KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location evalfreturnin

Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb1in

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalfbb2in

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalfbbin

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location evalfbb3in

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location evalfstop

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalfbb4in

Problem after Preprocessing

Start: evalfstart
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: evalfbb1in, evalfbb2in, evalfbb3in, evalfbb4in, evalfbbin, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
t₉: evalfbb1in(X₀, X₁) → evalfbb3in(1+X₀, X₁) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁
t₁₀: evalfbb2in(X₀, X₁) → evalfbb3in(X₀-X₁, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀
t₃: evalfbb3in(X₀, X₁) → evalfbb4in(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁
t₂: evalfbb3in(X₀, X₁) → evalfreturnin(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁
t₄: evalfbb4in(X₀, X₁) → evalfbbin(X₀, X₁) :|: 1+C ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₅: evalfbb4in(X₀, X₁) → evalfbbin(X₀, X₁) :|: 1 ≤ C ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₆: evalfbb4in(X₀, X₁) → evalfreturnin(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₇: evalfbbin(X₀, X₁) → evalfbb1in(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₈: evalfbbin(X₀, X₁) → evalfbb2in(X₀, X₁) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₁: evalfentryin(X₀, X₁) → evalfbb3in(X₁, X₀) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁
t₁₁: evalfreturnin(X₀, X₁) → evalfstop(X₀, X₁) :|: 1 ≤ X₀+X₁ ∧ 1 ≤ X₁
t₀: evalfstart(X₀, X₁) → evalfentryin(X₀, X₁)

Cut unreachable locations [evalfbb4in] from the program graph

Cut unsatisfiable transition [t₂: evalfbb3in→evalfreturnin; t₆₄: evalfbb3in→evalfreturnin]

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location evalfbb3in_v3

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location evalfreturnin

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalfbbin_v1

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location evalfbb3in

Found invariant 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location evalfbb3in_v1

Found invariant X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location evalfbb2in_v2

Found invariant 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ for location evalfbb3in_v2

Found invariant 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location evalfbb4in_v2

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalfbb2in_v1

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalfbb4in_v1

Found invariant 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location evalfbbin_v2

Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb1in_v1

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location evalfstop

Found invariant 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location evalfbb1in_v2

Analysing control-flow refined program

MPRF for transition t₆₇: evalfbb4in_v1(X₀, X₁) → evalfbbin_v1(X₀, X₁) :|: 1 ≤ C ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• evalfbb2in_v1: [X₀-1]
• evalfbb3in_v3: [X₀+X₁-1]
• evalfbb4in_v1: [X₀+X₁-1]
• evalfbbin_v1: [X₀+X₁-2]

MPRF for transition t₆₈: evalfbb4in_v1(X₀, X₁) → evalfbbin_v1(X₀, X₁) :|: 1+C ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• evalfbb2in_v1: [X₀-1]
• evalfbb3in_v3: [X₀+X₁-1]
• evalfbb4in_v1: [X₀+X₁-1]
• evalfbbin_v1: [X₀+X₁-2]

MPRF for transition t₆₉: evalfbbin_v1(X₀, X₁) → evalfbb2in_v1(X₀, X₁) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

• evalfbb2in_v1: [X₀-X₁]
• evalfbb3in_v3: [X₀]
• evalfbb4in_v1: [X₀]
• evalfbbin_v1: [1+X₀-X₁]

MPRF for transition t₈₁: evalfbb2in_v1(X₀, X₁) → evalfbb3in_v3(X₀-X₁, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

• evalfbb2in_v1: [1+X₀-X₁]
• evalfbb3in_v3: [X₀]
• evalfbb4in_v1: [X₀]
• evalfbbin_v1: [X₀]

MPRF for transition t₈₃: evalfbb3in_v3(X₀, X₁) → evalfbb4in_v1(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

• evalfbb2in_v1: [1+X₀-X₁]
• evalfbb3in_v3: [1+X₀]
• evalfbb4in_v1: [X₀]
• evalfbbin_v1: [X₀]

MPRF for transition t₇₂: evalfbb3in_v1(X₀, X₁) → evalfbb4in_v2(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₀+2⋅X₁+2 {O(n)}

MPRF:

• evalfbb1in_v2: [X₁-X₀]
• evalfbb3in_v1: [1+X₁-X₀]
• evalfbb4in_v2: [X₁-X₀]
• evalfbbin_v2: [X₁-X₀]

MPRF for transition t₇₄: evalfbb4in_v2(X₀, X₁) → evalfbbin_v2(X₀, X₁) :|: 1 ≤ C ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₀+2⋅X₁+2 {O(n)}

MPRF:

