KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ for location eval_t28_bb4_in

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location eval_t28_bb5_in

Found invariant X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location eval_t28_bb2_in

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁ for location eval_t28_bb3_in

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location eval_t28_bb7_in

Found invariant X₅ ≤ X₁ ∧ 1+X₄ ≤ 0 ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ 2+X₂+X₄ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location eval_t28_bb6_in

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location eval_t28_stop

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location eval_t28_bb1_in

Problem after Preprocessing

Start: eval_t28_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_t28_bb0_in, eval_t28_bb1_in, eval_t28_bb2_in, eval_t28_bb3_in, eval_t28_bb4_in, eval_t28_bb5_in, eval_t28_bb6_in, eval_t28_bb7_in, eval_t28_start, eval_t28_stop
Transitions:
t₁: eval_t28_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb1_in(X₄, X₅, X₂, X₃, X₄, X₅)
t₂: eval_t28_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₃: eval_t28_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb3_in(X₀, X₁, X₂, X₁, X₄, X₅) :|: X₀ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₄: eval_t28_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb1_in(999+X₀, 1000+X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₅: eval_t28_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₁
t₆: eval_t28_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb5_in(X₀, X₁, X₀, X₃, X₄, X₅) :|: X₃ ≤ 0 ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₁
t₇: eval_t28_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb3_in(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₁
t₈: eval_t28_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₂ ≤ 0 ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₃ ≤ 0
t₉: eval_t28_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₃ ≤ 0
t₁₀: eval_t28_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb5_in(X₀, X₁, 1+X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ 0 ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 1+X₂+X₃ ≤ 0 ∧ 1+X₃+X₄ ≤ 0 ∧ 1+X₄ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ 2+X₀+X₄ ≤ 0 ∧ 2+X₂+X₄ ≤ 0 ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₃ ≤ 0
t₁₁: eval_t28_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₃ ≤ 0
t₀: eval_t28_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

MPRF for transition t₂: eval_t28_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁ of depth 1:

new bound:

X₄+X₅ {O(n)}

MPRF:

• eval_t28_bb1_in: [X₀-X₁]
• eval_t28_bb2_in: [X₀-1-X₁]

MPRF for transition t₄: eval_t28_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb1_in(999+X₀, 1000+X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁ of depth 1:

new bound:

X₄+X₅ {O(n)}

MPRF:

• eval_t28_bb1_in: [X₀-X₁]
• eval_t28_bb2_in: [X₀-X₁]

MPRF for transition t₅: eval_t28_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₁ of depth 1:

new bound:

1000⋅X₄+1002⋅X₅ {O(n)}

MPRF:

• eval_t28_bb3_in: [X₃]
• eval_t28_bb4_in: [X₃-1]

MPRF for transition t₇: eval_t28_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb3_in(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₁ of depth 1:

new bound:

1000⋅X₄+1002⋅X₅ {O(n)}

MPRF:

• eval_t28_bb3_in: [X₃]
• eval_t28_bb4_in: [X₃]

MPRF for transition t₈: eval_t28_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₂ ≤ 0 ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₃ ≤ 0 of depth 1:

new bound:

1998⋅X₅+2002⋅X₄ {O(n)}

MPRF:

• eval_t28_bb5_in: [-X₂]
• eval_t28_bb6_in: [-1-X₂]

MPRF for transition t₁₀: eval_t28_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_t28_bb5_in(X₀, X₁, 1+X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ 0 ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 1+X₂+X₃ ≤ 0 ∧ 1+X₃+X₄ ≤ 0 ∧ 1+X₄ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ 2+X₀+X₄ ≤ 0 ∧ 2+X₂+X₄ ≤ 0 ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₃ ≤ 0 of depth 1:

new bound:

1998⋅X₅+2002⋅X₄ {O(n)}

MPRF:

• eval_t28_bb5_in: [-X₂]
• eval_t28_bb6_in: [-X₂]

