KoAT2 Proof Output

Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₂, X₃, X₂, X₃)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₀+X₁, X₁-1, X₂, X₃) :|: 0 ≤ X₁
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₀+X₁, X₁, X₂, X₃) :|: 1+X₁ ≤ 0
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃)
t₀: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant X₁ ≤ X₃ ∧ 0 ≤ X₀ for location eval_foo_bb2_in

Found invariant X₁ ≤ X₃ for location eval_foo_bb1_in

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

Found invariant X₁ ≤ X₃ ∧ 1+X₀ ≤ 0 for location eval_foo_bb3_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₂, X₃, X₂, X₃)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₁ ≤ X₃
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₀+X₁, X₁-1, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₀+X₁, X₁, X₂, X₃) :|: 1+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₁ ≤ X₃
t₀: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

MPRF for transition t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₀+X₁, X₁-1, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

• eval_foo_bb1_in: [1+X₁]
• eval_foo_bb2_in: [1+X₁]

MPRF for transition t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₃⋅X₃⋅X₃+4⋅X₃⋅X₃+X₂⋅X₃+2⋅X₂+7⋅X₃+6 {O(n^3)}

MPRF:

• eval_foo_bb1_in: [2+X₀]
• eval_foo_bb2_in: [1+X₀]

MPRF for transition t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₀+X₁, X₁, X₂, X₃) :|: 1+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₃⋅X₃⋅X₃+4⋅X₃⋅X₃+X₂⋅X₃+2⋅X₂+6⋅X₃+4 {O(n^3)}

MPRF:

• eval_foo_bb1_in: [1+X₀]
• eval_foo_bb2_in: [1+X₀]

Found invariant 1+X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2+X₁+X₃ ≤ 0 ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ for location eval_foo_bb1_in_v1

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 2+X₀+X₁ ∧ 0 ≤ 1+X₀ for location eval_foo_bb1_in_v3

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb1_in_v2

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

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location eval_foo_bb3_in

Found invariant 1+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2+X₁+X₃ ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₀ for location eval_foo_bb2_in_v4

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb2_in_v2

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location eval_foo_bb1_in

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location eval_foo_bb2_in_v1

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb2_in_v3

Analysing control-flow refined program

MPRF for transition t₄₆: eval_foo_bb1_in_v1(X₀, X₁, X₂, X₃) → eval_foo_bb2_in_v4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ 0 ∧ 2+X₁+X₃ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF:

• eval_foo_bb1_in_v1: [1+X₀]
• eval_foo_bb2_in_v4: [X₀]

MPRF for transition t₄₇: eval_foo_bb2_in_v4(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v1(X₀+X₁, X₁, X₂, X₃) :|: 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₃ ≤ 0 ∧ 2+X₁ ≤ X₂ ∧ 2+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ of depth 1:

new bound:

2⋅X₃+X₂ {O(n)}

MPRF:

• eval_foo_bb1_in_v1: [X₀-X₁]
• eval_foo_bb2_in_v4: [1+X₀]

MPRF for transition t₃₉: eval_foo_bb1_in_v2(X₀, X₁, X₂, X₃) → eval_foo_bb2_in_v2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₃+3 {O(n)}

MPRF:

• eval_foo_bb1_in_v2: [2+X₁]
• eval_foo_bb2_in_v2: [1+X₁]

MPRF for transition t₄₁: eval_foo_bb2_in_v2(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v2(X₀+X₁, X₁-1, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₃+2 {O(n)}

MPRF:

• eval_foo_bb1_in_v2: [1+X₁]
• eval_foo_bb2_in_v2: [1+X₁]

MPRF for transition t₄₃: eval_foo_bb1_in_v3(X₀, X₁, X₂, X₃) → eval_foo_bb2_in_v3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ 2+X₀+X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₃⋅X₃+12⋅X₃+X₂+17 {O(n^2)}

MPRF:

• eval_foo_bb1_in_v3: [1+X₀]
• eval_foo_bb2_in_v3: [X₀]

MPRF for transition t₄₄: eval_foo_bb2_in_v3(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v3(X₀+X₁, X₁, X₂, X₃) :|: 1+X₁ ≤ 0 ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₃⋅X₃+12⋅X₃+X₂+17 {O(n^2)}

MPRF:

• eval_foo_bb1_in_v3: [X₀-X₁]
• eval_foo_bb2_in_v3: [1+X₀]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n^2)

cfr-program:

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb1_in_v1, eval_foo_bb1_in_v2, eval_foo_bb1_in_v3, eval_foo_bb2_in_v1, eval_foo_bb2_in_v2, eval_foo_bb2_in_v3, eval_foo_bb2_in_v4, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₂, X₃, X₂, X₃)
t₃₆: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in_v1(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₃₅: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₄₆: eval_foo_bb1_in_v1(X₀, X₁, X₂, X₃) → eval_foo_bb2_in_v4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ 0 ∧ 2+X₁+X₃ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂
t₄₅: eval_foo_bb1_in_v1(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ 0 ∧ 2+X₁+X₃ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂
t₃₉: eval_foo_bb1_in_v2(X₀, X₁, X₂, X₃) → eval_foo_bb2_in_v2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₄₃: eval_foo_bb1_in_v3(X₀, X₁, X₂, X₃) → eval_foo_bb2_in_v3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ 2+X₀+X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₄₂: eval_foo_bb1_in_v3(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ 0 ≤ 2+X₀+X₁ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₃₇: eval_foo_bb2_in_v1(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v1(X₀+X₁, X₁, X₂, X₃) :|: 1+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂
t₃₈: eval_foo_bb2_in_v1(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v2(X₀+X₁, X₁-1, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂
t₄₁: eval_foo_bb2_in_v2(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v2(X₀+X₁, X₁-1, X₂, X₃) :|: 0 ≤ X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₄₀: eval_foo_bb2_in_v2(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v3(X₀+X₁, X₁, X₂, X₃) :|: 1+X₁ ≤ 0 ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₄₄: eval_foo_bb2_in_v3(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v3(X₀+X₁, X₁, X₂, X₃) :|: 1+X₁ ≤ 0 ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₄₇: eval_foo_bb2_in_v4(X₀, X₁, X₂, X₃) → eval_foo_bb1_in_v1(X₀+X₁, X₁, X₂, X₃) :|: 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₃ ≤ 0 ∧ 2+X₁ ≤ X₂ ∧ 2+X₁+X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₃
t₀: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