• evalfbb1in_v2: [X₁-X₀]
• evalfbb3in_v1: [1+X₁-X₀]
• evalfbb4in_v2: [1+X₁-X₀]
• evalfbbin_v2: [X₁-X₀]

MPRF for transition t₇₅: evalfbb4in_v2(X₀, X₁) → evalfbbin_v2(X₀, X₁) :|: 1+C ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₀+2⋅X₁+2 {O(n)}

MPRF:

• evalfbb1in_v2: [X₁-X₀]
• evalfbb3in_v1: [1+X₁-X₀]
• evalfbb4in_v2: [1+X₁-X₀]
• evalfbbin_v2: [X₁-X₀]

MPRF for transition t₇₇: evalfbbin_v2(X₀, X₁) → evalfbb1in_v2(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₀+2⋅X₁+1 {O(n)}

MPRF:

• evalfbb1in_v2: [X₁-1-X₀]
• evalfbb3in_v1: [X₁-X₀]
• evalfbb4in_v2: [X₁-X₀]
• evalfbbin_v2: [X₁-X₀]

MPRF for transition t₇₈: evalfbb1in_v2(X₀, X₁) → evalfbb3in_v1(1+X₀, X₁) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ of depth 1:

new bound:

2⋅X₀+2⋅X₁+1 {O(n)}

MPRF:

• evalfbb1in_v2: [X₁-X₀]
• evalfbb3in_v1: [X₁-X₀]
• evalfbb4in_v2: [X₁-X₀]
• evalfbbin_v2: [X₁-X₀]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n)

cfr-program:

Start: evalfstart
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: evalfbb1in_v1, evalfbb1in_v2, evalfbb2in_v1, evalfbb2in_v2, evalfbb3in, evalfbb3in_v1, evalfbb3in_v2, evalfbb3in_v3, evalfbb4in_v1, evalfbb4in_v2, evalfbbin_v1, evalfbbin_v2, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
t₇₁: evalfbb1in_v1(X₀, X₁) → evalfbb3in_v1(1+X₀, X₁) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁
t₇₈: evalfbb1in_v2(X₀, X₁) → evalfbb3in_v1(1+X₀, X₁) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁
t₈₁: evalfbb2in_v1(X₀, X₁) → evalfbb3in_v3(X₀-X₁, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀
t₇₉: evalfbb2in_v2(X₀, X₁) → evalfbb3in_v2(X₀-X₁, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₆₅: evalfbb3in(X₀, X₁) → evalfbb4in_v1(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 3 ≤ X₀+X₁
t₇₂: evalfbb3in_v1(X₀, X₁) → evalfbb4in_v2(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁
t₈₀: evalfbb3in_v2(X₀, X₁) → evalfreturnin(X₀, X₁) :|: X₀ ≤ 0 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁
t₈₃: evalfbb3in_v3(X₀, X₁) → evalfbb4in_v1(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₈₂: evalfbb3in_v3(X₀, X₁) → evalfreturnin(X₀, X₁) :|: X₀ ≤ 0 ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₆₇: evalfbb4in_v1(X₀, X₁) → evalfbbin_v1(X₀, X₁) :|: 1 ≤ C ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₆₈: evalfbb4in_v1(X₀, X₁) → evalfbbin_v1(X₀, X₁) :|: 1+C ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₆₆: evalfbb4in_v1(X₀, X₁) → evalfreturnin(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₇₄: evalfbb4in_v2(X₀, X₁) → evalfbbin_v2(X₀, X₁) :|: 1 ≤ C ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁
t₇₅: evalfbb4in_v2(X₀, X₁) → evalfbbin_v2(X₀, X₁) :|: 1+C ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁
t₇₃: evalfbb4in_v2(X₀, X₁) → evalfreturnin(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁
t₇₀: evalfbbin_v1(X₀, X₁) → evalfbb1in_v1(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₆₉: evalfbbin_v1(X₀, X₁) → evalfbb2in_v1(X₀, X₁) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁
t₇₇: evalfbbin_v2(X₀, X₁) → evalfbb1in_v2(X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁
t₇₆: evalfbbin_v2(X₀, X₁) → evalfbb2in_v2(X₀, X₁) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁
t₁: evalfentryin(X₀, X₁) → evalfbb3in(X₁, X₀) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁
t₁₁: evalfreturnin(X₀, X₁) → evalfstop(X₀, X₁) :|: 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₀: evalfstart(X₀, X₁) → evalfentryin(X₀, X₁)

