Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ X₂ ≤ X₁
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂-1) :|: 1 ≤ X₀ ∧ X₂ ≤ X₁+1
t₂: l1(X₀, X₁, X₂) → l1(X₀, X₁+X₂-1, X₂-1) :|: 0 ≤ X₀ ∧ 0 ≤ X₁
Preprocessing
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₀ for location l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ X₂ ≤ X₁
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂-1) :|: 1 ≤ X₀ ∧ X₂ ≤ X₁+1 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l1(X₀, X₁+X₂-1, X₂-1) :|: 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀
Analysing control-flow refined program
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___2
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₀ for location l1
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___1
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___2
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₀ for location l1
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___1
Time-Bound by TWN-Loops:
TWN-Loops: t₅₈ 4⋅X₀+4⋅X₁+4⋅X₂+16 {O(n)}
TWN-Loops:
entry: t₆₀: l1(X₀, X₁, X₂) → n_l1___3(X₀-1, X₁, X₂-1) :|: X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [1+X₂ ≤ X₁ ∧ 0 ≤ X₀] , (X₀,X₁,X₂) -> (X₀-1,X₁,X₂-1) :|: X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₁
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
0 < 1 ∧ 1 < 0
∨ 1 < 0 ∧ 0 < 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 1+X₂ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < 1 ∧ 1 < 0 ∧ 1+X₂ < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 < 0 ∧ 1+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 < 0
∨ 0 < 1 ∧ 1 < 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 < 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 1 < 0
∨ 1 < X₀ ∧ 0 < 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 1 < X₀ ∧ 1+X₂ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < 1 ∧ 1 < X₀ ∧ 1+X₂ < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 < X₀ ∧ 1+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 1 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 < 0
∨ 0 < 1 ∧ 1 < X₀ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 < X₀ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < 1 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 < 0
∨ 0 < 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ 1 < 0 ∧ 0 < 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1 < 0 ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ < X₁ ∧ 1+X₂ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₂ < X₁ ∧ 1 < 0 ∧ 1+X₂ < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1 < 0 ∧ 1+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 < 0
∨ X₂ < X₁ ∧ 1 < 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1 < 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ 1 < X₀ ∧ 0 < 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1 < X₀ ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ < X₁ ∧ 1 < X₀ ∧ 1+X₂ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₂ < X₁ ∧ 1 < X₀ ∧ 1+X₂ < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1 < X₀ ∧ 1+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ < X₁ ∧ 1 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 < 0
∨ X₂ < X₁ ∧ 1 < X₀ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1 < X₀ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₂ < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 < 0
∨ X₂ < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 < 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < 0 ∧ 0 < 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < 0 ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₂ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < 0 ∧ 1+X₂ < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < 0 ∧ 1+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < X₀ ∧ 0 < 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < X₀ ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < X₀ ∧ 1+X₂ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < X₀ ∧ 1+X₂ < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < X₀ ∧ 1+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < X₀ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < X₀ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
Stabilization-Threshold for: X₂ ≤ X₁
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: 1+X₂ ≤ X₁
alphas_abs: 1+X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+4 {O(n)}
Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
relevant size-bounds w.r.t. t₆₀:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
X₂: X₂+1 {O(n)}
Runtime-bound of t₆₀: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+4⋅X₂+16 {O(n)}
4⋅X₀+4⋅X₁+4⋅X₂+16 {O(n)}
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 2⋅X₀ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}