KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location eval_foo_10

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location eval_foo_11

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location eval_foo_7

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location eval_foo_bb3_in

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location eval_foo_8

Found invariant X₉ ≤ X₃ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₇ ∧ 0 ≤ X₁₀+X₁₁ for location eval_foo_bb2_in

Found invariant X₉ ≤ X₃ ∧ X₈ ≤ X₁ ∧ 0 ≤ X₁₀+X₁₁ for location eval_foo_bb1_in

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location eval_foo_9

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁
Temp_Vars: nondef.0, nondef.1, nondef.2
Locations: eval_foo_.critedge_in, eval_foo_10, eval_foo_11, eval_foo_7, eval_foo_8, eval_foo_9, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_start, eval_foo_stop
Transitions:
t₂₁: eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₁₉: eval_foo_10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_11(X₀, X₁, X₂, X₃, X₄, X₅, nondef.2, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₂₀: eval_foo_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb1_in(X₅, X₀, X₆, X₂, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₁₁: eval_foo_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_8(X₀, X₁, X₂, X₃, nondef.0, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₁₃: eval_foo_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_9(X₀, X₁, X₂, X₃, X₄, nondef.1, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₁₆: eval_foo_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb1_in(X₅, X₀, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 0 ≤ X₄ ∧ X₄ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₁₄: eval_foo_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₄ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₁₅: eval_foo_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1 ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₂: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁₀+X₁₁ ≤ 0
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb1_in(X₁₀, X₈, X₁₁, X₉, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 0 ≤ X₁₀+X₁₁
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₆: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₀ ≤ 2⋅X₁+X₂ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₇: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₂ ≤ X₃ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₈: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 2⋅X₁+X₂ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₉: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₁₇: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)

MPRF for transition t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 2⋅X₁+X₂ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF:

• eval_foo_10: [X₇-1-X₁]
• eval_foo_11: [X₇-1-X₁]
• eval_foo_7: [X₇-1-X₁]
• eval_foo_8: [X₇-1-X₁]
• eval_foo_9: [X₇-1-X₁]
• eval_foo_bb1_in: [X₇-X₁]
• eval_foo_bb2_in: [X₇-X₁]
• eval_foo_bb3_in: [X₇-1-X₁]
• eval_foo_bb4_in: [X₇-1-X₁]

MPRF for transition t₉: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF:

• eval_foo_10: [X₇-X₀]
• eval_foo_11: [X₇-X₀]
• eval_foo_7: [X₇-X₀]
• eval_foo_8: [X₇-X₀]
• eval_foo_9: [X₇-X₀]
• eval_foo_bb1_in: [X₇-X₁]
• eval_foo_bb2_in: [X₇-X₁]
• eval_foo_bb3_in: [X₇-X₁]
• eval_foo_bb4_in: [X₇-X₀]

MPRF for transition t₁₁: eval_foo_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_8(X₀, X₁, X₂, X₃, nondef.0, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF:

• eval_foo_10: [X₇-1-X₁]
• eval_foo_11: [X₇-X₀]
• eval_foo_7: [X₇-X₁]
• eval_foo_8: [X₇-1-X₁]
• eval_foo_9: [X₇-1-X₁]
• eval_foo_bb1_in: [X₇-X₁]
• eval_foo_bb2_in: [X₇-X₁]
• eval_foo_bb3_in: [X₇-X₁]
• eval_foo_bb4_in: [X₇-1-X₁]

MPRF for transition t₁₃: eval_foo_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_9(X₀, X₁, X₂, X₃, X₄, nondef.1, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF:

• eval_foo_10: [X₇-X₀]
• eval_foo_11: [X₇-X₀]
• eval_foo_7: [X₇-X₁]
• eval_foo_8: [1+X₇-X₀]
• eval_foo_9: [X₇-X₀]
• eval_foo_bb1_in: [X₇-X₁]
• eval_foo_bb2_in: [X₇-X₁]
• eval_foo_bb3_in: [X₇-X₁]
• eval_foo_bb4_in: [X₇-X₀]

MPRF for transition t₁₄: eval_foo_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₄ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁ of depth 1:

new bound:

X₇+X₈+1 {O(n)}

MPRF:

• eval_foo_10: [1+X₇-X₀]
• eval_foo_11: [1+X₇-X₀]
• eval_foo_7: [1+X₇-X₁]
• eval_foo_8: [1+X₇-X₁]
• eval_foo_9: [2+X₇-X₀]
• eval_foo_bb1_in: [1+X₇-X₁]
• eval_foo_bb2_in: [1+X₇-X₁]
• eval_foo_bb3_in: [1+X₇-X₁]
• eval_foo_bb4_in: [1+X₇-X₀]

MPRF for transition t₁₅: eval_foo_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1 ≤ X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF:

