KoAT2 Proof Output

Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₂, X₃, X₂, X₃)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀
t₆: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(1+X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₇: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₈: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(1+X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₉: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃)
t₀: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

Preprocessing

Cut unsatisfiable transition [t₆: eval_foo_bb2_in→eval_foo_bb1_in; t₇: eval_foo_bb2_in→eval_foo_bb1_in]

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location eval_foo_bb2_in

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location eval_foo_bb1_in

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location eval_foo_stop

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location eval_foo_bb3_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₂, X₃, X₂, X₃)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₈: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(1+X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₉: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁
t₀: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

MPRF for transition t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ of depth 1:

new bound:

X₂+X₃ {O(n)}

MPRF:

• eval_foo_bb1_in: [X₁-X₀]
• eval_foo_bb2_in: [X₁-1-X₀]

MPRF for transition t₈: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(1+X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF:

• eval_foo_bb1_in: [1+X₁-X₀]
• eval_foo_bb2_in: [1+X₁-X₀]

MPRF for transition t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ of depth 1:

new bound:

2⋅X₂⋅X₂+2⋅X₃⋅X₃+4⋅X₂⋅X₃+6⋅X₂+6⋅X₃+5 {O(n^2)}

MPRF:

• eval_foo_bb1_in: [2+X₀-X₁]
• eval_foo_bb2_in: [1+X₀-X₁]

MPRF for transition t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ of depth 1:

new bound:

2⋅X₂⋅X₂+2⋅X₃⋅X₃+4⋅X₂⋅X₃+5⋅X₂+5⋅X₃+3 {O(n^2)}

MPRF:

• eval_foo_bb1_in: [1+X₀-X₁]
• eval_foo_bb2_in: [1+X₀-X₁]

Found invariant X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ for location eval_foo_bb1_in_v1

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ for location eval_foo_bb1_in_v2

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location eval_foo_stop

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location eval_foo_bb3_in

Found invariant 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location eval_foo_bb2_in_v4

Found invariant X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location eval_foo_bb2_in_v2

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location eval_foo_bb1_in

Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location eval_foo_bb2_in_v1

Found invariant X₃ ≤ X₁ ∧ 2+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location eval_foo_bb2_in_v3

Analysing control-flow refined program

MPRF for transition t₆₁: eval_foo_bb1_in_v2(X₀, X₁, X₂, X₃) → eval_foo_bb2_in_v4(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ of depth 1:

new bound:

X₂+X₃+2 {O(n)}

MPRF:

• eval_foo_bb1_in_v2: [1+X₀-X₁]
• eval_foo_bb2_in_v4: [X₀-X₁]

MPRF for transition t₆₂: eval_foo_bb2_in_v4(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v2(X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 2+X₃ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF:

• eval_foo_bb1_in_v2: [X₀-X₁]
• eval_foo_bb2_in_v4: [X₀-X₁]

MPRF for transition t₅₇: eval_foo_bb1_in_v1(X₀, X₁, X₂, X₃) → eval_foo_bb2_in_v3(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ X₀ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₂+X₃+2 {O(n)}

MPRF:

• eval_foo_bb1_in_v1: [1+X₃-X₀]
• eval_foo_bb2_in_v3: [X₃-X₀]

MPRF for transition t₅₈: eval_foo_bb2_in_v3(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v1(1+X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₂+X₃+2 {O(n)}

MPRF:

• eval_foo_bb1_in_v1: [1+X₃-X₀]
• eval_foo_bb2_in_v3: [1+X₃-X₀]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n)

cfr-program:

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb1_in_v1, eval_foo_bb1_in_v2, eval_foo_bb2_in_v1, eval_foo_bb2_in_v2, eval_foo_bb2_in_v3, eval_foo_bb2_in_v4, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₂, X₃, X₂, X₃)
t₅₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in_v1(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₅₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in_v2(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₅₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₅₇: eval_foo_bb1_in_v1(X₀, X₁, X₂, X₃) → eval_foo_bb2_in_v3(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ X₀ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₅₆: eval_foo_bb1_in_v1(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ X₀ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₆₁: eval_foo_bb1_in_v2(X₀, X₁, X₂, X₃) → eval_foo_bb2_in_v4(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂
t₆₀: eval_foo_bb1_in_v2(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂
t₅₉: eval_foo_bb2_in_v1(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v2(X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₅₅: eval_foo_bb2_in_v2(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v1(1+X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₅₈: eval_foo_bb2_in_v3(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v1(1+X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₆₂: eval_foo_bb2_in_v4(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v2(X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 2+X₃ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁
t₉: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁
t₀: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

