KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₂ ≤ 0 for location eval_start_10

Found invariant 1 ≤ X₂ for location eval_start_bb1_in

Found invariant X₂ ≤ 0 for location eval_start_bb6_in

Found invariant X₃ ≤ X₂ ∧ 1 ≤ X₂ for location eval_start_bb5_in

Found invariant X₂ ≤ 0 for location eval_start_11

Found invariant X₃ ≤ X₂ ∧ 1 ≤ X₂ for location eval_start_8

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_start_bb3_in

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_start_bb4_in

Found invariant X₃ ≤ X₂ ∧ 1 ≤ X₂ for location eval_start_9

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_start_bb2_in

Problem after Preprocessing

Cut unsatisfiable transition [t₁₀: eval_start_bb2_in→eval_start_bb4_in; t₁₁: eval_start_bb2_in→eval_start_bb4_in; t₁₁₁: eval_start_bb2_in→eval_start_bb4_in; t₁₁₂: eval_start_bb2_in→eval_start_bb4_in]

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location eval_start_bb2_in_v3

Found invariant X₂ ≤ 0 for location eval_start_10

Found invariant 1 ≤ X₂ for location eval_start_bb1_in

Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_start_bb3_in_v4

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location eval_start_bb3_in_v2

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_start_bb2_in_v1

Found invariant X₂ ≤ 0 for location eval_start_bb6_in

Found invariant X₃ ≤ X₂ ∧ 1 ≤ X₂ for location eval_start_bb5_in

Found invariant X₂ ≤ 0 for location eval_start_11

Found invariant X₃ ≤ X₂ ∧ 1 ≤ X₂ for location eval_start_8

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_start_bb4_in

Found invariant X₃ ≤ X₂ ∧ 1 ≤ X₂ for location eval_start_9

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_start_bb2_in_v2

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location eval_start_bb3_in_v1

Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_start_bb3_in_v3

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location eval_start_bb2_in

Analysing control-flow refined program

MPRF for transition t₁₂₄: eval_start_bb2_in_v1(X₀, X₁, X₂, X₃) → eval_start_bb3_in_v4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_start_bb2_in_v1: [1+X₁]
• eval_start_bb3_in_v4: [X₁]

MPRF for transition t₁₂₅: eval_start_bb3_in_v4(X₀, X₁, X₂, X₃) → eval_start_bb2_in_v1(X₀, X₁-1, X₂, X₃) :|: 2 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ 5 ≤ X₂+X₃ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

• eval_start_bb2_in_v1: [X₁]
• eval_start_bb3_in_v4: [X₁]

MPRF for transition t₁₂₁: eval_start_bb2_in_v2(X₀, X₁, X₂, X₃) → eval_start_bb3_in_v3(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_start_bb2_in_v2: [1+X₁]
• eval_start_bb3_in_v3: [X₁]

MPRF for transition t₁₂₂: eval_start_bb3_in_v3(X₀, X₁, X₂, X₃) → eval_start_bb2_in_v2(X₀, X₁-1, X₂, X₃) :|: X₀ ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 5 ≤ X₂+X₃ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

• eval_start_bb2_in_v2: [X₁]
• eval_start_bb3_in_v3: [X₁]

MPRF for transition t₁₁₈: eval_start_bb2_in_v3(X₀, X₁, X₂, X₃) → eval_start_bb3_in_v2(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₂+X₃+2 {O(n)}

MPRF:

• eval_start_bb2_in_v3: [1+X₃-X₁]
• eval_start_bb3_in_v2: [X₃-X₁]

MPRF for transition t₁₁₉: eval_start_bb3_in_v2(X₀, X₁, X₂, X₃) → eval_start_bb2_in_v3(X₀, 1+X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₁+X₃ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF:

• eval_start_bb2_in_v3: [X₃-X₁]
• eval_start_bb3_in_v2: [X₃-X₁]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n)

cfr-program:

