KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₃ ≤ 256 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 512 ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 256 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_cryptRandWriteFile_bb5_in

Found invariant X₃ ≤ 256 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 512 ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 256+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 256 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_cryptRandWriteFile_bb3_in

Found invariant 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location eval_cryptRandWriteFile_bb2_in

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 0 for location eval_cryptRandWriteFile_bb6_in

Found invariant X₀ ≤ X₂ for location eval_cryptRandWriteFile_bb1_in

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 0 for location eval_cryptRandWriteFile_stop

Found invariant X₃ ≤ 255 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 511 ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 256+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 256 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_cryptRandWriteFile_bb4_in

Problem after Preprocessing

Start: eval_cryptRandWriteFile_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_cryptRandWriteFile_bb0_in, eval_cryptRandWriteFile_bb1_in, eval_cryptRandWriteFile_bb2_in, eval_cryptRandWriteFile_bb3_in, eval_cryptRandWriteFile_bb4_in, eval_cryptRandWriteFile_bb5_in, eval_cryptRandWriteFile_bb6_in, eval_cryptRandWriteFile_start, eval_cryptRandWriteFile_stop
Transitions:
t₁: eval_cryptRandWriteFile_bb0_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb1_in(X₂, X₁, X₂, X₃)
t₂: eval_cryptRandWriteFile_bb1_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb2_in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂
t₃: eval_cryptRandWriteFile_bb1_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb6_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ X₂
t₄: eval_cryptRandWriteFile_bb2_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb3_in(X₀, X₀, X₂, 0) :|: X₀ ≤ 255 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂
t₅: eval_cryptRandWriteFile_bb2_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb3_in(X₀, 256, X₂, 0) :|: 256 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂
t₆: eval_cryptRandWriteFile_bb3_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb4_in(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 512 ∧ X₁ ≤ 256 ∧ X₁ ≤ 256+X₃ ∧ X₃ ≤ 256 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃
t₇: eval_cryptRandWriteFile_bb3_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb5_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₁+X₃ ≤ 512 ∧ X₁ ≤ 256 ∧ X₁ ≤ 256+X₃ ∧ X₃ ≤ 256 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃
t₈: eval_cryptRandWriteFile_bb4_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb3_in(X₀, X₁, X₂, 1+X₃) :|: X₁+X₃ ≤ 511 ∧ X₁ ≤ 256 ∧ X₁ ≤ 256+X₃ ∧ X₃ ≤ 255 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃
t₉: eval_cryptRandWriteFile_bb5_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb1_in(X₀-X₁, X₁, X₂, X₃) :|: X₁+X₃ ≤ 512 ∧ X₁ ≤ 256 ∧ X₃ ≤ 256 ∧ 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 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₂
t₁₀: eval_cryptRandWriteFile_bb6_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_stop(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ X₂
t₀: eval_cryptRandWriteFile_start(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb0_in(X₀, X₁, X₂, X₃)

MPRF for transition t₂: eval_cryptRandWriteFile_bb1_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb2_in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

• eval_cryptRandWriteFile_bb1_in: [X₀]
• eval_cryptRandWriteFile_bb2_in: [X₀-1]
• eval_cryptRandWriteFile_bb3_in: [X₀-1]
• eval_cryptRandWriteFile_bb4_in: [X₀-1]
• eval_cryptRandWriteFile_bb5_in: [X₀-1]

MPRF for transition t₄: eval_cryptRandWriteFile_bb2_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb3_in(X₀, X₀, X₂, 0) :|: X₀ ≤ 255 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

• eval_cryptRandWriteFile_bb1_in: [X₀]
• eval_cryptRandWriteFile_bb2_in: [X₀]
• eval_cryptRandWriteFile_bb3_in: [X₀-1]
• eval_cryptRandWriteFile_bb4_in: [X₀-1]
• eval_cryptRandWriteFile_bb5_in: [X₀-1]

MPRF for transition t₅: eval_cryptRandWriteFile_bb2_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb3_in(X₀, 256, X₂, 0) :|: 256 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

MPRF for transition t₆: eval_cryptRandWriteFile_bb3_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb4_in(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 512 ∧ X₁ ≤ 256 ∧ X₁ ≤ 256+X₃ ∧ X₃ ≤ 256 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₂+257 {O(n)}