All Bounds

Timebounds

Overall timebound:6002⋅X₅+6006⋅X₄+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄+X₅ {O(n)}
t₃: 1 {O(1)}
t₄: X₄+X₅ {O(n)}
t₅: 1000⋅X₄+1002⋅X₅ {O(n)}
t₆: 1 {O(1)}
t₇: 1000⋅X₄+1002⋅X₅ {O(n)}
t₈: 1998⋅X₅+2002⋅X₄ {O(n)}
t₉: 1 {O(1)}
t₁₀: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 6002⋅X₅+6006⋅X₄+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄+X₅ {O(n)}
t₃: 1 {O(1)}
t₄: X₄+X₅ {O(n)}
t₅: 1000⋅X₄+1002⋅X₅ {O(n)}
t₆: 1 {O(1)}
t₇: 1000⋅X₄+1002⋅X₅ {O(n)}
t₈: 1998⋅X₅+2002⋅X₄ {O(n)}
t₉: 1 {O(1)}
t₁₀: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₁: 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: 1000⋅X₄+999⋅X₅ {O(n)}
t₂, X₁: 1000⋅X₄+1001⋅X₅ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 1001⋅X₄+999⋅X₅ {O(n)}
t₃, X₁: 1000⋅X₄+1002⋅X₅ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 1000⋅X₄+1002⋅X₅ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₀: 1000⋅X₄+999⋅X₅ {O(n)}
t₄, X₁: 1000⋅X₄+1001⋅X₅ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₅, X₀: 1001⋅X₄+999⋅X₅ {O(n)}
t₅, X₁: 1000⋅X₄+1002⋅X₅ {O(n)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 1000⋅X₄+1002⋅X₅ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₅, X₅: 2⋅X₅ {O(n)}
t₆, X₀: 1998⋅X₅+2002⋅X₄ {O(n)}
t₆, X₁: 2000⋅X₄+2004⋅X₅ {O(n)}
t₆, X₂: 1998⋅X₅+2002⋅X₄ {O(n)}
t₆, X₃: 2000⋅X₄+2004⋅X₅ {O(n)}
t₆, X₄: 4⋅X₄ {O(n)}
t₆, X₅: 4⋅X₅ {O(n)}
t₇, X₀: 1001⋅X₄+999⋅X₅ {O(n)}
t₇, X₁: 1000⋅X₄+1002⋅X₅ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 1000⋅X₄+1002⋅X₅ {O(n)}
t₇, X₄: 2⋅X₄ {O(n)}
t₇, X₅: 2⋅X₅ {O(n)}
t₈, X₀: 1998⋅X₅+2002⋅X₄ {O(n)}
t₈, X₁: 2000⋅X₄+2004⋅X₅ {O(n)}
t₈, X₂: 1998⋅X₅+2002⋅X₄ {O(n)}
t₈, X₃: 2000⋅X₄+2004⋅X₅ {O(n)}
t₈, X₄: 4⋅X₄ {O(n)}
t₈, X₅: 4⋅X₅ {O(n)}
t₉, X₀: 3996⋅X₅+4004⋅X₄ {O(n)}
t₉, X₁: 4000⋅X₄+4008⋅X₅ {O(n)}
t₉, X₂: 3996⋅X₅+4004⋅X₄ {O(n)}
t₉, X₃: 4000⋅X₄+4008⋅X₅ {O(n)}
t₉, X₄: 8⋅X₄ {O(n)}
t₉, X₅: 8⋅X₅ {O(n)}
t₁₀, X₀: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₀, X₁: 2000⋅X₄+2004⋅X₅ {O(n)}
t₁₀, X₂: 1998⋅X₅+2002⋅X₄ {O(n)}
t₁₀, X₃: 2000⋅X₄+2004⋅X₅ {O(n)}
t₁₀, X₄: 4⋅X₄ {O(n)}
t₁₀, X₅: 4⋅X₅ {O(n)}
t₁₁, X₀: 3996⋅X₅+4004⋅X₄ {O(n)}
t₁₁, X₁: 4000⋅X₄+4008⋅X₅ {O(n)}
t₁₁, X₂: 3996⋅X₅+4004⋅X₄ {O(n)}
t₁₁, X₃: 4000⋅X₄+4008⋅X₅ {O(n)}
t₁₁, X₄: 8⋅X₄ {O(n)}
t₁₁, X₅: 8⋅X₅ {O(n)}