Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₁: l10(X₀, X₁, X₂, X₃) → l9(X₀-1, X₁, X₂, X₃) :|: 0 < X₀ ∧ 0 < X₀
t₁₂: l10(X₀, X₁, X₂, X₃) → l9(X₁, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₀ ≤ 0
t₁₃: l10(X₀, X₁, X₂, X₃) → l9(X₀-1, X₁, X₂-1, X₃) :|: X₀ ≤ 0 ∧ 0 < X₀
t₁₄: l10(X₀, X₁, X₂, X₃) → l9(X₁, X₁, X₂-1, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ 0
t₁₅: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₈: l8(X₀, X₁, X₂, X₃) → l9(X₃, X₁, X₁, X₃)
t₉: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: 0 < X₂
t₁₀: l9(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
Preprocessing
Cut unsatisfiable transition t₁₂: l10→l9
Cut unsatisfiable transition t₁₃: l10→l9
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ for location l11
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ for location l12
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l10
Found invariant X₂ ≤ X₁ for location l9
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₁: l10(X₀, X₁, X₂, X₃) → l9(X₀-1, X₁, X₂, X₃) :|: 0 < X₀ ∧ 0 < X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₄: l10(X₀, X₁, X₂, X₃) → l9(X₁, X₁, X₂-1, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₅: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₈: l8(X₀, X₁, X₂, X₃) → l9(X₃, X₁, X₁, X₃)
t₉: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: 0 < X₂ ∧ X₂ ≤ X₁
t₁₀: l9(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁
MPRF for transition t₁₄: l10(X₀, X₁, X₂, X₃) → l9(X₁, X₁, X₂-1, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁ {O(n)}
TWN: t₉: l9→l10
cycle: [t₉: l9→l10; t₁₁: l10→l9]
loop: (0 < X₂ ∧ 0 < X₀ ∧ 0 < X₀,(X₀,X₂) -> (X₀-1,X₂)
order: [X₀; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₂: X₂
Termination: true
Formula:
1 < 0 ∧ 0 < X₂
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₂
Stabilization-Threshold for: 0 < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
loop: (0 < X₂ ∧ 0 < X₀ ∧ 0 < X₀,(X₀,X₂) -> (X₀-1,X₂)
order: [X₀; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₂: X₂
Termination: true
Formula:
1 < 0 ∧ 0 < X₂
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₂
Stabilization-Threshold for: 0 < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
TWN - Lifting for t₉: l9→l10 of 2⋅X₀+5 {O(n)}
relevant size-bounds w.r.t. t₈:
X₀: X₃ {O(n)}
Runtime-bound of t₈: 1 {O(1)}
Results in: 2⋅X₃+5 {O(n)}
TWN - Lifting for t₉: l9→l10 of 2⋅X₀+5 {O(n)}
relevant size-bounds w.r.t. t₁₄:
X₀: X₁ {O(n)}
Runtime-bound of t₁₄: X₁ {O(n)}
Results in: 2⋅X₁⋅X₁+5⋅X₁ {O(n^2)}
TWN: t₁₁: l10→l9
TWN - Lifting for t₁₁: l10→l9 of 2⋅X₀+5 {O(n)}
relevant size-bounds w.r.t. t₈:
X₀: X₃ {O(n)}
Runtime-bound of t₈: 1 {O(1)}
Results in: 2⋅X₃+5 {O(n)}
TWN - Lifting for t₁₁: l10→l9 of 2⋅X₀+5 {O(n)}
relevant size-bounds w.r.t. t₁₄:
X₀: X₁ {O(n)}
Runtime-bound of t₁₄: X₁ {O(n)}
Results in: 2⋅X₁⋅X₁+5⋅X₁ {O(n^2)}
Chain transitions t₉: l9→l10 and t₁₄: l10→l9 to t₈₈: l9→l9
Chain transitions t₉: l9→l10 and t₁₁: l10→l9 to t₈₉: l9→l9
Analysing control-flow refined program
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ for location l11
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ for location l12
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l10
Found invariant X₂ ≤ X₁ for location l9
MPRF for transition t₈₈: l9(X₀, X₁, X₂, X₃) -{2}> l9(X₁, X₁, X₂-1, X₃) :|: 0 < X₂ ∧ X₀ ≤ 0 ∧ X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₁ of depth 1:
new bound:
X₁ {O(n)}
TWN: t₈₉: l9→l9
cycle: [t₈₉: l9→l9]
loop: (0 < X₂ ∧ 0 < X₀ ∧ 0 < X₀,(X₀,X₂) -> (X₀-1,X₂)
order: [X₀; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₂: X₂
Termination: true
Formula:
1 < 0 ∧ 0 < X₂
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₂
Stabilization-Threshold for: 0 < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
loop: (0 < X₂ ∧ 0 < X₀ ∧ 0 < X₀,(X₀,X₂) -> (X₀-1,X₂)
order: [X₀; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₂: X₂
Termination: true
Formula:
1 < 0 ∧ 0 < X₂
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₂
Stabilization-Threshold for: 0 < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
TWN - Lifting for t₈₉: l9→l9 of 2⋅X₀+5 {O(n)}
relevant size-bounds w.r.t. t₈₈:
X₀: 2⋅X₁ {O(n)}
Runtime-bound of t₈₈: X₁ {O(n)}
Results in: 4⋅X₁⋅X₁+5⋅X₁ {O(n^2)}
TWN - Lifting for t₈₉: l9→l9 of 2⋅X₀+5 {O(n)}
relevant size-bounds w.r.t. t₈:
X₀: X₃ {O(n)}
Runtime-bound of t₈: 1 {O(1)}
Results in: 2⋅X₃+5 {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₁₇₄: n_l9___2→l11
Cut unsatisfiable transition t₁₇₆: n_l9___6→l11