Start: eval_start_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_start_0, eval_start_1, eval_start_10, eval_start_11, eval_start_2, eval_start_3, eval_start_8, eval_start_9, eval_start_bb0_in, eval_start_bb1_in, eval_start_bb2_in, eval_start_bb2_in_v1, eval_start_bb2_in_v2, eval_start_bb2_in_v3, eval_start_bb3_in_v1, eval_start_bb3_in_v2, eval_start_bb3_in_v3, eval_start_bb3_in_v4, eval_start_bb4_in, eval_start_bb5_in, eval_start_bb6_in, eval_start_start, eval_start_stop
Transitions:
t₂: eval_start_0(X₀, X₁, X₂, X₃) → eval_start_1(X₀, X₁, X₂, X₃)
t₃: eval_start_1(X₀, X₁, X₂, X₃) → eval_start_2(X₀, X₁, X₂, X₃)
t₂₀: eval_start_10(X₀, X₁, X₂, X₃) → eval_start_11(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂₁: eval_start_11(X₀, X₁, X₂, X₃) → eval_start_stop(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₄: eval_start_2(X₀, X₁, X₂, X₃) → eval_start_3(X₀, X₁, X₂, X₃)
t₅: eval_start_3(X₀, X₁, X₂, X₃) → eval_start_bb1_in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂
t₆: eval_start_3(X₀, X₁, X₂, X₃) → eval_start_bb6_in(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₁₇: eval_start_8(X₀, X₁, X₂, X₃) → eval_start_9(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ X₂
t₁₈: eval_start_9(X₀, X₁, X₂, X₃) → eval_start_stop(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ X₂
t₁: eval_start_bb0_in(X₀, X₁, X₂, X₃) → eval_start_0(X₀, X₁, X₂, X₃)
t₇: eval_start_bb1_in(X₀, X₁, X₂, X₃) → eval_start_bb2_in(X₀, X₂, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 1 ≤ X₂
t₈: eval_start_bb1_in(X₀, X₁, X₂, X₃) → eval_start_bb5_in(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ 1 ≤ X₂
t₁₁₃: eval_start_bb2_in(X₀, X₁, X₂, X₃) → eval_start_bb3_in_v1(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃
t₁₂₄: eval_start_bb2_in_v1(X₀, X₁, X₂, X₃) → eval_start_bb3_in_v4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃
t₁₂₃: eval_start_bb2_in_v1(X₀, X₁, X₂, X₃) → eval_start_bb4_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃
t₁₂₁: eval_start_bb2_in_v2(X₀, X₁, X₂, X₃) → eval_start_bb3_in_v3(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃
t₁₂₀: eval_start_bb2_in_v2(X₀, X₁, X₂, X₃) → eval_start_bb4_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ X₀ ≤ 1 ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃
t₁₁₈: eval_start_bb2_in_v3(X₀, X₁, X₂, X₃) → eval_start_bb3_in_v2(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃
t₁₁₇: eval_start_bb2_in_v3(X₀, X₁, X₂, X₃) → eval_start_bb4_in(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃
t₁₁₄: eval_start_bb3_in_v1(X₀, X₁, X₂, X₃) → eval_start_bb2_in_v1(X₀, X₁-1, X₂, X₃) :|: 2 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₁₁₅: eval_start_bb3_in_v1(X₀, X₁, X₂, X₃) → eval_start_bb2_in_v2(X₀, X₁-1, X₂, X₃) :|: X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₁₁₆: eval_start_bb3_in_v1(X₀, X₁, X₂, X₃) → eval_start_bb2_in_v3(X₀, 1+X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₁₁₉: eval_start_bb3_in_v2(X₀, X₁, X₂, X₃) → eval_start_bb2_in_v3(X₀, 1+X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 4 ≤ X₂+X₃ ∧ 5 ≤ X₁+X₃ ∧ X₀ ≤ X₂
t₁₂₂: eval_start_bb3_in_v3(X₀, X₁, X₂, X₃) → eval_start_bb2_in_v2(X₀, X₁-1, X₂, X₃) :|: X₀ ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 5 ≤ X₂+X₃
t₁₂₅: eval_start_bb3_in_v4(X₀, X₁, X₂, X₃) → eval_start_bb2_in_v1(X₀, X₁-1, X₂, X₃) :|: 2 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ 5 ≤ X₂+X₃
t₁₅: eval_start_bb4_in(X₀, X₁, X₂, X₃) → eval_start_stop(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁+X₂ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃
t₁₆: eval_start_bb5_in(X₀, X₁, X₂, X₃) → eval_start_8(X₀, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ X₂
t₁₉: eval_start_bb6_in(X₀, X₁, X₂, X₃) → eval_start_10(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₀: eval_start_start(X₀, X₁, X₂, X₃) → eval_start_bb0_in(X₀, X₁, X₂, X₃)

All Bounds

Timebounds

Overall timebound:2⋅X₃+6⋅X₂+28 {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)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₁₁₃: 1 {O(1)}
t₁₁₄: 1 {O(1)}
t₁₁₅: 1 {O(1)}
t₁₁₆: 1 {O(1)}
t₁₁₇: 1 {O(1)}
t₁₁₈: X₂+X₃+2 {O(n)}
t₁₁₉: X₂+X₃+1 {O(n)}
t₁₂₀: 1 {O(1)}
t₁₂₁: X₂+1 {O(n)}
t₁₂₂: X₂ {O(n)}
t₁₂₃: 1 {O(1)}
t₁₂₄: X₂+1 {O(n)}
t₁₂₅: X₂ {O(n)}

