KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location eval_sipmabubble_bb6_in

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ for location eval_sipmabubble_29

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_sipmabubble_bb2_in

Found invariant X₁ ≤ X₃ for location eval_sipmabubble_bb1_in

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_sipmabubble_bb3_in

Found invariant X₁ ≤ X₃ ∧ 1+X₁ ≤ 0 for location eval_sipmabubble_bb7_in

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_sipmabubble_bb4_in

Found invariant X₁ ≤ X₃ ∧ 1+X₁ ≤ 0 for location eval_sipmabubble_stop

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_sipmabubble_bb5_in

Problem after Preprocessing

Start: eval_sipmabubble_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: nondef_0, nondef_1
Locations: eval_sipmabubble_0, eval_sipmabubble_1, eval_sipmabubble_2, eval_sipmabubble_29, eval_sipmabubble_3, eval_sipmabubble_30, eval_sipmabubble_4, eval_sipmabubble_5, eval_sipmabubble_6, eval_sipmabubble_bb0_in, eval_sipmabubble_bb1_in, eval_sipmabubble_bb2_in, eval_sipmabubble_bb3_in, eval_sipmabubble_bb4_in, eval_sipmabubble_bb5_in, eval_sipmabubble_bb6_in, eval_sipmabubble_bb7_in, eval_sipmabubble_start, eval_sipmabubble_stop
Transitions:
t₂: eval_sipmabubble_0(X₀, X₁, X₂, X₃) → eval_sipmabubble_1(X₀, X₁, X₂, X₃)
t₃: eval_sipmabubble_1(X₀, X₁, X₂, X₃) → eval_sipmabubble_2(X₀, X₁, X₂, X₃)
t₄: eval_sipmabubble_2(X₀, X₁, X₂, X₃) → eval_sipmabubble_3(X₀, X₁, X₂, X₃)
t₁₈: eval_sipmabubble_29(X₀, X₁, X₂, X₃) → eval_sipmabubble_30(X₀, X₁, X₂, X₃) :|: 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₁ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₅: eval_sipmabubble_3(X₀, X₁, X₂, X₃) → eval_sipmabubble_4(X₀, X₁, X₂, X₃)
t₁₉: eval_sipmabubble_30(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb1_in(X₀, X₀, X₂, X₃) :|: 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₁ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₆: eval_sipmabubble_4(X₀, X₁, X₂, X₃) → eval_sipmabubble_5(X₀, X₁, X₂, X₃)
t₇: eval_sipmabubble_5(X₀, X₁, X₂, X₃) → eval_sipmabubble_6(X₀, X₁, X₂, X₃)
t₈: eval_sipmabubble_6(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb1_in(X₀, X₃, X₂, X₃)
t₁: eval_sipmabubble_bb0_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_0(X₀, X₁, X₂, X₃)
t₉: eval_sipmabubble_bb1_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb2_in(X₀, X₁, 0, X₃) :|: 0 ≤ X₁ ∧ X₁ ≤ X₃
t₁₀: eval_sipmabubble_bb1_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb7_in(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ 0 ∧ X₁ ≤ X₃
t₁₁: eval_sipmabubble_bb2_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb3_in(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₁₂: eval_sipmabubble_bb2_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb6_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₁₃: eval_sipmabubble_bb3_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb4_in(X₀, X₁, X₂, X₃) :|: 1+nondef_1 ≤ nondef_0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂
t₁₄: eval_sipmabubble_bb3_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb5_in(X₀, X₁, X₂, X₃) :|: nondef_0 ≤ nondef_1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂
t₁₅: eval_sipmabubble_bb4_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb5_in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂
t₁₆: eval_sipmabubble_bb5_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb2_in(X₀, X₁, 1+X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂
t₁₇: eval_sipmabubble_bb6_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_29(X₁-1, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₂₀: eval_sipmabubble_bb7_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_stop(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ 0 ∧ X₁ ≤ X₃
t₀: eval_sipmabubble_start(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb0_in(X₀, X₁, X₂, X₃)

