Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
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 ≤ X₁
t₃: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 0
t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ X₀
t₅: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0
t₆: l3(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂)
t₇: l4(X₀, X₁, X₂) → l1(X₂, X₁-1, X₂)
t₈: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₁: l6(X₀, X₁, X₂) → l1(D, X₂, X₂)
Preprocessing
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location l2
Found invariant X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l7
Found invariant X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l5
Found invariant X₁ ≤ X₂ for location l1
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
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 ≤ X₁ ∧ X₁ ≤ X₂
t₃: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ X₁ ≤ X₂
t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₅: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁
t₆: l3(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l4(X₀, X₁, X₂) → l1(X₂, X₁-1, X₂) :|: 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₈: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ X₁ ≤ 0
t₁: l6(X₀, X₁, X₂) → l1(D, X₂, X₂)
MPRF for transition t₅: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l2 [X₁ ]
l3 [X₁ ]
l4 [X₁-1 ]
l1 [X₁ ]
MPRF for transition t₇: l4(X₀, X₁, X₂) → l1(X₂, X₁-1, X₂) :|: 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l2 [X₁ ]
l3 [X₁ ]
l4 [X₁ ]
l1 [X₁ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₉₂: n_l1___12→l5
Cut unsatisfiable transition t₉₃: n_l1___3→l5
Cut unsatisfiable transition t₉₄: n_l1___6→l5
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___12
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location n_l2___15
Found invariant X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___6
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___4
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___9
Found invariant X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___5
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___11
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l4___13
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___2
Found invariant X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l7
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___14
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___1
Found invariant X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l5
Found invariant X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l1
Found invariant X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___8
Found invariant X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___7
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___10
MPRF for transition t₆₈: n_l1___6(X₀, X₁, X₂) → n_l2___5(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₂ {O(n)}
MPRF:
n_l2___2 [X₁-1 ]
n_l2___5 [X₁-1 ]
n_l2___8 [X₁ ]
n_l3___4 [X₁-1 ]
n_l1___3 [X₁-1 ]
n_l3___7 [X₀+X₁-X₂ ]
n_l1___6 [X₁ ]
n_l4___1 [X₁-1 ]
n_l1___9 [X₁ ]
MPRF for transition t₆₉: n_l1___9(X₀, X₁, X₂) → n_l2___8(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₂+2 {O(n)}
