :|: 0 ≤ X₅ ∧ X₀ ≤ 2⋅X₅ ∧ 2⋅X₅ ≤ X₀ ∧ X₁ ≤ 2⋅X₅ ∧ 2⋅X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₄₅₄: n_l1___9(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: 0 ≤ X₅ ∧ X₀ ≤ 2⋅X₅ ∧ 2⋅X₅ ≤ X₀ ∧ X₁ ≤ 2⋅X₅ ∧ 2⋅X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₂ < 0 ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₄₅₅: n_l1___9(X₀, X₁, X₂, X₅) → n_l4___8(X₀-1, X₁, X₂, X₅) :|: 0 ≤ X₅ ∧ X₀ ≤ 2⋅X₅ ∧ 2⋅X₅ ≤ X₀ ∧ X₁ ≤ 2⋅X₅ ∧ 2⋅X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 < X₂ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₄₅₆: n_l2___11(X₀, X₁, X₂, X₅) → n_l3___10(X₀, X₁, X₂, X₅) :|: 0 ≤ X₅ ∧ X₀ ≤ 2⋅X₅ ∧ 2⋅X₅ ≤ X₀ ∧ X₁ ≤ 2⋅X₅ ∧ 2⋅X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₄₅₇: n_l2___3(X₀, X₁, X₂, X₅) → n_l3___2(X₀, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄₅₈: n_l2___6(X₀, X₁, X₂, X₅) → n_l3___5(X₀, X₁, X₂, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₄₅₉: n_l3___10(X₀, X₁, X₂, X₅) → n_l1___9(X₀, X₁, NoDet0, X₅) :|: 0 ≤ X₅ ∧ X₀ ≤ 2⋅X₅ ∧ 2⋅X₅ ≤ X₀ ∧ X₁ ≤ 2⋅X₅ ∧ 2⋅X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₄₆₀: n_l3___2(X₀, X₁, X₂, X₅) → n_l1___1(X₀, X₁, NoDet0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄₆₁: n_l3___5(X₀, X₁, X₂, X₅) → n_l1___4(X₀, X₁, NoDet0, X₅) :|: X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀
t₄₇₆: n_l4___7(X₀, X₁, X₂, X₅) → l6(X₀, X₁, X₂, X₅) :|: X₀ < X₅ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₄₆₃: n_l4___7(X₀, X₁, X₂, X₅) → n_l2___3(X₀, X₁, X₂, X₅) :|: 0 ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₄₇₇: n_l4___8(X₀, X₁, X₂, X₅) → l6(X₀, X₁, X₂, X₅) :|: X₀ < X₅ ∧ 0 ≤ X₅ ∧ X₅ ≤ 1+X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₀+X₅ ∧ 0 ≤ 1+X₀
