KoAT2 Proof Output

Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
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, X₄, X₅) → eval_foo_bb1_in(X₄, X₅, X₂, X₃, X₄, X₅) :|: X₂ ≤ 1+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₄ ≤ 0
t₂: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₃
t₃: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2+X₃ ≤ X₂
t₄: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₄
t₅: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀
t₆: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₁
t₇: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ 0 ∧ 1+X₁ ≤ 0
t₈: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb1_in(X₀+X₂-1-X₃, X₁+X₃-1-X₂, X₂, X₃, X₄, X₅)
t₉: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅)
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Found invariant 1+X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ for location eval_foo_bb2_in

Found invariant 1+X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
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, X₄, X₅) → eval_foo_bb1_in(X₄, X₅, X₂, X₃, X₄, X₅) :|: X₂ ≤ 1+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₄ ≤ 0
t₂: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₃
t₃: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2+X₃ ≤ X₂
t₄: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₄
t₅: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ X₂ ≤ 1+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₄ ≤ 0
t₆: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₄ ≤ 0
t₇: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ 0 ∧ 1+X₁ ≤ 0 ∧ X₂ ≤ 1+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₄ ≤ 0
t₈: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb1_in(X₀+X₂-1-X₃, X₁+X₃-1-X₂, X₂, X₃, X₄, X₅) :|: X₂ ≤ 1+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₄ ≤ 0
t₉: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅)
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

MPRF for transition t₆: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₁ ∧ X₂ ≤ 1+X₃ ∧ 1+X₃ ≤ X₂ ∧ 1+X₄ ≤ 0 of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

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

Cut unsatisfiable transition [t₅₂: eval_foo_bb1_in→eval_foo_bb2_in_v2]

Found invariant 0 ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 1+X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ for location eval_foo_bb1_in_v1

Found invariant 0 ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 1+X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ for location eval_foo_bb1_in_v3

Found invariant 0 ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 1+X₄ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ for location eval_foo_bb1_in_v2

Found invariant 0 ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 0 ≤ X₀ for location eval_foo_bb2_in_v2

Found invariant X₅ ≤ X₁ ∧ X₁ ≤ X₅ ∧ 1+X₄ ≤ 0 ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1+X₀ ≤ 0 for location eval_foo_bb1_in

Found invariant 0 ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 0 ≤ X₁ for location eval_foo_bb2_in_v1

Found invariant 0 ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb2_in_v3

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: inf {Infinity}
t₆: X₅+1 {O(n)}
t₇: 1 {O(1)}
t₈: inf {Infinity}
t₉: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: inf {Infinity}
t₆: X₅+1 {O(n)}
t₇: 1 {O(1)}
t₈: inf {Infinity}
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)}
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: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₅ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₅, X₀: X₄ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₆, X₀: X₄ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₇, X₀: 2⋅X₄ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₃ {O(n)}
t₇, X₄: 2⋅X₄ {O(n)}
t₇, X₅: 2⋅X₅ {O(n)}
t₈, X₀: X₄ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₉, X₀: 2⋅X₄+3⋅X₀ {O(n)}
t₉, X₂: 5⋅X₂ {O(n)}
t₉, X₃: 5⋅X₃ {O(n)}
t₉, X₄: 5⋅X₄ {O(n)}
t₉, X₅: 5⋅X₅ {O(n)}