KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location eval_zwritehexstring_at_extracted_bb2_in

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 64 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 128 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 63+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 64 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_zwritehexstring_at_extracted_bb3_in

Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location eval_zwritehexstring_at_extracted_bb5_in

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 65 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 63+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 64 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_zwritehexstring_at_extracted_bb4_in

Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location eval_zwritehexstring_at_extracted_stop

Found invariant X₀ ≤ X₃ for location eval_zwritehexstring_at_extracted_bb1_in

Problem after Preprocessing

Start: eval_zwritehexstring_at_extracted_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_zwritehexstring_at_extracted_bb0_in, eval_zwritehexstring_at_extracted_bb1_in, eval_zwritehexstring_at_extracted_bb2_in, eval_zwritehexstring_at_extracted_bb3_in, eval_zwritehexstring_at_extracted_bb4_in, eval_zwritehexstring_at_extracted_bb5_in, eval_zwritehexstring_at_extracted_start, eval_zwritehexstring_at_extracted_stop
Transitions:
t₁: eval_zwritehexstring_at_extracted_bb0_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb1_in(X₃, X₁, X₂, X₃)
t₂: eval_zwritehexstring_at_extracted_bb1_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb2_in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₀ ≤ X₃
t₃: eval_zwritehexstring_at_extracted_bb1_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb5_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ X₃
t₄: eval_zwritehexstring_at_extracted_bb2_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb3_in(X₀, X₀, X₀, X₃) :|: X₀ ≤ 63 ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃
t₅: eval_zwritehexstring_at_extracted_bb2_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb3_in(X₀, 64, 64, X₃) :|: 64 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃
t₆: eval_zwritehexstring_at_extracted_bb3_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb3_in(X₀, X₁, X₂-1, X₃) :|: 2 ≤ X₂ ∧ X₁+X₂ ≤ 128 ∧ X₁ ≤ 64 ∧ X₂ ≤ 64 ∧ X₁ ≤ 63+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₃
t₇: eval_zwritehexstring_at_extracted_bb3_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb4_in(X₀, X₁, X₂, X₃) :|: X₂ ≤ 1 ∧ X₁+X₂ ≤ 128 ∧ X₁ ≤ 64 ∧ X₂ ≤ 64 ∧ X₁ ≤ 63+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₃
t₈: eval_zwritehexstring_at_extracted_bb4_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb1_in(X₀-X₁, X₁, X₂, X₃) :|: X₁+X₂ ≤ 65 ∧ X₁ ≤ 64 ∧ X₁ ≤ 63+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₃
t₉: eval_zwritehexstring_at_extracted_bb5_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_stop(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ X₃
t₀: eval_zwritehexstring_at_extracted_start(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb0_in(X₀, X₁, X₂, X₃)

MPRF for transition t₂: eval_zwritehexstring_at_extracted_bb1_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb2_in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

• eval_zwritehexstring_at_extracted_bb1_in: [X₀]
• eval_zwritehexstring_at_extracted_bb2_in: [X₀-1]
• eval_zwritehexstring_at_extracted_bb3_in: [X₀-1]
• eval_zwritehexstring_at_extracted_bb4_in: [X₀-1]

MPRF for transition t₄: eval_zwritehexstring_at_extracted_bb2_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb3_in(X₀, X₀, X₀, X₃) :|: X₀ ≤ 63 ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

• eval_zwritehexstring_at_extracted_bb1_in: [X₀]
• eval_zwritehexstring_at_extracted_bb2_in: [X₀]
• eval_zwritehexstring_at_extracted_bb3_in: [X₀-1]
• eval_zwritehexstring_at_extracted_bb4_in: [X₀-X₁]

MPRF for transition t₅: eval_zwritehexstring_at_extracted_bb2_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb3_in(X₀, 64, 64, X₃) :|: 64 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

• eval_zwritehexstring_at_extracted_bb1_in: [1+X₀]
• eval_zwritehexstring_at_extracted_bb2_in: [1+X₀]
• eval_zwritehexstring_at_extracted_bb3_in: [X₀]
• eval_zwritehexstring_at_extracted_bb4_in: [1+X₀-X₂]