• eval_foo_10: [X₇-X₀]
• eval_foo_11: [X₇-X₀]
• eval_foo_7: [1+X₇-X₀]
• eval_foo_8: [1+X₇-X₀]
• eval_foo_9: [1+X₇-X₀]
• eval_foo_bb1_in: [X₇-X₁]
• eval_foo_bb2_in: [X₇-X₁]
• eval_foo_bb3_in: [1+X₇-X₀]
• eval_foo_bb4_in: [X₇-X₀]

MPRF for transition t₁₆: eval_foo_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb1_in(X₅, X₀, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 0 ≤ X₄ ∧ X₄ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF:

MPRF for transition t₁₇: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁ of depth 1:

new bound:

X₇+X₈+1 {O(n)}

MPRF:

• eval_foo_10: [1+X₇-X₀]
• eval_foo_11: [1+X₇-X₀]
• eval_foo_7: [1+X₇-X₁]
• eval_foo_8: [1+X₇-X₁]
• eval_foo_9: [1+X₇-X₁]
• eval_foo_bb1_in: [1+X₇-X₁]
• eval_foo_bb2_in: [1+X₇-X₁]
• eval_foo_bb3_in: [1+X₇-X₁]
• eval_foo_bb4_in: [2+X₇-X₀]

MPRF for transition t₁₉: eval_foo_10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_11(X₀, X₁, X₂, X₃, X₄, X₅, nondef.2, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF:

• eval_foo_10: [1+X₇-X₀]
• eval_foo_11: [X₇-X₀]
• eval_foo_7: [1+X₇-X₀]
• eval_foo_8: [1+X₇-X₀]
• eval_foo_9: [1+X₇-X₀]
• eval_foo_bb1_in: [X₇-X₁]
• eval_foo_bb2_in: [X₇-X₁]
• eval_foo_bb3_in: [1+X₇-X₀]
• eval_foo_bb4_in: [1+X₇-X₀]

MPRF for transition t₂₀: eval_foo_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb1_in(X₅, X₀, X₆, X₂, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 1+X₁ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF:

• eval_foo_10: [1+X₇-X₀]
• eval_foo_11: [1+X₇-X₀]
• eval_foo_7: [1+X₇-X₀]
• eval_foo_8: [1+X₇-X₀]
• eval_foo_9: [1+X₇-X₀]
• eval_foo_bb1_in: [X₇-X₁]
• eval_foo_bb2_in: [X₇-X₁]
• eval_foo_bb3_in: [1+X₇-X₀]
• eval_foo_bb4_in: [1+X₇-X₀]

knowledge_propagation leads to new time bound 2⋅X₇+2⋅X₈+1 {O(n)} for transition t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₀ ≤ X₇ ∧ X₈ ≤ X₁ ∧ X₉ ≤ X₃ ∧ 0 ≤ X₁₀+X₁₁

All Bounds

Timebounds

Overall timebound:12⋅X₇+12⋅X₈+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 2⋅X₇+2⋅X₈+1 {O(n)}
t₄: 1 {O(1)}
t₅: X₇+X₈ {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₇+X₈ {O(n)}
t₁₁: X₇+X₈ {O(n)}
t₁₃: X₇+X₈ {O(n)}
t₁₄: X₇+X₈+1 {O(n)}
t₁₅: X₇+X₈ {O(n)}
t₁₆: X₇+X₈ {O(n)}
t₁₇: X₇+X₈+1 {O(n)}
t₁₉: X₇+X₈ {O(n)}
t₂₀: X₇+X₈ {O(n)}
t₂₁: 1 {O(1)}