MPRF:

• eval_cryptRandWriteFile_bb1_in: [257+X₀]
• eval_cryptRandWriteFile_bb2_in: [257+X₀]
• eval_cryptRandWriteFile_bb3_in: [257+X₀-X₃]
• eval_cryptRandWriteFile_bb4_in: [256+X₀-X₃]
• eval_cryptRandWriteFile_bb5_in: [257+X₀-X₃]

MPRF for transition t₇: eval_cryptRandWriteFile_bb3_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb5_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₁+X₃ ≤ 512 ∧ X₁ ≤ 256 ∧ X₁ ≤ 256+X₃ ∧ X₃ ≤ 256 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₂+255 {O(n)}

MPRF:

• eval_cryptRandWriteFile_bb1_in: [255+X₀]
• eval_cryptRandWriteFile_bb2_in: [255+X₀]
• eval_cryptRandWriteFile_bb3_in: [255+X₀]
• eval_cryptRandWriteFile_bb4_in: [255+X₀]
• eval_cryptRandWriteFile_bb5_in: [254+X₀]

MPRF for transition t₈: eval_cryptRandWriteFile_bb4_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb3_in(X₀, X₁, X₂, 1+X₃) :|: X₁+X₃ ≤ 511 ∧ X₁ ≤ 256 ∧ X₁ ≤ 256+X₃ ∧ X₃ ≤ 255 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₂+510 {O(n)}

MPRF:

• eval_cryptRandWriteFile_bb1_in: [510+X₀]
• eval_cryptRandWriteFile_bb2_in: [510+X₀]
• eval_cryptRandWriteFile_bb3_in: [510+X₀-X₃]
• eval_cryptRandWriteFile_bb4_in: [510+X₀-X₃]
• eval_cryptRandWriteFile_bb5_in: [510+X₀-X₃]

MPRF for transition t₉: eval_cryptRandWriteFile_bb5_in(X₀, X₁, X₂, X₃) → eval_cryptRandWriteFile_bb1_in(X₀-X₁, X₁, X₂, X₃) :|: X₁+X₃ ≤ 512 ∧ X₁ ≤ 256 ∧ X₃ ≤ 256 ∧ 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 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₂ of depth 1:

new bound:

X₂+255 {O(n)}

MPRF:

All Bounds

Timebounds

Overall timebound:7⋅X₂+1281 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂ {O(n)}
t₃: 1 {O(1)}
t₄: X₂ {O(n)}
t₅: X₂ {O(n)}
t₆: X₂+257 {O(n)}
t₇: X₂+255 {O(n)}
t₈: X₂+510 {O(n)}
t₉: X₂+255 {O(n)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 7⋅X₂+1281 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂ {O(n)}
t₃: 1 {O(1)}
t₄: X₂ {O(n)}
t₅: X₂ {O(n)}
t₆: X₂+257 {O(n)}
t₇: X₂+255 {O(n)}
t₈: X₂+510 {O(n)}
t₉: X₂+255 {O(n)}
t₁₀: 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: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₂+255 {O(n)}
t₂, X₁: X₁+256 {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃+256 {O(n)}
t₃, X₀: 2⋅X₂+255 {O(n)}
t₃, X₁: X₁+256 {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: X₃+256 {O(n)}
t₄, X₀: 255 {O(1)}
t₄, X₁: 255 {O(1)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: 0 {O(1)}
t₅, X₀: X₂+255 {O(n)}
t₅, X₁: 256 {O(1)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: 0 {O(1)}
t₆, X₀: X₂+255 {O(n)}
t₆, X₁: 256 {O(1)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: 255 {O(1)}
t₇, X₀: X₂+255 {O(n)}
t₇, X₁: 256 {O(1)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: 256 {O(1)}
t₈, X₀: X₂+255 {O(n)}
t₈, X₁: 256 {O(1)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: 256 {O(1)}
t₉, X₀: X₂+255 {O(n)}
t₉, X₁: 256 {O(1)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: 256 {O(1)}
t₁₀, X₀: 2⋅X₂+255 {O(n)}
t₁₀, X₁: X₁+256 {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₀, X₃: X₃+256 {O(n)}