Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₇: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃+X₀)
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃-X₀)
t₃: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₃
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂
t₆: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₉: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₁: l6(X₀, X₁, X₂, X₃) → l3(1, X₂, X₀, X₁) :|: 1 ≤ X₀
t₂: l6(X₀, X₁, X₂, X₃) → l3(-1, X₂, X₀, X₁) :|: X₀ ≤ 0
Preprocessing
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ X₀+X₂ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l2
Found invariant 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l7
Found invariant 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l5
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l1
Found invariant X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l4
Found invariant X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₇: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃+X₀) :|: X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₈: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃-X₀) :|: X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ X₀+X₂ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₃: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₆: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₉: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₁: l6(X₀, X₁, X₂, X₃) → l3(1, X₂, X₀, X₁) :|: 1 ≤ X₀
t₂: l6(X₀, X₁, X₂, X₃) → l3(-1, X₂, X₀, X₁) :|: X₀ ≤ 0
Analysing control-flow refined program
Found invariant X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___4
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l4___6
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location n_l4___3
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location n_l2___2
Found invariant 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l7
Found invariant 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l5
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___5
Found invariant X₃ ≤ 1+X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location n_l3___1
Found invariant X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l3
MPRF for transition t₇₄: n_l2___2(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃-X₀) :|: X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+1 ≤ 0 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF:
n_l3___1 [X₁-X₀-X₃ ]
n_l4___3 [X₁+1-X₃ ]
n_l2___2 [X₁+1-X₃ ]
MPRF for transition t₇₅: n_l3___1(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ 1+X₀ ∧ X₀+X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
X₁+X₂ {O(n)}
MPRF:
n_l3___1 [X₁+1-X₃ ]
n_l4___3 [X₁-X₃ ]
n_l2___2 [X₀+X₁+1-X₃ ]
MPRF for transition t₇₉: n_l4___3(X₀, X₁, X₂, X₃) → n_l2___2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+1 ≤ 0 ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF:
n_l3___1 [X₁-X₀-X₃ ]
n_l4___3 [X₁+1-X₃ ]
n_l2___2 [X₁-X₃ ]
MPRF for transition t₇₃: n_l1___5(X₀, X₁, X₂, X₃) → n_l3___4(X₀, X₁, X₂, X₀+X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF:
n_l3___4 [X₀+X₁-X₃ ]
n_l4___6 [X₁+1-X₃ ]
n_l1___5 [X₁+1-X₃ ]
MPRF for transition t₇₆: n_l3___4(X₀, X₁, X₂, X₃) → n_l4___6(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₀+X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF:
n_l3___4 [X₁+2-X₃ ]
n_l4___6 [X₁+1-X₃ ]
n_l1___5 [X₁+2-X₀-X₃ ]
MPRF for transition t₈₀: n_l4___6(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
MPRF:
n_l3___4 [X₀+X₁-X₃ ]
n_l4___6 [X₁+1-X₃ ]
n_l1___5 [X₁-X₃ ]
CFR: Improvement to new bound with the following program:
new bound:
6⋅X₁+6⋅X₂+5 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l3, l5, l6, l7, n_l1___5, n_l2___2, n_l3___1, n_l3___4, n_l4___3, n_l4___6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₇₇: l3(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₇₈: l3(X₀, X₁, X₂, X₃) → n_l4___6(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₉: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀
t₁: l6(X₀, X₁, X₂, X₃) → l3(1, X₂, X₀, X₁) :|: 1 ≤ X₀
t₂: l6(X₀, X₁, X₂, X₃) → l3(-1, X₂, X₀, X₁) :|: X₀ ≤ 0
t₇₃: n_l1___5(X₀, X₁, X₂, X₃) → n_l3___4(X₀, X₁, X₂, X₀+X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₇₄: n_l2___2(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃-X₀) :|: X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+1 ≤ 0 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₈₉: n_l3___1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ 1+X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₇₅: n_l3___1(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ 1+X₀ ∧ X₀+X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₉₀: n_l3___4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₃ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₇₆: n_l3___4(X₀, X₁, X₂, X₃) → n_l4___6(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 0 ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₀+X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₇₉: n_l4___3(X₀, X₁, X₂, X₃) → n_l2___2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀+1 ≤ 0 ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1+X₀+X₂ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₈₀: n_l4___6(X₀, X₁, X₂, X₃) → n_l1___5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ 1 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:6⋅X₁+6⋅X₂+14 {O(n)}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₇₃: X₁+X₂+1 {O(n)}
t₇₄: X₁+X₂+1 {O(n)}
t₇₅: X₁+X₂ {O(n)}
t₈₉: 1 {O(1)}
t₇₆: X₁+X₂+1 {O(n)}
t₉₀: 1 {O(1)}
t₇₉: X₁+X₂+1 {O(n)}
t₈₀: X₁+X₂+1 {O(n)}
Costbounds
Overall costbound: 6⋅X₁+6⋅X₂+14 {O(n)}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₇₃: X₁+X₂+1 {O(n)}
t₇₄: X₁+X₂+1 {O(n)}
t₇₅: X₁+X₂ {O(n)}
t₈₉: 1 {O(1)}
t₇₆: X₁+X₂+1 {O(n)}
t₉₀: 1 {O(1)}
t₇₉: X₁+X₂+1 {O(n)}
t₈₀: X₁+X₂+1 {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₄, X₀: 1 {O(1)}
t₄, X₁: 2⋅X₂ {O(n)}
t₄, X₂: 2⋅X₀ {O(n)}
t₄, X₃: 2⋅X₁ {O(n)}
t₇₇, X₀: 1 {O(1)}
t₇₇, X₁: X₂ {O(n)}
t₇₇, X₂: X₀ {O(n)}
t₇₇, X₃: X₁ {O(n)}
t₇₈, X₀: 1 {O(1)}
t₇₈, X₁: X₂ {O(n)}
t₇₈, X₂: X₀ {O(n)}
t₇₈, X₃: X₁ {O(n)}
t₉, X₀: 1 {O(1)}
t₉, X₁: 4⋅X₂ {O(n)}
t₉, X₂: 4⋅X₀ {O(n)}
t₉, X₃: 2⋅X₂+6⋅X₁+2 {O(n)}
t₁, X₀: 1 {O(1)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₀ {O(n)}
t₁, X₃: X₁ {O(n)}
t₂, X₀: 1 {O(1)}
t₂, X₁: X₂ {O(n)}
t₂, X₂: X₀ {O(n)}
t₂, X₃: X₁ {O(n)}
t₇₃, X₀: 1 {O(1)}
t₇₃, X₁: X₂ {O(n)}
t₇₃, X₂: X₀ {O(n)}
t₇₃, X₃: 2⋅X₁+X₂+1 {O(n)}
t₇₄, X₀: 1 {O(1)}
t₇₄, X₁: X₂ {O(n)}
t₇₄, X₂: X₀ {O(n)}
t₇₄, X₃: 2⋅X₁+X₂+1 {O(n)}
t₇₅, X₀: 1 {O(1)}
t₇₅, X₁: X₂ {O(n)}
t₇₅, X₂: X₀ {O(n)}
t₇₅, X₃: 2⋅X₁+X₂+1 {O(n)}
t₈₉, X₀: 1 {O(1)}
t₈₉, X₁: X₂ {O(n)}
t₈₉, X₂: X₀ {O(n)}
t₈₉, X₃: 2⋅X₁+X₂+1 {O(n)}
t₇₆, X₀: 1 {O(1)}
t₇₆, X₁: X₂ {O(n)}
t₇₆, X₂: X₀ {O(n)}
t₇₆, X₃: 2⋅X₁+X₂+1 {O(n)}
t₉₀, X₀: 1 {O(1)}
t₉₀, X₁: X₂ {O(n)}
t₉₀, X₂: X₀ {O(n)}
t₉₀, X₃: 2⋅X₁+X₂+1 {O(n)}
t₇₉, X₀: 1 {O(1)}
t₇₉, X₁: X₂ {O(n)}
t₇₉, X₂: X₀ {O(n)}
t₇₉, X₃: 2⋅X₁+X₂+1 {O(n)}
t₈₀, X₀: 1 {O(1)}
t₈₀, X₁: X₂ {O(n)}
t₈₀, X₂: X₀ {O(n)}
t₈₀, X₃: 2⋅X₁+X₂+1 {O(n)}