Costbounds

Overall costbound: 2⋅X₃+6⋅X₂+28 {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)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₁₁₃: 1 {O(1)}
t₁₁₄: 1 {O(1)}
t₁₁₅: 1 {O(1)}
t₁₁₆: 1 {O(1)}
t₁₁₇: 1 {O(1)}
t₁₁₈: X₂+X₃+2 {O(n)}
t₁₁₉: X₂+X₃+1 {O(n)}
t₁₂₀: 1 {O(1)}
t₁₂₁: X₂+1 {O(n)}
t₁₂₂: X₂ {O(n)}
t₁₂₃: 1 {O(1)}
t₁₂₄: X₂+1 {O(n)}
t₁₂₅: X₂ {O(n)}

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: X₂ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₁₅, X₀: 4⋅X₀+1 {O(n)}
t₁₅, X₁: 3⋅X₂+X₃+3 {O(n)}
t₁₅, X₂: 6⋅X₂ {O(n)}
t₁₅, X₃: 6⋅X₃ {O(n)}
t₁₆, X₀: X₀ {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₉, X₀: X₀ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₂₀, X₀: X₀ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₁, X₀: X₀ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₁₁₃, X₀: X₀ {O(n)}
t₁₁₃, X₁: X₂ {O(n)}
t₁₁₃, X₂: X₂ {O(n)}
t₁₁₃, X₃: X₃ {O(n)}
t₁₁₄, X₀: X₀ {O(n)}
t₁₁₄, X₁: X₂ {O(n)}
t₁₁₄, X₂: X₂ {O(n)}
t₁₁₄, X₃: X₃ {O(n)}
t₁₁₅, X₀: X₀ {O(n)}
t₁₁₅, X₁: X₂ {O(n)}
t₁₁₅, X₂: X₂ {O(n)}
t₁₁₅, X₃: X₃ {O(n)}
t₁₁₆, X₀: 1 {O(1)}
t₁₁₆, X₁: X₂+1 {O(n)}
t₁₁₆, X₂: X₂ {O(n)}
t₁₁₆, X₃: X₃ {O(n)}
t₁₁₇, X₀: 1 {O(1)}
t₁₁₇, X₁: 3⋅X₂+X₃+3 {O(n)}
t₁₁₇, X₂: 2⋅X₂ {O(n)}
t₁₁₇, X₃: 2⋅X₃ {O(n)}
t₁₁₈, X₀: 1 {O(1)}
t₁₁₈, X₁: 2⋅X₂+X₃+2 {O(n)}
t₁₁₈, X₂: X₂ {O(n)}
t₁₁₈, X₃: X₃ {O(n)}
t₁₁₉, X₀: 1 {O(1)}
t₁₁₉, X₁: 2⋅X₂+X₃+2 {O(n)}
t₁₁₉, X₂: X₂ {O(n)}
t₁₁₉, X₃: X₃ {O(n)}
t₁₂₀, X₀: 2⋅X₀ {O(n)}
t₁₂₀, X₁: 0 {O(1)}
t₁₂₀, X₂: 2⋅X₂ {O(n)}
t₁₂₀, X₃: 2⋅X₃ {O(n)}
t₁₂₁, X₀: X₀ {O(n)}
t₁₂₁, X₁: X₂ {O(n)}
t₁₂₁, X₂: X₂ {O(n)}
t₁₂₁, X₃: X₃ {O(n)}
t₁₂₂, X₀: X₀ {O(n)}
t₁₂₂, X₁: X₂ {O(n)}
t₁₂₂, X₂: X₂ {O(n)}
t₁₂₂, X₃: X₃ {O(n)}
t₁₂₃, X₀: 2⋅X₀ {O(n)}
t₁₂₃, X₁: 0 {O(1)}
t₁₂₃, X₂: 2⋅X₂ {O(n)}
t₁₂₃, X₃: 2⋅X₃ {O(n)}
t₁₂₄, X₀: X₀ {O(n)}
t₁₂₄, X₁: X₂ {O(n)}
t₁₂₄, X₂: X₂ {O(n)}
t₁₂₄, X₃: X₃ {O(n)}
t₁₂₅, X₀: X₀ {O(n)}
t₁₂₅, X₁: X₂ {O(n)}
t₁₂₅, X₂: X₂ {O(n)}
t₁₂₅, X₃: X₃ {O(n)}