Costbounds

Overall costbound: 12⋅X₇+12⋅X₈+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 2⋅X₇+2⋅X₈+1 {O(n)}
t₄: 1 {O(1)}
t₅: X₇+X₈ {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₇+X₈ {O(n)}
t₁₁: X₇+X₈ {O(n)}
t₁₃: X₇+X₈ {O(n)}
t₁₄: X₇+X₈+1 {O(n)}
t₁₅: X₇+X₈ {O(n)}
t₁₆: X₇+X₈ {O(n)}
t₁₇: X₇+X₈+1 {O(n)}
t₁₉: X₇+X₈ {O(n)}
t₂₀: X₇+X₈ {O(n)}
t₂₁: 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)}
t₀, X₆: X₆ {O(n)}
t₀, X₇: X₇ {O(n)}
t₀, X₈: X₈ {O(n)}
t₀, X₉: X₉ {O(n)}
t₀, X₁₀: X₁₀ {O(n)}
t₀, X₁₁: X₁₁ {O(n)}
t₁, X₀: X₁₀ {O(n)}
t₁, X₁: X₈ {O(n)}
t₁, X₂: X₁₁ {O(n)}
t₁, X₃: X₉ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₁, X₇: X₇ {O(n)}
t₁, X₈: X₈ {O(n)}
t₁, X₉: X₉ {O(n)}
t₁, X₁₀: X₁₀ {O(n)}
t₁, X₁₁: X₁₁ {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)}
t₂, X₆: X₆ {O(n)}
t₂, X₇: X₇ {O(n)}
t₂, X₈: X₈ {O(n)}
t₂, X₉: X₉ {O(n)}
t₂, X₁₀: X₁₀ {O(n)}
t₂, X₁₁: X₁₁ {O(n)}
t₃, X₇: X₇ {O(n)}
t₃, X₈: X₈ {O(n)}
t₃, X₉: X₉ {O(n)}
t₃, X₁₀: X₁₀ {O(n)}
t₃, X₁₁: X₁₁ {O(n)}
t₄, X₇: 3⋅X₇ {O(n)}
t₄, X₈: 3⋅X₈ {O(n)}
t₄, X₉: 3⋅X₉ {O(n)}
t₄, X₁₀: 3⋅X₁₀ {O(n)}
t₄, X₁₁: 3⋅X₁₁ {O(n)}
t₅, X₇: X₇ {O(n)}
t₅, X₈: X₈ {O(n)}
t₅, X₉: X₉ {O(n)}
t₅, X₁₀: X₁₀ {O(n)}
t₅, X₁₁: X₁₁ {O(n)}
t₆, X₇: X₇ {O(n)}
t₆, X₈: X₈ {O(n)}
t₆, X₉: X₉ {O(n)}
t₆, X₁₀: X₁₀ {O(n)}
t₆, X₁₁: X₁₁ {O(n)}
t₇, X₇: X₇ {O(n)}
t₇, X₈: X₈ {O(n)}
t₇, X₉: X₉ {O(n)}
t₇, X₁₀: X₁₀ {O(n)}
t₇, X₁₁: X₁₁ {O(n)}
t₈, X₇: X₇ {O(n)}
t₈, X₈: X₈ {O(n)}
t₈, X₉: X₉ {O(n)}
t₈, X₁₀: X₁₀ {O(n)}
t₈, X₁₁: X₁₁ {O(n)}
t₉, X₇: X₇ {O(n)}
t₉, X₈: X₈ {O(n)}
t₉, X₉: X₉ {O(n)}
t₉, X₁₀: X₁₀ {O(n)}
t₉, X₁₁: X₁₁ {O(n)}
t₁₁, X₇: X₇ {O(n)}
t₁₁, X₈: X₈ {O(n)}
t₁₁, X₉: X₉ {O(n)}
t₁₁, X₁₀: X₁₀ {O(n)}
t₁₁, X₁₁: X₁₁ {O(n)}
t₁₃, X₇: X₇ {O(n)}
t₁₃, X₈: X₈ {O(n)}
t₁₃, X₉: X₉ {O(n)}
t₁₃, X₁₀: X₁₀ {O(n)}
t₁₃, X₁₁: X₁₁ {O(n)}
t₁₄, X₇: X₇ {O(n)}
t₁₄, X₈: X₈ {O(n)}
t₁₄, X₉: X₉ {O(n)}
t₁₄, X₁₀: X₁₀ {O(n)}
t₁₄, X₁₁: X₁₁ {O(n)}
t₁₅, X₇: X₇ {O(n)}
t₁₅, X₈: X₈ {O(n)}
t₁₅, X₉: X₉ {O(n)}
t₁₅, X₁₀: X₁₀ {O(n)}
t₁₅, X₁₁: X₁₁ {O(n)}
t₁₆, X₄: 0 {O(1)}
t₁₆, X₇: X₇ {O(n)}
t₁₆, X₈: X₈ {O(n)}
t₁₆, X₉: X₉ {O(n)}
t₁₆, X₁₀: X₁₀ {O(n)}
t₁₆, X₁₁: X₁₁ {O(n)}
t₁₇, X₇: X₇ {O(n)}
t₁₇, X₈: X₈ {O(n)}
t₁₇, X₉: X₉ {O(n)}
t₁₇, X₁₀: X₁₀ {O(n)}
t₁₇, X₁₁: X₁₁ {O(n)}
t₁₉, X₇: X₇ {O(n)}
t₁₉, X₈: X₈ {O(n)}
t₁₉, X₉: X₉ {O(n)}
t₁₉, X₁₀: X₁₀ {O(n)}
t₁₉, X₁₁: X₁₁ {O(n)}
t₂₀, X₇: X₇ {O(n)}
t₂₀, X₈: X₈ {O(n)}
t₂₀, X₉: X₉ {O(n)}
t₂₀, X₁₀: X₁₀ {O(n)}
t₂₀, X₁₁: X₁₁ {O(n)}
t₂₁, X₇: 7⋅X₇ {O(n)}
t₂₁, X₈: 7⋅X₈ {O(n)}
t₂₁, X₉: 7⋅X₉ {O(n)}
t₂₁, X₁₀: 7⋅X₁₀ {O(n)}
t₂₁, X₁₁: 7⋅X₁₁ {O(n)}