All Bounds

Timebounds

Overall timebound:4⋅X₂+4⋅X₃+18 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 1 {O(1)}
t₉: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₇: X₂+X₃+2 {O(n)}
t₅₈: X₂+X₃+2 {O(n)}
t₅₉: 1 {O(1)}
t₆₀: 1 {O(1)}
t₆₁: X₂+X₃+2 {O(n)}
t₆₂: X₂+X₃+1 {O(n)}

Costbounds

Overall costbound: 4⋅X₂+4⋅X₃+18 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 1 {O(1)}
t₉: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₇: X₂+X₃+2 {O(n)}
t₅₈: X₂+X₃+2 {O(n)}
t₅₉: 1 {O(1)}
t₆₀: 1 {O(1)}
t₆₁: X₂+X₃+2 {O(n)}
t₆₂: X₂+X₃+1 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₃ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₉, X₀: 7⋅X₂+X₃+5 {O(n)}
t₉, X₁: 7⋅X₃+X₂+4 {O(n)}
t₉, X₂: 6⋅X₂ {O(n)}
t₉, X₃: 6⋅X₃ {O(n)}
t₅₂, X₀: X₂ {O(n)}
t₅₂, X₁: X₃ {O(n)}
t₅₂, X₂: X₂ {O(n)}
t₅₂, X₃: X₃ {O(n)}
t₅₃, X₀: X₂ {O(n)}
t₅₃, X₁: X₃ {O(n)}
t₅₃, X₂: X₂ {O(n)}
t₅₃, X₃: X₃ {O(n)}
t₅₄, X₀: X₂ {O(n)}
t₅₄, X₁: X₃ {O(n)}
t₅₄, X₂: X₂ {O(n)}
t₅₄, X₃: X₃ {O(n)}
t₅₅, X₀: X₂+1 {O(n)}
t₅₅, X₁: X₃ {O(n)}
t₅₅, X₂: X₂ {O(n)}
t₅₅, X₃: X₃ {O(n)}
t₅₆, X₀: 3⋅X₂+X₃+5 {O(n)}
t₅₆, X₁: 2⋅X₃ {O(n)}
t₅₆, X₂: 2⋅X₂ {O(n)}
t₅₆, X₃: 2⋅X₃ {O(n)}
t₅₇, X₀: 2⋅X₂+X₃+4 {O(n)}
t₅₇, X₁: X₃ {O(n)}
t₅₇, X₂: X₂ {O(n)}
t₅₇, X₃: X₃ {O(n)}
t₅₈, X₀: 2⋅X₂+X₃+4 {O(n)}
t₅₈, X₁: X₃ {O(n)}
t₅₈, X₂: X₂ {O(n)}
t₅₈, X₃: X₃ {O(n)}
t₅₉, X₀: X₂ {O(n)}
t₅₉, X₁: X₃+1 {O(n)}
t₅₉, X₂: X₂ {O(n)}
t₅₉, X₃: X₃ {O(n)}
t₆₀, X₀: 2⋅X₂ {O(n)}
t₆₀, X₁: 3⋅X₃+X₂+4 {O(n)}
t₆₀, X₂: 2⋅X₂ {O(n)}
t₆₀, X₃: 2⋅X₃ {O(n)}
t₆₁, X₀: X₂ {O(n)}
t₆₁, X₁: 2⋅X₃+X₂+4 {O(n)}
t₆₁, X₂: X₂ {O(n)}
t₆₁, X₃: X₃ {O(n)}
t₆₂, X₀: X₂ {O(n)}
t₆₂, X₁: 2⋅X₃+X₂+3 {O(n)}
t₆₂, X₂: X₂ {O(n)}
t₆₂, X₃: X₃ {O(n)}