MPRF:
n_l2___2 [X₁ ]
n_l2___5 [X₁ ]
n_l2___8 [X₁ ]
n_l3___4 [X₁ ]
n_l1___3 [X₁ ]
n_l3___7 [X₁ ]
n_l1___6 [X₁ ]
n_l4___1 [X₁ ]
n_l1___9 [X₁+1 ]
MPRF for transition t₇₅: n_l2___2(X₀, X₁, X₂) → n_l4___1(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 0 ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
2⋅X₂ {O(n)}
MPRF:
n_l2___2 [X₁ ]
n_l2___5 [X₁ ]
n_l2___8 [X₁ ]
n_l3___4 [X₁ ]
n_l1___3 [X₁ ]
n_l3___7 [X₁+X₂-X₀ ]
n_l1___6 [X₁ ]
n_l4___1 [X₁-1 ]
n_l1___9 [X₁ ]
MPRF for transition t₇₆: n_l2___5(X₀, X₁, X₂) → n_l3___4(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₂ {O(n)}
MPRF:
n_l2___2 [X₁-1 ]
n_l2___5 [X₁ ]
n_l2___8 [X₁ ]
n_l3___4 [X₁-1 ]
n_l1___3 [X₁-1 ]
n_l3___7 [X₁ ]
n_l1___6 [X₁ ]
n_l4___1 [X₁-1 ]
n_l1___9 [X₁ ]
MPRF for transition t₇₇: n_l2___8(X₀, X₁, X₂) → n_l3___7(X₀, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₂ {O(n)}
MPRF:
n_l2___2 [X₁-1 ]
n_l2___5 [X₁-1 ]
n_l2___8 [X₁ ]
n_l3___4 [X₁-1 ]
n_l1___3 [X₁-1 ]
n_l3___7 [X₁-1 ]
n_l1___6 [X₁-1 ]
n_l4___1 [X₁-1 ]
n_l1___9 [X₁ ]
MPRF for transition t₈₀: n_l3___7(X₀, X₁, X₂) → n_l1___6(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₂+2 {O(n)}
MPRF:
n_l2___2 [X₁ ]
n_l2___5 [X₁ ]
n_l2___8 [X₁+1 ]
n_l3___4 [X₁ ]
n_l1___3 [X₁ ]
n_l3___7 [X₁+1 ]
n_l1___6 [X₁ ]
n_l4___1 [X₁ ]
n_l1___9 [X₁+1 ]
MPRF for transition t₈₁: n_l4___1(X₀, X₁, X₂) → n_l1___9(X₂, X₁-1, X₂) :|: X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:
new bound:
4⋅X₂+2 {O(n)}
MPRF:
n_l2___2 [2⋅X₁ ]
n_l2___5 [2⋅X₁+X₂-X₀ ]
n_l2___8 [2⋅X₁+1 ]
n_l3___4 [2⋅X₁ ]
n_l1___3 [2⋅X₁ ]
n_l3___7 [2⋅X₁+X₂+1-X₀ ]
n_l1___6 [2⋅X₁+X₂-X₀ ]
n_l4___1 [2⋅X₁ ]
n_l1___9 [2⋅X₁+1 ]
MPRF for transition t₆₇: n_l1___3(X₀, X₁, X₂) → n_l2___2(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
16⋅X₂⋅X₂+12⋅X₂ {O(n^2)}
MPRF:
n_l1___9 [2⋅X₀ ]
n_l2___2 [X₀+X₂-X₁ ]
n_l4___1 [X₀+X₂-X₁ ]
n_l2___5 [2⋅X₀ ]
n_l2___8 [2⋅X₀ ]
n_l3___4 [X₀+X₂-X₁ ]
n_l1___3 [X₀+X₂+1-X₁ ]
n_l3___7 [X₀+X₂ ]
n_l1___6 [2⋅X₀ ]
MPRF for transition t₇₄: n_l2___2(X₀, X₁, X₂) → n_l3___4(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
8⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
MPRF:
n_l1___9 [X₂ ]
n_l2___2 [X₀ ]
n_l4___1 [0 ]
n_l2___5 [X₀ ]
n_l2___8 [X₂ ]
n_l3___4 [X₀-1 ]
n_l1___3 [X₀ ]
n_l3___7 [2⋅X₀-X₂ ]
n_l1___6 [X₀ ]
MPRF for transition t₇₉: n_l3___4(X₀, X₁, X₂) → n_l1___3(X₀-1, X₁, X₂) :|: X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
8⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
MPRF:
n_l1___9 [X₂ ]
n_l2___2 [X₀ ]
n_l4___1 [X₀ ]
n_l2___5 [X₀ ]
n_l2___8 [X₂ ]
n_l3___4 [X₀ ]
n_l1___3 [X₀ ]
n_l3___7 [X₀ ]
n_l1___6 [X₀ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₅: X₂ {O(n)}
t₆: inf {Infinity}
t₇: X₂ {O(n)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₅: X₂ {O(n)}
t₆: inf {Infinity}
t₇: X₂ {O(n)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₂, X₁: X₂ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₁: 2⋅X₂ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₄, X₁: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₅, X₁: X₂ {O(n)}
t₅, X₂: X₂ {O(n)}
t₆, X₁: X₂ {O(n)}
t₆, X₂: X₂ {O(n)}
t₇, X₀: X₂ {O(n)}
t₇, X₁: X₂ {O(n)}
t₇, X₂: X₂ {O(n)}
t₈, X₁: 2⋅X₂ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₂ {O(n)}