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ for location l11
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l10___3
Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l10___1
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l10___4
Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l9___2
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ for location l12
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l9___6
Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l9
Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location n_l10___7
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l9___5
MPRF for transition t₁₅₈: n_l10___1(X₀, X₁, X₂, X₃) → n_l9___6(X₀-1, X₁, X₂, X₃) :|: 0 < X₀ ∧ 0 < X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
4⋅X₁+1 {O(n)}
MPRF for transition t₁₅₉: n_l10___3(X₀, X₁, X₂, X₃) → n_l9___2(X₀-1, X₁, X₂, X₃) :|: 1+X₂ ≤ X₀ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₁+1 {O(n)}
MPRF for transition t₁₆₀: n_l10___4(X₀, X₁, X₂, X₃) → n_l9___5(X₁, X₁, X₂-1, X₃) :|: X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
2⋅X₁ {O(n)}
MPRF for transition t₁₆₄: n_l9___2(X₀, X₁, X₂, X₃) → n_l10___1(X₀, X₁, X₂, X₃) :|: 0 < X₂ ∧ 1 ≤ X₂ ∧ 0 < X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 < X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
4⋅X₁+1 {O(n)}
MPRF for transition t₁₆₅: n_l9___5(X₀, X₁, X₂, X₃) → n_l10___3(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 < X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₁+1 {O(n)}
TWN: t₁₆₁: n_l10___4→n_l9___6
cycle: [t₁₆₁: n_l10___4→n_l9___6; t₁₆₆: n_l9___6→n_l10___4]
loop: (0 < X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 < X₂ ∧ 0 < X₀,(X₀,X₂) -> (X₀-1,X₂)
order: [X₀; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₂: X₂
Termination: true
Formula:
1 < 0 ∧ 0 < X₂ ∧ 1 < X₂
∨ 1 < 0 ∧ 0 < X₂ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₂ ∧ 1 < X₂
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₂ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1
Stabilization-Threshold for: 0 < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
loop: (0 < X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 < X₂ ∧ 0 < X₀,(X₀,X₂) -> (X₀-1,X₂)
order: [X₀; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₂: X₂
Termination: true
Formula:
1 < 0 ∧ 0 < X₂ ∧ 1 < X₂
∨ 1 < 0 ∧ 0 < X₂ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₂ ∧ 1 < X₂
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₂ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1
Stabilization-Threshold for: 0 < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
TWN - Lifting for t₁₆₁: n_l10___4→n_l9___6 of 2⋅X₀+6 {O(n)}
relevant size-bounds w.r.t. t₁₆₃:
X₀: X₃ {O(n)}
Runtime-bound of t₁₆₃: 1 {O(1)}
Results in: 2⋅X₃+6 {O(n)}
TWN - Lifting for t₁₆₁: n_l10___4→n_l9___6 of 2⋅X₀+6 {O(n)}
relevant size-bounds w.r.t. t₁₅₈:
X₀: 3⋅X₁ {O(n)}
Runtime-bound of t₁₅₈: 4⋅X₁+1 {O(n)}
Results in: 24⋅X₁⋅X₁+30⋅X₁+6 {O(n^2)}
TWN: t₁₆₆: n_l9___6→n_l10___4
TWN - Lifting for t₁₆₆: n_l9___6→n_l10___4 of 2⋅X₀+6 {O(n)}
relevant size-bounds w.r.t. t₁₆₃:
X₀: X₃ {O(n)}
Runtime-bound of t₁₆₃: 1 {O(1)}
Results in: 2⋅X₃+6 {O(n)}
TWN - Lifting for t₁₆₆: n_l9___6→n_l10___4 of 2⋅X₀+6 {O(n)}
relevant size-bounds w.r.t. t₁₅₈:
X₀: 3⋅X₁ {O(n)}
Runtime-bound of t₁₅₈: 4⋅X₁+1 {O(n)}
Results in: 24⋅X₁⋅X₁+30⋅X₁+6 {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₁⋅X₁+11⋅X₁+4⋅X₃+21 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 2⋅X₁⋅X₁+2⋅X₃+5⋅X₁+5 {O(n^2)}
t₁₀: 1 {O(1)}
t₁₁: 2⋅X₁⋅X₁+2⋅X₃+5⋅X₁+5 {O(n^2)}
t₁₄: X₁ {O(n)}
t₁₅: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₁⋅X₁+11⋅X₁+4⋅X₃+21 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 2⋅X₁⋅X₁+2⋅X₃+5⋅X₁+5 {O(n^2)}
t₁₀: 1 {O(1)}
t₁₁: 2⋅X₁⋅X₁+2⋅X₃+5⋅X₁+5 {O(n^2)}
t₁₄: X₁ {O(n)}
t₁₅: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₃ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₁ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: X₁+X₃ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₁ {O(n)}
t₉, X₃: X₃ {O(n)}
t₁₀, X₀: X₁+X₃ {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}
t₁₀, X₂: 2⋅X₁ {O(n)}
t₁₀, X₃: 2⋅X₃ {O(n)}
t₁₁, X₀: X₁+X₃ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₁ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₄, X₀: X₁ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₁ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₅, X₀: X₁+X₃ {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}
t₁₅, X₂: 2⋅X₁ {O(n)}
t₁₅, X₃: 2⋅X₃ {O(n)}