MPRF for transition t₆: eval_zwritehexstring_at_extracted_bb3_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb3_in(X₀, X₁, X₂-1, X₃) :|: 2 ≤ X₂ ∧ X₁+X₂ ≤ 128 ∧ X₁ ≤ 64 ∧ X₂ ≤ 64 ∧ X₁ ≤ 63+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₃ of depth 1:

new bound:

63⋅X₃+1 {O(n)}

MPRF:

• eval_zwritehexstring_at_extracted_bb1_in: [63⋅X₀-1]
• eval_zwritehexstring_at_extracted_bb2_in: [63⋅X₀-1]
• eval_zwritehexstring_at_extracted_bb3_in: [63⋅X₀+X₂-65]
• eval_zwritehexstring_at_extracted_bb4_in: [63⋅X₀+64⋅X₂-65-63⋅X₁]

MPRF for transition t₇: eval_zwritehexstring_at_extracted_bb3_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb4_in(X₀, X₁, X₂, X₃) :|: X₂ ≤ 1 ∧ X₁+X₂ ≤ 128 ∧ X₁ ≤ 64 ∧ X₂ ≤ 64 ∧ X₁ ≤ 63+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₃ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

• eval_zwritehexstring_at_extracted_bb1_in: [X₀]
• eval_zwritehexstring_at_extracted_bb2_in: [X₀]
• eval_zwritehexstring_at_extracted_bb3_in: [X₀]
• eval_zwritehexstring_at_extracted_bb4_in: [X₀-1]

MPRF for transition t₈: eval_zwritehexstring_at_extracted_bb4_in(X₀, X₁, X₂, X₃) → eval_zwritehexstring_at_extracted_bb1_in(X₀-X₁, X₁, X₂, X₃) :|: X₁+X₂ ≤ 65 ∧ X₁ ≤ 64 ∧ X₁ ≤ 63+X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₃ of depth 1:

new bound:

X₃+126 {O(n)}

MPRF:

• eval_zwritehexstring_at_extracted_bb1_in: [126+X₀]
• eval_zwritehexstring_at_extracted_bb2_in: [126+X₀]
• eval_zwritehexstring_at_extracted_bb3_in: [126+X₀]
• eval_zwritehexstring_at_extracted_bb4_in: [127+X₀-X₁]

All Bounds

Timebounds

Overall timebound:68⋅X₃+132 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃ {O(n)}
t₃: 1 {O(1)}
t₄: X₃ {O(n)}
t₅: X₃+1 {O(n)}
t₆: 63⋅X₃+1 {O(n)}
t₇: X₃ {O(n)}
t₈: X₃+126 {O(n)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: 68⋅X₃+132 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃ {O(n)}
t₃: 1 {O(1)}
t₄: X₃ {O(n)}
t₅: X₃+1 {O(n)}
t₆: 63⋅X₃+1 {O(n)}
t₇: X₃ {O(n)}
t₈: X₃+126 {O(n)}
t₉: 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: X₃ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₃+63 {O(n)}
t₂, X₁: X₁+64 {O(n)}
t₂, X₂: X₂+1 {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: 2⋅X₃+63 {O(n)}
t₃, X₁: X₁+64 {O(n)}
t₃, X₂: X₂+1 {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₄, X₀: 63 {O(1)}
t₄, X₁: 63 {O(1)}
t₄, X₂: 63 {O(1)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₃+63 {O(n)}
t₅, X₁: 64 {O(1)}
t₅, X₂: 64 {O(1)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₃+63 {O(n)}
t₆, X₁: 64 {O(1)}
t₆, X₂: 63 {O(1)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₃+63 {O(n)}
t₇, X₁: 64 {O(1)}
t₇, X₂: 1 {O(1)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₃+63 {O(n)}
t₈, X₁: 64 {O(1)}
t₈, X₂: 1 {O(1)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: 2⋅X₃+63 {O(n)}
t₉, X₁: X₁+64 {O(n)}
t₉, X₂: X₂+1 {O(n)}
t₉, X₃: 2⋅X₃ {O(n)}