MPRF for transition t₉: eval_sipmabubble_bb1_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb2_in(X₀, X₁, 0, X₃) :|: 0 ≤ X₁ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

• eval_sipmabubble_29: [1+X₀]
• eval_sipmabubble_30: [1+X₀]
• eval_sipmabubble_bb1_in: [1+X₁]
• eval_sipmabubble_bb2_in: [X₁]
• eval_sipmabubble_bb3_in: [X₁]
• eval_sipmabubble_bb4_in: [X₁]
• eval_sipmabubble_bb5_in: [X₁]
• eval_sipmabubble_bb6_in: [X₁]

MPRF for transition t₁₂: eval_sipmabubble_bb2_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb6_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

• eval_sipmabubble_29: [X₂]
• eval_sipmabubble_30: [1+X₀+X₂-X₁]
• eval_sipmabubble_bb1_in: [1+X₁]
• eval_sipmabubble_bb2_in: [1+X₁]
• eval_sipmabubble_bb3_in: [1+X₁]
• eval_sipmabubble_bb4_in: [1+X₁]
• eval_sipmabubble_bb5_in: [1+X₁]
• eval_sipmabubble_bb6_in: [X₁]

MPRF for transition t₁₇: eval_sipmabubble_bb6_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_29(X₁-1, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

• eval_sipmabubble_29: [X₂]
• eval_sipmabubble_30: [1+X₀]
• eval_sipmabubble_bb1_in: [1+X₁]
• eval_sipmabubble_bb2_in: [1+X₁]
• eval_sipmabubble_bb3_in: [1+X₁]
• eval_sipmabubble_bb4_in: [1+X₁]
• eval_sipmabubble_bb5_in: [1+X₁]
• eval_sipmabubble_bb6_in: [1+X₂]

MPRF for transition t₁₈: eval_sipmabubble_29(X₀, X₁, X₂, X₃) → eval_sipmabubble_30(X₀, X₁, X₂, X₃) :|: 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₁ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

• eval_sipmabubble_29: [1+X₁]
• eval_sipmabubble_30: [X₁]
• eval_sipmabubble_bb1_in: [1+X₁]
• eval_sipmabubble_bb2_in: [1+X₁]
• eval_sipmabubble_bb3_in: [1+X₁]
• eval_sipmabubble_bb4_in: [1+X₁]
• eval_sipmabubble_bb5_in: [1+X₁]
• eval_sipmabubble_bb6_in: [1+X₂]

MPRF for transition t₁₉: eval_sipmabubble_30(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb1_in(X₀, X₀, X₂, X₃) :|: 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₁ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

• eval_sipmabubble_29: [1+X₁]
• eval_sipmabubble_30: [1+X₁]
• eval_sipmabubble_bb1_in: [1+X₁]
• eval_sipmabubble_bb2_in: [1+X₁]
• eval_sipmabubble_bb3_in: [1+X₁]
• eval_sipmabubble_bb4_in: [1+X₁]
• eval_sipmabubble_bb5_in: [1+X₁]
• eval_sipmabubble_bb6_in: [1+X₁]

MPRF for transition t₁₁: eval_sipmabubble_bb2_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb3_in(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₃⋅X₃+3⋅X₃+2 {O(n^2)}

MPRF:

• eval_sipmabubble_29: [X₃-X₂]
• eval_sipmabubble_30: [X₃-X₂]
• eval_sipmabubble_bb1_in: [1+X₃]
• eval_sipmabubble_bb2_in: [1+X₃-X₂]
• eval_sipmabubble_bb3_in: [X₃-X₂]
• eval_sipmabubble_bb4_in: [X₃-X₂]
• eval_sipmabubble_bb5_in: [X₃-X₂]
• eval_sipmabubble_bb6_in: [X₃-X₂]

MPRF for transition t₁₃: eval_sipmabubble_bb3_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb4_in(X₀, X₁, X₂, X₃) :|: 1+nondef_1 ≤ nondef_0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₃⋅X₃+2⋅X₃ {O(n^2)}

MPRF:

• eval_sipmabubble_29: [X₃-X₂]
• eval_sipmabubble_30: [X₃-X₂]
• eval_sipmabubble_bb1_in: [X₃]
• eval_sipmabubble_bb2_in: [X₃-X₂]
• eval_sipmabubble_bb3_in: [X₃-X₂]
• eval_sipmabubble_bb4_in: [X₃-1-X₂]
• eval_sipmabubble_bb5_in: [X₃-1-X₂]
• eval_sipmabubble_bb6_in: [X₃-X₂]

MPRF for transition t₁₄: eval_sipmabubble_bb3_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb5_in(X₀, X₁, X₂, X₃) :|: nondef_0 ≤ nondef_1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₃⋅X₃+2⋅X₃ {O(n^2)}

MPRF:

• eval_sipmabubble_29: [X₃-X₂]
• eval_sipmabubble_30: [2+2⋅X₀-X₂-X₃]
• eval_sipmabubble_bb1_in: [X₃]
• eval_sipmabubble_bb2_in: [X₃-X₂]
• eval_sipmabubble_bb3_in: [X₃-X₂]
• eval_sipmabubble_bb4_in: [X₃-X₂]
• eval_sipmabubble_bb5_in: [X₃-1-X₂]
• eval_sipmabubble_bb6_in: [X₃-X₂]

MPRF for transition t₁₅: eval_sipmabubble_bb4_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb5_in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₃⋅X₃+3⋅X₃+1 {O(n^2)}

MPRF:

• eval_sipmabubble_29: [0]
• eval_sipmabubble_30: [0]
• eval_sipmabubble_bb1_in: [X₁]
• eval_sipmabubble_bb2_in: [X₁-X₂]
• eval_sipmabubble_bb3_in: [X₁-X₂]
• eval_sipmabubble_bb4_in: [X₁-X₂]
• eval_sipmabubble_bb5_in: [X₁-1-X₂]
• eval_sipmabubble_bb6_in: [0]

MPRF for transition t₁₆: eval_sipmabubble_bb5_in(X₀, X₁, X₂, X₃) → eval_sipmabubble_bb2_in(X₀, X₁, 1+X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:

new bound:

3⋅X₃⋅X₃+9⋅X₃+3 {O(n^2)}

MPRF:

• eval_sipmabubble_29: [X₀+X₂]
• eval_sipmabubble_30: [X₀+X₂]
• eval_sipmabubble_bb1_in: [3⋅X₁]
• eval_sipmabubble_bb2_in: [3⋅X₁-X₂]
• eval_sipmabubble_bb3_in: [3⋅X₁-X₂]
• eval_sipmabubble_bb4_in: [3⋅X₁-X₂]
• eval_sipmabubble_bb5_in: [3⋅X₁-X₂]
• eval_sipmabubble_bb6_in: [3⋅X₁-X₂]

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_sipmabubble_bb5_in_v1

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_sipmabubble_bb2_in

Found invariant X₁ ≤ X₃ for location eval_sipmabubble_bb1_in

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location eval_sipmabubble_bb4_in_v2

Found invariant X₁ ≤ X₃ ∧ 1+X₁ ≤ 0 for location eval_sipmabubble_bb7_in

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_sipmabubble_bb4_in_v1

Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_sipmabubble_bb3_in_v1

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location eval_sipmabubble_bb3_in_v2

Found invariant X₁ ≤ X₃ ∧ 1+X₁ ≤ 0 for location eval_sipmabubble_stop

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_sipmabubble_bb2_in_v1

All Bounds

Timebounds

Overall timebound:7⋅X₃⋅X₃+24⋅X₃+22 {O(n^2)}
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: X₃+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₃⋅X₃+3⋅X₃+2 {O(n^2)}
t₁₂: X₃+1 {O(n)}
t₁₃: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₄: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₅: X₃⋅X₃+3⋅X₃+1 {O(n^2)}
t₁₆: 3⋅X₃⋅X₃+9⋅X₃+3 {O(n^2)}
t₁₇: X₃+1 {O(n)}
t₁₈: X₃+1 {O(n)}
t₁₉: X₃+1 {O(n)}
t₂₀: 1 {O(1)}