t₄₆₄: n_l4___8(X₀, X₁, X₂, X₅) → n_l2___6(X₀, X₁, X₂, X₅) :|: 0 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ 1+X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₀+X₅ ∧ 0 ≤ 1+X₀
All Bounds
Timebounds
Overall timebound:600⋅X₅⋅X₅+688⋅X₅+199 {O(n^2)}
t₃₇: 1 {O(1)}
t₄₆₂: 1 {O(1)}
t₄₅: 1 {O(1)}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
t₄₄₇: 6⋅X₅+2 {O(n)}
t₄₄₈: 6⋅X₅+2 {O(n)}
t₄₄₉: 6⋅X₅+2 {O(n)}
t₄₅₀: 12⋅X₅+8 {O(n)}
t₄₅₁: 120⋅X₅⋅X₅+128⋅X₅+32 {O(n^2)}
t₄₅₂: 120⋅X₅⋅X₅+128⋅X₅+32 {O(n^2)}
t₄₅₃: 1 {O(1)}
t₄₅₄: 1 {O(1)}
t₄₅₅: 1 {O(1)}
t₄₅₆: 1 {O(1)}
t₄₅₇: 6⋅X₅+2 {O(n)}
t₄₅₈: 120⋅X₅⋅X₅+128⋅X₅+34 {O(n^2)}
t₄₅₉: 1 {O(1)}
t₄₆₀: 6⋅X₅+2 {O(n)}
t₄₆₁: 120⋅X₅⋅X₅+128⋅X₅+34 {O(n^2)}
t₄₆₃: 6⋅X₅+2 {O(n)}
t₄₇₆: 1 {O(1)}
t₄₆₄: 120⋅X₅⋅X₅+128⋅X₅+34 {O(n^2)}
t₄₇₇: 1 {O(1)}
Costbounds
Overall costbound: 600⋅X₅⋅X₅+688⋅X₅+199 {O(n^2)}
t₃₇: 1 {O(1)}
t₄₆₂: 1 {O(1)}
t₄₅: 1 {O(1)}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
t₄₄₇: 6⋅X₅+2 {O(n)}
t₄₄₈: 6⋅X₅+2 {O(n)}
t₄₄₉: 6⋅X₅+2 {O(n)}
t₄₅₀: 12⋅X₅+8 {O(n)}
t₄₅₁: 120⋅X₅⋅X₅+128⋅X₅+32 {O(n^2)}
t₄₅₂: 120⋅X₅⋅X₅+128⋅X₅+32 {O(n^2)}
t₄₅₃: 1 {O(1)}
t₄₅₄: 1 {O(1)}
t₄₅₅: 1 {O(1)}
t₄₅₆: 1 {O(1)}
t₄₅₇: 6⋅X₅+2 {O(n)}
t₄₅₈: 120⋅X₅⋅X₅+128⋅X₅+34 {O(n^2)}
t₄₅₉: 1 {O(1)}
t₄₆₀: 6⋅X₅+2 {O(n)}
t₄₆₁: 120⋅X₅⋅X₅+128⋅X₅+34 {O(n^2)}
t₄₆₃: 6⋅X₅+2 {O(n)}
t₄₇₆: 1 {O(1)}
t₄₆₄: 120⋅X₅⋅X₅+128⋅X₅+34 {O(n^2)}
t₄₇₇: 1 {O(1)}
Sizebounds
t₃₇, X₀: X₀ {O(n)}
t₃₇, X₁: X₁ {O(n)}
t₃₇, X₂: X₂ {O(n)}
t₃₇, X₅: X₅ {O(n)}
t₄₆₂, X₀: 2⋅X₅ {O(n)}
t₄₆₂, X₁: 2⋅X₅ {O(n)}
t₄₆₂, X₂: X₂ {O(n)}
t₄₆₂, X₅: X₅ {O(n)}
t₄₅, X₀: 2⋅X₅ {O(n)}
t₄₅, X₁: 2⋅X₅ {O(n)}
t₄₅, X₂: X₂ {O(n)}
t₄₅, X₅: X₅ {O(n)}
t₄₆, X₀: 172⋅X₅+X₀+117 {O(n)}
t₄₆, X₁: 114⋅X₅+X₁+61 {O(n)}
