KoAT2 Proof Output

Initial Problem

Start: eval_terminate_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_terminate_0, eval_terminate_1, eval_terminate_2, eval_terminate_3, eval_terminate_4, eval_terminate_5, eval_terminate_6, eval_terminate_7, eval_terminate_bb0_in, eval_terminate_bb1_in, eval_terminate_bb2_in, eval_terminate_bb3_in, eval_terminate_start, eval_terminate_stop
Transitions:
t₂: eval_terminate_0(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_1(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: eval_terminate_1(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_2(X₀, X₁, X₂, X₃, X₄, X₅)
t₄: eval_terminate_2(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_3(X₀, X₁, X₂, X₃, X₄, X₅)
t₅: eval_terminate_3(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_4(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: eval_terminate_4(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_5(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: eval_terminate_5(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_6(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: eval_terminate_6(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_7(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: eval_terminate_7(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb1_in(X₃, X₄, X₅, X₃, X₄, X₅)
t₁: eval_terminate_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_0(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₀: eval_terminate_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂
t₁₁: eval_terminate_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 101 ≤ X₀
t₁₂: eval_terminate_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₂ ≤ X₁
t₁₃: eval_terminate_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb1_in(X₁, 1+X₀, X₂-1, X₃, X₄, X₅)
t₁₄: eval_terminate_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_stop(X₀, X₁, X₂, X₃, X₄, X₅)
t₀: eval_terminate_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Found invariant X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 100 for location eval_terminate_bb2_in

Found invariant X₂ ≤ X₅ for location eval_terminate_bb3_in

Found invariant X₂ ≤ X₅ for location eval_terminate_stop

Found invariant X₂ ≤ X₅ for location eval_terminate_bb1_in

Problem after Preprocessing

Start: eval_terminate_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_terminate_0, eval_terminate_1, eval_terminate_2, eval_terminate_3, eval_terminate_4, eval_terminate_5, eval_terminate_6, eval_terminate_7, eval_terminate_bb0_in, eval_terminate_bb1_in, eval_terminate_bb2_in, eval_terminate_bb3_in, eval_terminate_start, eval_terminate_stop
Transitions:
t₂: eval_terminate_0(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_1(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: eval_terminate_1(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_2(X₀, X₁, X₂, X₃, X₄, X₅)
t₄: eval_terminate_2(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_3(X₀, X₁, X₂, X₃, X₄, X₅)
t₅: eval_terminate_3(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_4(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: eval_terminate_4(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_5(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: eval_terminate_5(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_6(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: eval_terminate_6(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_7(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: eval_terminate_7(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb1_in(X₃, X₄, X₅, X₃, X₄, X₅)
t₁: eval_terminate_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_0(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₀: eval_terminate_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₅
t₁₁: eval_terminate_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 101 ≤ X₀ ∧ X₂ ≤ X₅
t₁₂: eval_terminate_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₂ ≤ X₁ ∧ X₂ ≤ X₅
t₁₃: eval_terminate_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb1_in(X₁, 1+X₀, X₂-1, X₃, X₄, X₅) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₂ ≤ X₅
t₁₄: eval_terminate_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₅
t₀: eval_terminate_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

MPRF for transition t₁₀: eval_terminate_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₅ of depth 1:

new bound:

X₃+X₄+X₅+101 {O(n)}

MPRF:

• eval_terminate_bb1_in: [101+X₅-X₀-X₁]
• eval_terminate_bb2_in: [100+X₅-X₀-X₁]

MPRF for transition t₁₃: eval_terminate_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_terminate_bb1_in(X₁, 1+X₀, X₂-1, X₃, X₄, X₅) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₂ ≤ X₅ of depth 1:

new bound:

X₃+X₄+X₅+101 {O(n)}

MPRF:

• eval_terminate_bb1_in: [101+X₅-X₀-X₁]
• eval_terminate_bb2_in: [101+X₅-X₀-X₁]

All Bounds

Timebounds

Overall timebound:2⋅X₃+2⋅X₄+2⋅X₅+215 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: X₃+X₄+X₅+101 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: X₃+X₄+X₅+101 {O(n)}
t₁₄: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃+2⋅X₄+2⋅X₅+215 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: X₃+X₄+X₅+101 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: X₃+X₄+X₅+101 {O(n)}
t₁₄: 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: X₀ {O(n)}
t₁, X₁: X₁ {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: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₉, X₀: X₃ {O(n)}
t₉, X₁: X₄ {O(n)}
t₉, X₂: X₅ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₅ {O(n)}
t₁₀, X₀: 2⋅X₃+2⋅X₄+X₅+101 {O(n)}
t₁₀, X₁: 2⋅X₃+2⋅X₄+X₅+101 {O(n)}
t₁₀, X₂: 2⋅X₅+X₃+X₄+101 {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₁, X₀: 2⋅X₄+3⋅X₃+X₅+101 {O(n)}
t₁₁, X₁: 2⋅X₃+3⋅X₄+X₅+101 {O(n)}
t₁₁, X₂: 3⋅X₅+X₃+X₄+101 {O(n)}
t₁₁, X₃: 2⋅X₃ {O(n)}
t₁₁, X₄: 2⋅X₄ {O(n)}
t₁₁, X₅: 2⋅X₅ {O(n)}
t₁₂, X₀: 2⋅X₄+3⋅X₃+X₅+101 {O(n)}
t₁₂, X₁: 2⋅X₃+3⋅X₄+X₅+101 {O(n)}
t₁₂, X₂: 3⋅X₅+X₃+X₄+101 {O(n)}
t₁₂, X₃: 2⋅X₃ {O(n)}
t₁₂, X₄: 2⋅X₄ {O(n)}
t₁₂, X₅: 2⋅X₅ {O(n)}
t₁₃, X₀: 2⋅X₃+2⋅X₄+X₅+101 {O(n)}
t₁₃, X₁: 2⋅X₃+2⋅X₄+X₅+101 {O(n)}
t₁₃, X₂: 2⋅X₅+X₃+X₄+101 {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₄, X₀: 2⋅X₅+4⋅X₄+6⋅X₃+202 {O(n)}
t₁₄, X₁: 2⋅X₅+4⋅X₃+6⋅X₄+202 {O(n)}
t₁₄, X₂: 2⋅X₃+2⋅X₄+6⋅X₅+202 {O(n)}
t₁₄, X₃: 4⋅X₃ {O(n)}
t₁₄, X₄: 4⋅X₄ {O(n)}
t₁₄, X₅: 4⋅X₅ {O(n)}