Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ X₂+1 ≤ X₁
t₃: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ 0
t₄: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ X₂
t₅: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ X₀
t₆: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0
t₇: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1)
t₈: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1)
t₉: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₁: l6(X₀, X₁, X₂) → l1(X₂, X₁, X₀) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
Preprocessing
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l2
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l7
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l5
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l1
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ X₂+1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₃: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₄: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₅: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₆: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₇: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l4(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₉: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₁: l6(X₀, X₁, X₂) → l1(X₂, X₁, X₀) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
Analysing control-flow refined program
Cut unsatisfiable transition t₃: l1→l5
Cut unsatisfiable transition t₄: l1→l5
Cut unsatisfiable transition t₉₉: n_l1___3→l5
Cut unsatisfiable transition t₉₈: n_l1___6→l5
Found invariant X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___6
Found invariant 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___4
Found invariant 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___5
Found invariant 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___3
Found invariant 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l2___2
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l7
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location n_l2___9
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___8
Found invariant 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l4___1
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l5
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location l1
Found invariant 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l4___7
MPRF for transition t₇₈: n_l1___6(X₀, X₁, X₂) → n_l2___5(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+X₁+2 {O(n)}
MPRF:
n_l2___5 [X₁-X₂ ]
n_l3___4 [X₁-X₂ ]
n_l1___6 [X₁+1-X₂ ]
MPRF for transition t₈₀: n_l2___5(X₀, X₁, X₂) → n_l3___4(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
n_l2___5 [X₁-X₂ ]
n_l3___4 [X₁-X₂-1 ]
n_l1___6 [X₁-X₂ ]
MPRF for transition t₈₃: n_l3___4(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
n_l2___5 [X₁-X₂ ]
n_l3___4 [X₁-X₂ ]
n_l1___6 [X₁-X₂ ]
MPRF for transition t₇₇: n_l1___3(X₀, X₁, X₂) → n_l2___2(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
n_l2___2 [X₂ ]
n_l4___1 [X₂ ]
n_l1___3 [X₂+1 ]
MPRF for transition t₇₉: n_l2___2(X₀, X₁, X₂) → n_l4___1(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₀ {O(n)}
MPRF:
n_l2___2 [X₂ ]
n_l4___1 [X₂-1 ]
n_l1___3 [X₂ ]
MPRF for transition t₈₅: n_l4___1(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₀ {O(n)}
MPRF:
n_l2___2 [X₂ ]
n_l4___1 [X₂ ]
n_l1___3 [X₂ ]
CFR: Improvement to new bound with the following program:
new bound:
3⋅X₁+6⋅X₀+5 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l5, l6, l7, n_l1___3, n_l1___6, n_l2___2, n_l2___5, n_l2___9, n_l3___4, n_l3___8, n_l4___1, n_l4___7
Transitions:
t₀: l0(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₇₆: l1(X₀, X₁, X₂) → n_l2___9(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₉: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₁: l6(X₀, X₁, X₂) → l1(X₂, X₁, X₀) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₉₇: n_l1___3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₇₇: n_l1___3(X₀, X₁, X₂) → n_l2___2(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₀₀: n_l1___6(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇₈: n_l1___6(X₀, X₁, X₂) → n_l2___5(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇₉: n_l2___2(X₀, X₁, X₂) → n_l4___1(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₈₀: n_l2___5(X₀, X₁, X₂) → n_l3___4(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₁: n_l2___9(X₀, X₁, X₂) → n_l3___8(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₈₂: n_l2___9(X₀, X₁, X₂) → n_l4___7(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁
t₈₃: n_l3___4(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₄: n_l3___8(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₅: n_l4___1(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₈₆: n_l4___7(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0
All Bounds
Timebounds
Overall timebound:3⋅X₁+6⋅X₀+15 {O(n)}
t₀: 1 {O(1)}
t₇₆: 1 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
t₇₇: X₀+1 {O(n)}
t₉₇: 1 {O(1)}
t₇₈: X₀+X₁+2 {O(n)}
t₁₀₀: 1 {O(1)}
t₇₉: X₀ {O(n)}
t₈₀: X₀+X₁+1 {O(n)}
t₈₁: 1 {O(1)}
t₈₂: 1 {O(1)}
t₈₃: X₀+X₁+1 {O(n)}
t₈₄: 1 {O(1)}
t₈₅: X₀ {O(n)}
t₈₆: 1 {O(1)}
Costbounds
Overall costbound: 3⋅X₁+6⋅X₀+15 {O(n)}
t₀: 1 {O(1)}
t₇₆: 1 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
t₇₇: X₀+1 {O(n)}
t₉₇: 1 {O(1)}
t₇₈: X₀+X₁+2 {O(n)}
t₁₀₀: 1 {O(1)}
t₇₉: X₀ {O(n)}
t₈₀: X₀+X₁+1 {O(n)}
t₈₁: 1 {O(1)}
t₈₂: 1 {O(1)}
t₈₃: X₀+X₁+1 {O(n)}
t₈₄: 1 {O(1)}
t₈₅: X₀ {O(n)}
t₈₆: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₇₆, X₀: X₂ {O(n)}
t₇₆, X₁: X₁ {O(n)}
t₇₆, X₂: X₀ {O(n)}
t₉, X₀: 4⋅X₂ {O(n)}
t₉, X₁: 4⋅X₁ {O(n)}
t₉, X₂: 3⋅X₀+X₁+3 {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₀ {O(n)}
t₇₇, X₀: X₂ {O(n)}
t₇₇, X₁: X₁ {O(n)}
t₇₇, X₂: X₀ {O(n)}
t₉₇, X₀: 2⋅X₂ {O(n)}
t₉₇, X₁: 2⋅X₁ {O(n)}
t₉₇, X₂: 0 {O(1)}
t₇₈, X₀: X₂ {O(n)}
t₇₈, X₁: X₁ {O(n)}
t₇₈, X₂: 2⋅X₀+X₁+2 {O(n)}
t₁₀₀, X₀: 2⋅X₂ {O(n)}
t₁₀₀, X₁: 2⋅X₁ {O(n)}
t₁₀₀, X₂: 3⋅X₀+X₁+3 {O(n)}
t₇₉, X₀: X₂ {O(n)}
t₇₉, X₁: X₁ {O(n)}
t₇₉, X₂: X₀ {O(n)}
t₈₀, X₀: X₂ {O(n)}
t₈₀, X₁: X₁ {O(n)}
t₈₀, X₂: 2⋅X₀+X₁+2 {O(n)}
t₈₁, X₀: X₂ {O(n)}
t₈₁, X₁: X₁ {O(n)}
t₈₁, X₂: X₀ {O(n)}
t₈₂, X₀: X₂ {O(n)}
t₈₂, X₁: X₁ {O(n)}
t₈₂, X₂: X₀ {O(n)}
t₈₃, X₀: X₂ {O(n)}
t₈₃, X₁: X₁ {O(n)}
t₈₃, X₂: 2⋅X₀+X₁+2 {O(n)}
t₈₄, X₀: X₂ {O(n)}
t₈₄, X₁: X₁ {O(n)}
t₈₄, X₂: X₀+1 {O(n)}
t₈₅, X₀: X₂ {O(n)}
t₈₅, X₁: X₁ {O(n)}
t₈₅, X₂: X₀ {O(n)}
t₈₆, X₀: X₂ {O(n)}
t₈₆, X₁: X₁ {O(n)}
t₈₆, X₂: X₀ {O(n)}