t₄₆, X₅: 4⋅X₅ {O(n)}
t₄₇, X₀: X₀ {O(n)}
t₄₇, X₁: X₁ {O(n)}
t₄₇, X₂: X₂ {O(n)}
t₄₇, X₅: X₅ {O(n)}
t₄₈, X₀: X₀ {O(n)}
t₄₈, X₁: X₁ {O(n)}
t₄₈, X₂: X₂ {O(n)}
t₄₈, X₅: X₅ {O(n)}
t₄₄₇, X₀: 20⋅X₅+13 {O(n)}
t₄₄₇, X₁: 18⋅X₅+10 {O(n)}
t₄₄₇, X₂: 0 {O(1)}
t₄₄₇, X₅: 3⋅X₅ {O(n)}
t₄₄₈, X₀: 20⋅X₅+14 {O(n)}
t₄₄₈, X₁: 18⋅X₅+10 {O(n)}
t₄₄₈, X₅: 3⋅X₅ {O(n)}
t₄₄₉, X₀: 20⋅X₅+14 {O(n)}
t₄₄₉, X₁: 18⋅X₅+10 {O(n)}
t₄₄₉, X₅: 3⋅X₅ {O(n)}
t₄₅₀, X₀: 18⋅X₅+11 {O(n)}
t₄₅₀, X₁: 18⋅X₅+10 {O(n)}
t₄₅₀, X₂: 0 {O(1)}
t₄₅₀, X₅: 3⋅X₅ {O(n)}
t₄₅₁, X₀: 44⋅X₅+31 {O(n)}
t₄₅₁, X₁: 18⋅X₅+10 {O(n)}
t₄₅₁, X₅: 3⋅X₅ {O(n)}
t₄₅₂, X₀: 44⋅X₅+31 {O(n)}
t₄₅₂, X₁: 18⋅X₅+10 {O(n)}
t₄₅₂, X₅: 3⋅X₅ {O(n)}
t₄₅₃, X₀: 2⋅X₅+1 {O(n)}
t₄₅₃, X₁: 2⋅X₅+1 {O(n)}
t₄₅₃, X₂: 0 {O(1)}
t₄₅₃, X₅: X₅ {O(n)}
t₄₅₄, X₀: 2⋅X₅+1 {O(n)}
t₄₅₄, X₁: 2⋅X₅ {O(n)}
t₄₅₄, X₅: X₅ {O(n)}
t₄₅₅, X₀: 2⋅X₅+1 {O(n)}
t₄₅₅, X₁: 2⋅X₅ {O(n)}
t₄₅₅, X₅: X₅ {O(n)}
t₄₅₆, X₀: 2⋅X₅ {O(n)}
t₄₅₆, X₁: 2⋅X₅ {O(n)}
t₄₅₆, X₂: X₂ {O(n)}
t₄₅₆, X₅: X₅ {O(n)}
t₄₅₇, X₀: 20⋅X₅+13 {O(n)}
t₄₅₇, X₁: 18⋅X₅+10 {O(n)}
t₄₅₇, X₂: 0 {O(1)}
t₄₅₇, X₅: 3⋅X₅ {O(n)}
t₄₅₈, X₀: 44⋅X₅+31 {O(n)}
t₄₅₈, X₁: 18⋅X₅+10 {O(n)}
t₄₅₈, X₅: 3⋅X₅ {O(n)}
t₄₅₉, X₀: 2⋅X₅ {O(n)}
t₄₅₉, X₁: 2⋅X₅ {O(n)}
t₄₅₉, X₅: X₅ {O(n)}
t₄₆₀, X₀: 20⋅X₅+13 {O(n)}
t₄₆₀, X₁: 18⋅X₅+10 {O(n)}
t₄₆₀, X₅: 3⋅X₅ {O(n)}
t₄₆₁, X₀: 44⋅X₅+31 {O(n)}
t₄₆₁, X₁: 18⋅X₅+10 {O(n)}
t₄₆₁, X₅: 3⋅X₅ {O(n)}
t₄₆₃, X₀: 20⋅X₅+13 {O(n)}
t₄₆₃, X₁: 18⋅X₅+10 {O(n)}
t₄₆₃, X₂: 0 {O(1)}
t₄₆₃, X₅: 3⋅X₅ {O(n)}
t₄₇₆, X₀: 40⋅X₅+25 {O(n)}
t₄₇₆, X₁: 38⋅X₅+21 {O(n)}
t₄₇₆, X₂: 0 {O(1)}
t₄₇₆, X₅: 7⋅X₅ {O(n)}
t₄₆₄, X₀: 44⋅X₅+31 {O(n)}
t₄₆₄, X₁: 18⋅X₅+10 {O(n)}
t₄₆₄, X₅: 3⋅X₅ {O(n)}
t₄₇₇, X₀: 132⋅X₅+92 {O(n)}
t₄₇₇, X₁: 76⋅X₅+40 {O(n)}
t₄₇₇, X₅: 14⋅X₅ {O(n)}