All Bounds

Timebounds

Overall timebound:4⋅X₃⋅X₃+29⋅X₃+4⋅X₂+51 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: X₃+3 {O(n)}
t₄₀: 1 {O(1)}
t₄₁: X₃+2 {O(n)}
t₄₂: 1 {O(1)}
t₄₃: 2⋅X₃⋅X₃+12⋅X₃+X₂+17 {O(n^2)}
t₄₄: 2⋅X₃⋅X₃+12⋅X₃+X₂+17 {O(n^2)}
t₄₅: 1 {O(1)}
t₄₆: X₂+X₃+1 {O(n)}
t₄₇: 2⋅X₃+X₂ {O(n)}

Costbounds

Overall costbound: 4⋅X₃⋅X₃+29⋅X₃+4⋅X₂+51 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: X₃+3 {O(n)}
t₄₀: 1 {O(1)}
t₄₁: X₃+2 {O(n)}
t₄₂: 1 {O(1)}
t₄₃: 2⋅X₃⋅X₃+12⋅X₃+X₂+17 {O(n^2)}
t₄₄: 2⋅X₃⋅X₃+12⋅X₃+X₂+17 {O(n^2)}
t₄₅: 1 {O(1)}
t₄₆: X₂+X₃+1 {O(n)}
t₄₇: 2⋅X₃+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: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₃, X₀: X₂ {O(n)}
t₃, X₁: X₃ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₆, X₀: 3⋅X₃+4⋅X₂+1 {O(n)}
t₆, X₁: 4⋅X₃+1 {O(n)}
t₆, X₂: 6⋅X₂ {O(n)}
t₆, X₃: 6⋅X₃ {O(n)}
t₃₅, X₀: X₂ {O(n)}
t₃₅, X₁: X₃ {O(n)}
t₃₅, X₂: X₂ {O(n)}
t₃₅, X₃: X₃ {O(n)}
t₃₆, X₀: X₂ {O(n)}
t₃₆, X₁: X₃ {O(n)}
t₃₆, X₂: X₂ {O(n)}
t₃₆, X₃: X₃ {O(n)}
t₃₇, X₀: X₂+X₃ {O(n)}
t₃₇, X₁: X₃ {O(n)}
t₃₇, X₂: X₂ {O(n)}
t₃₇, X₃: X₃ {O(n)}
t₃₈, X₀: X₂+X₃ {O(n)}
t₃₈, X₁: X₃+1 {O(n)}
t₃₈, X₂: X₂ {O(n)}
t₃₈, X₃: X₃ {O(n)}
t₃₉, X₀: 2⋅X₃⋅X₃+12⋅X₃+X₂+15 {O(n^2)}
t₃₉, X₁: X₃+2 {O(n)}
t₃₉, X₂: X₂ {O(n)}
t₃₉, X₃: X₃ {O(n)}
t₄₀, X₀: 2⋅X₃⋅X₃+12⋅X₃+X₂+16 {O(n^2)}
t₄₀, X₁: 1 {O(1)}
t₄₀, X₂: X₂ {O(n)}
t₄₀, X₃: X₃ {O(n)}
t₄₁, X₀: 2⋅X₃⋅X₃+12⋅X₃+X₂+15 {O(n^2)}
t₄₁, X₁: X₃+2 {O(n)}
t₄₁, X₂: X₂ {O(n)}
t₄₁, X₃: X₃ {O(n)}
t₄₂, X₀: 1 {O(1)}
t₄₂, X₁: 1 {O(1)}
t₄₂, X₂: 2⋅X₂ {O(n)}
t₄₂, X₃: 2⋅X₃ {O(n)}
t₄₃, X₀: 2⋅X₃⋅X₃+12⋅X₃+X₂+17 {O(n^2)}
t₄₃, X₁: 1 {O(1)}
t₄₃, X₂: X₂ {O(n)}
t₄₃, X₃: X₃ {O(n)}
t₄₄, X₀: 2⋅X₃⋅X₃+12⋅X₃+X₂+17 {O(n^2)}
t₄₄, X₁: 1 {O(1)}
t₄₄, X₂: X₂ {O(n)}
t₄₄, X₃: X₃ {O(n)}
t₄₅, X₀: 2⋅X₂+3⋅X₃ {O(n)}
t₄₅, X₁: 2⋅X₃ {O(n)}
t₄₅, X₂: 2⋅X₂ {O(n)}
t₄₅, X₃: 2⋅X₃ {O(n)}
t₄₆, X₀: 2⋅X₃+X₂ {O(n)}
t₄₆, X₁: X₃ {O(n)}
t₄₆, X₂: X₂ {O(n)}
t₄₆, X₃: X₃ {O(n)}
t₄₇, X₀: 2⋅X₃+X₂ {O(n)}
t₄₇, X₁: X₃ {O(n)}
t₄₇, X₂: X₂ {O(n)}
t₄₇, X₃: X₃ {O(n)}