KoAT2 Proof Output

Initial Problem

Start: evalexministart
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: evalexminibb1in, evalexminibbin, evalexminientryin, evalexminireturnin, evalexministart, evalexministop
Transitions:
t₂: evalexminibb1in(X₀, X₁, X₂) → evalexminibbin(X₀, X₁, X₂) :|: X₁ ≤ 100 ∧ X₂ ≤ X₀
t₃: evalexminibb1in(X₀, X₁, X₂) → evalexminireturnin(X₀, X₁, X₂) :|: 101 ≤ X₁
t₄: evalexminibb1in(X₀, X₁, X₂) → evalexminireturnin(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂
t₅: evalexminibbin(X₀, X₁, X₂) → evalexminibb1in(X₀-1, X₂, 1+X₁)
t₁: evalexminientryin(X₀, X₁, X₂) → evalexminibb1in(X₁, X₀, X₂)
t₆: evalexminireturnin(X₀, X₁, X₂) → evalexministop(X₀, X₁, X₂)
t₀: evalexministart(X₀, X₁, X₂) → evalexminientryin(X₀, X₁, X₂)

Preprocessing

Found invariant X₂ ≤ X₀ ∧ X₁ ≤ 100 for location evalexminibbin

Problem after Preprocessing

Start: evalexministart
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: evalexminibb1in, evalexminibbin, evalexminientryin, evalexminireturnin, evalexministart, evalexministop
Transitions:
t₂: evalexminibb1in(X₀, X₁, X₂) → evalexminibbin(X₀, X₁, X₂) :|: X₁ ≤ 100 ∧ X₂ ≤ X₀
t₃: evalexminibb1in(X₀, X₁, X₂) → evalexminireturnin(X₀, X₁, X₂) :|: 101 ≤ X₁
t₄: evalexminibb1in(X₀, X₁, X₂) → evalexminireturnin(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂
t₅: evalexminibbin(X₀, X₁, X₂) → evalexminibb1in(X₀-1, X₂, 1+X₁) :|: X₁ ≤ 100 ∧ X₂ ≤ X₀
t₁: evalexminientryin(X₀, X₁, X₂) → evalexminibb1in(X₁, X₀, X₂)
t₆: evalexminireturnin(X₀, X₁, X₂) → evalexministop(X₀, X₁, X₂)
t₀: evalexministart(X₀, X₁, X₂) → evalexminientryin(X₀, X₁, X₂)

MPRF for transition t₂: evalexminibb1in(X₀, X₁, X₂) → evalexminibbin(X₀, X₁, X₂) :|: X₁ ≤ 100 ∧ X₂ ≤ X₀ of depth 1:

new bound:

X₀+X₁+X₂+101 {O(n)}

MPRF:

• evalexminibb1in: [101+X₀-X₁-X₂]
• evalexminibbin: [99+X₀-X₁-X₂]

MPRF for transition t₅: evalexminibbin(X₀, X₁, X₂) → evalexminibb1in(X₀-1, X₂, 1+X₁) :|: X₁ ≤ 100 ∧ X₂ ≤ X₀ of depth 1:

new bound:

X₀+X₁+X₂+102 {O(n)}

MPRF:

• evalexminibb1in: [102+X₀-X₁-X₂]
• evalexminibbin: [101+X₀-X₁-X₂]

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+2⋅X₂+208 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+X₂+101 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₀+X₁+X₂+102 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+2⋅X₂+208 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+X₂+101 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₀+X₁+X₂+102 {O(n)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: 2⋅X₁+X₀+X₂+102 {O(n)}
t₂, X₁: 2⋅X₀+2⋅X₂+X₁+102 {O(n)}
t₂, X₂: 2⋅X₀+2⋅X₂+X₁+102 {O(n)}
t₃, X₀: 3⋅X₁+X₀+X₂+102 {O(n)}
t₃, X₁: 2⋅X₂+3⋅X₀+X₁+102 {O(n)}
t₃, X₂: 2⋅X₀+3⋅X₂+X₁+102 {O(n)}
t₄, X₀: 3⋅X₁+X₀+X₂+102 {O(n)}
t₄, X₁: 2⋅X₂+3⋅X₀+X₁+102 {O(n)}
t₄, X₂: 2⋅X₀+3⋅X₂+X₁+102 {O(n)}
t₅, X₀: 2⋅X₁+X₀+X₂+102 {O(n)}
t₅, X₁: 2⋅X₀+2⋅X₂+X₁+102 {O(n)}
t₅, X₂: 2⋅X₀+2⋅X₂+X₁+102 {O(n)}
t₆, X₀: 2⋅X₀+2⋅X₂+6⋅X₁+204 {O(n)}
t₆, X₁: 2⋅X₁+4⋅X₂+6⋅X₀+204 {O(n)}
t₆, X₂: 2⋅X₁+4⋅X₀+6⋅X₂+204 {O(n)}