All Bounds

Timebounds

Overall timebound:12⋅X₀+15⋅X₁+22 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₁₁: 1 {O(1)}
t₆₅: 1 {O(1)}
t₆₆: 1 {O(1)}
t₆₇: X₀+X₁+1 {O(n)}
t₆₈: X₀+X₁+1 {O(n)}
t₆₉: X₁ {O(n)}
t₇₀: 1 {O(1)}
t₇₁: 1 {O(1)}
t₇₂: 2⋅X₀+2⋅X₁+2 {O(n)}
t₇₃: 1 {O(1)}
t₇₄: 2⋅X₀+2⋅X₁+2 {O(n)}
t₇₅: 2⋅X₀+2⋅X₁+2 {O(n)}
t₇₆: 1 {O(1)}
t₇₇: 2⋅X₀+2⋅X₁+1 {O(n)}
t₇₈: 2⋅X₀+2⋅X₁+1 {O(n)}
t₇₉: 1 {O(1)}
t₈₀: 1 {O(1)}
t₈₁: X₁ {O(n)}
t₈₂: 1 {O(1)}
t₈₃: X₁ {O(n)}

Costbounds

Overall costbound: 12⋅X₀+15⋅X₁+22 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₁₁: 1 {O(1)}
t₆₅: 1 {O(1)}
t₆₆: 1 {O(1)}
t₆₇: X₀+X₁+1 {O(n)}
t₆₈: X₀+X₁+1 {O(n)}
t₆₉: X₁ {O(n)}
t₇₀: 1 {O(1)}
t₇₁: 1 {O(1)}
t₇₂: 2⋅X₀+2⋅X₁+2 {O(n)}
t₇₃: 1 {O(1)}
t₇₄: 2⋅X₀+2⋅X₁+2 {O(n)}
t₇₅: 2⋅X₀+2⋅X₁+2 {O(n)}
t₇₆: 1 {O(1)}
t₇₇: 2⋅X₀+2⋅X₁+1 {O(n)}
t₇₈: 2⋅X₀+2⋅X₁+1 {O(n)}
t₇₉: 1 {O(1)}
t₈₀: 1 {O(1)}
t₈₁: X₁ {O(n)}
t₈₂: 1 {O(1)}
t₈₃: X₁ {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁₁, X₀: 2⋅X₀+6⋅X₁+2 {O(n)}
t₁₁, X₁: 9⋅X₀ {O(n)}
t₆₅, X₀: X₁ {O(n)}
t₆₅, X₁: X₀ {O(n)}
t₆₆, X₀: 2⋅X₁ {O(n)}
t₆₆, X₁: 2⋅X₀ {O(n)}
t₆₇, X₀: X₁ {O(n)}
t₆₇, X₁: X₀ {O(n)}
t₆₈, X₀: X₁ {O(n)}
t₆₈, X₁: X₀ {O(n)}
t₆₉, X₀: X₁ {O(n)}
t₆₉, X₁: X₀ {O(n)}
t₇₀, X₀: 2⋅X₁ {O(n)}
t₇₀, X₁: 2⋅X₀ {O(n)}
t₇₁, X₀: 2⋅X₁+1 {O(n)}
t₇₁, X₁: 2⋅X₀ {O(n)}
t₇₂, X₀: 2⋅X₀+4⋅X₁+2 {O(n)}
t₇₂, X₁: 2⋅X₀ {O(n)}
t₇₃, X₀: 2⋅X₀+4⋅X₁+2 {O(n)}
t₇₃, X₁: 2⋅X₀ {O(n)}
t₇₄, X₀: 2⋅X₀+4⋅X₁+2 {O(n)}
t₇₄, X₁: 2⋅X₀ {O(n)}
t₇₅, X₀: 2⋅X₀+4⋅X₁+2 {O(n)}
t₇₅, X₁: 2⋅X₀ {O(n)}
t₇₆, X₀: 4⋅X₀+8⋅X₁+4 {O(n)}
t₇₆, X₁: 4⋅X₀ {O(n)}
t₇₇, X₀: 2⋅X₀+4⋅X₁+2 {O(n)}
t₇₇, X₁: 2⋅X₀ {O(n)}
t₇₈, X₀: 2⋅X₀+4⋅X₁+2 {O(n)}
t₇₈, X₁: 2⋅X₀ {O(n)}
t₇₉, X₀: 0 {O(1)}
t₇₉, X₁: 4⋅X₀ {O(n)}
t₈₀, X₀: 0 {O(1)}
t₈₀, X₁: 4⋅X₀ {O(n)}
t₈₁, X₀: X₁ {O(n)}
t₈₁, X₁: X₀ {O(n)}
t₈₂, X₀: 0 {O(1)}
t₈₂, X₁: X₀ {O(n)}
t₈₃, X₀: X₁ {O(n)}
t₈₃, X₁: X₀ {O(n)}