Costbounds

Overall costbound: 7⋅X₃⋅X₃+24⋅X₃+22 {O(n^2)}
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: X₃+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₃⋅X₃+3⋅X₃+2 {O(n^2)}
t₁₂: X₃+1 {O(n)}
t₁₃: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₄: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₅: X₃⋅X₃+3⋅X₃+1 {O(n^2)}
t₁₆: 3⋅X₃⋅X₃+9⋅X₃+3 {O(n^2)}
t₁₇: X₃+1 {O(n)}
t₁₈: X₃+1 {O(n)}
t₁₉: X₃+1 {O(n)}
t₂₀: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₃ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: X₀+X₃+1 {O(n)}
t₉, X₁: X₃+1 {O(n)}
t₉, X₂: 0 {O(1)}
t₉, X₃: X₃ {O(n)}
t₁₀, X₀: X₀+X₃+1 {O(n)}
t₁₀, X₁: 2⋅X₃+1 {O(n)}
t₁₀, X₂: 3⋅X₃⋅X₃+9⋅X₃+X₂+3 {O(n^2)}
t₁₀, X₃: 2⋅X₃ {O(n)}
t₁₁, X₀: X₀+X₃+1 {O(n)}
t₁₁, X₁: X₃+1 {O(n)}
t₁₁, X₂: 3⋅X₃⋅X₃+9⋅X₃+3 {O(n^2)}
t₁₁, X₃: X₃ {O(n)}
t₁₂, X₀: 2⋅X₀+2⋅X₃+2 {O(n)}
t₁₂, X₁: X₃+1 {O(n)}
t₁₂, X₂: 3⋅X₃⋅X₃+9⋅X₃+3 {O(n^2)}
t₁₂, X₃: X₃ {O(n)}
t₁₃, X₀: X₀+X₃+1 {O(n)}
t₁₃, X₁: X₃+1 {O(n)}
t₁₃, X₂: 3⋅X₃⋅X₃+9⋅X₃+3 {O(n^2)}
t₁₃, X₃: X₃ {O(n)}
t₁₄, X₀: X₀+X₃+1 {O(n)}
t₁₄, X₁: X₃+1 {O(n)}
t₁₄, X₂: 3⋅X₃⋅X₃+9⋅X₃+3 {O(n^2)}
t₁₄, X₃: X₃ {O(n)}
t₁₅, X₀: X₀+X₃+1 {O(n)}
t₁₅, X₁: X₃+1 {O(n)}
t₁₅, X₂: 3⋅X₃⋅X₃+9⋅X₃+3 {O(n^2)}
t₁₅, X₃: X₃ {O(n)}
t₁₆, X₀: X₀+X₃+1 {O(n)}
t₁₆, X₁: X₃+1 {O(n)}
t₁₆, X₂: 3⋅X₃⋅X₃+9⋅X₃+3 {O(n^2)}
t₁₆, X₃: X₃ {O(n)}
t₁₇, X₀: X₃+1 {O(n)}
t₁₇, X₁: X₃+1 {O(n)}
t₁₇, X₂: 3⋅X₃⋅X₃+9⋅X₃+3 {O(n^2)}
t₁₇, X₃: X₃ {O(n)}
t₁₈, X₀: X₃+1 {O(n)}
t₁₈, X₁: X₃+1 {O(n)}
t₁₈, X₂: 3⋅X₃⋅X₃+9⋅X₃+3 {O(n^2)}
t₁₈, X₃: X₃ {O(n)}
t₁₉, X₀: X₃+1 {O(n)}
t₁₉, X₁: X₃+1 {O(n)}
t₁₉, X₂: 3⋅X₃⋅X₃+9⋅X₃+3 {O(n^2)}
t₁₉, X₃: X₃ {O(n)}
t₂₀, X₀: X₀+X₃+1 {O(n)}
t₂₀, X₁: 2⋅X₃+1 {O(n)}
t₂₀, X₂: 3⋅X₃⋅X₃+9⋅X₃+X₂+3 {O(n^2)}
t₂₀, X₃: 2⋅X₃ {O(n)}