KoAT2 Proof Output

Initial Problem

Start: eval_speedDis1_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_speedDis1_bb0_in, eval_speedDis1_bb1_in, eval_speedDis1_bb2_in, eval_speedDis1_bb3_in, eval_speedDis1_start, eval_speedDis1_stop
Transitions:
t₁: eval_speedDis1_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb1_in(X₄, X₅, X₂, X₃, X₄, X₅)
t₂: eval_speedDis1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃
t₃: eval_speedDis1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₀
t₄: eval_speedDis1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb1_in(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₂
t₅: eval_speedDis1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb1_in(1+X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₂ ∧ X₂ ≤ X₁
t₆: eval_speedDis1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₂ ∧ X₂ ≤ X₁
t₇: eval_speedDis1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb1_in(1+X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₁
t₈: eval_speedDis1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_stop(X₀, X₁, X₂, X₃, X₄, X₅)
t₀: eval_speedDis1_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Cut unsatisfiable transition [t₅: eval_speedDis1_bb2_in→eval_speedDis1_bb1_in; t₆: eval_speedDis1_bb2_in→eval_speedDis1_bb1_in]

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location eval_speedDis1_bb1_in

Found invariant X₅ ≤ X₁ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1+X₀ ≤ X₃ for location eval_speedDis1_bb2_in

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₀ for location eval_speedDis1_stop

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₀ for location eval_speedDis1_bb3_in

Problem after Preprocessing

Start: eval_speedDis1_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_speedDis1_bb0_in, eval_speedDis1_bb1_in, eval_speedDis1_bb2_in, eval_speedDis1_bb3_in, eval_speedDis1_start, eval_speedDis1_stop
Transitions:
t₁: eval_speedDis1_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb1_in(X₄, X₅, X₂, X₃, X₄, X₅)
t₂: eval_speedDis1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₃: eval_speedDis1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₄: eval_speedDis1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb1_in(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₇: eval_speedDis1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb1_in(1+X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₈: eval_speedDis1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₀: eval_speedDis1_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

MPRF for transition t₄: eval_speedDis1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb1_in(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁ of depth 1:

new bound:

X₂+X₅ {O(n)}

MPRF:

• eval_speedDis1_bb1_in: [X₂-X₁]
• eval_speedDis1_bb2_in: [X₂-X₁]

MPRF for transition t₇: eval_speedDis1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb1_in(1+X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF:

• eval_speedDis1_bb1_in: [X₃-X₀]
• eval_speedDis1_bb2_in: [X₃-X₀]

knowledge_propagation leads to new time bound X₂+X₃+X₄+X₅+1 {O(n)} for transition t₂: eval_speedDis1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_speedDis1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁

All Bounds

Timebounds

Overall timebound:2⋅X₂+2⋅X₃+2⋅X₄+2⋅X₅+5 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+X₃+X₄+X₅+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₂+X₅ {O(n)}
t₇: X₃+X₄ {O(n)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₂+2⋅X₃+2⋅X₄+2⋅X₅+5 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+X₃+X₄+X₅+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₂+X₅ {O(n)}
t₇: X₃+X₄ {O(n)}
t₈: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₅ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: 2⋅X₄+X₃ {O(n)}
t₂, X₁: 2⋅X₅+X₂ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 3⋅X₄+X₃ {O(n)}
t₃, X₁: 3⋅X₅+X₂ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₀: 2⋅X₄+X₃ {O(n)}
t₄, X₁: 2⋅X₅+X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₇, X₀: 2⋅X₄+X₃ {O(n)}
t₇, X₁: 2⋅X₅+X₂ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₈, X₀: 3⋅X₄+X₃ {O(n)}
t₈, X₁: 3⋅X₅+X₂ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₈, X₃: 2⋅X₃ {O(n)}
t₈, X₄: 2⋅X₄ {O(n)}
t₈, X₅: 2⋅X₅ {O(n)}