KoAT2 Proof Output

Initial Problem

Start: eval_ex3_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_ex3_0, eval_ex3_1, eval_ex3_2, eval_ex3_3, eval_ex3_4, eval_ex3_bb0_in, eval_ex3_bb1_in, eval_ex3_bb2_in, eval_ex3_bb3_in, eval_ex3_start, eval_ex3_stop
Transitions:
t₂: eval_ex3_0(X₀, X₁, X₂) → eval_ex3_1(X₀, X₁, X₂)
t₃: eval_ex3_1(X₀, X₁, X₂) → eval_ex3_2(X₀, X₁, X₂)
t₄: eval_ex3_2(X₀, X₁, X₂) → eval_ex3_3(X₀, X₁, X₂)
t₅: eval_ex3_3(X₀, X₁, X₂) → eval_ex3_4(X₀, X₁, X₂)
t₆: eval_ex3_4(X₀, X₁, X₂) → eval_ex3_bb1_in(X₂, X₁, X₂)
t₁: eval_ex3_bb0_in(X₀, X₁, X₂) → eval_ex3_0(X₀, X₁, X₂)
t₇: eval_ex3_bb1_in(X₀, X₁, X₂) → eval_ex3_bb2_in(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ 1 ≤ X₀
t₈: eval_ex3_bb1_in(X₀, X₁, X₂) → eval_ex3_bb3_in(X₀, X₁, X₂) :|: X₀ ≤ 0
t₉: eval_ex3_bb1_in(X₀, X₁, X₂) → eval_ex3_bb3_in(X₀, X₁, X₂) :|: 255 ≤ X₀
t₁₀: eval_ex3_bb2_in(X₀, X₁, X₂) → eval_ex3_bb1_in(1+X₀, X₁, X₂) :|: 1+X₁ ≤ 0
t₁₁: eval_ex3_bb2_in(X₀, X₁, X₂) → eval_ex3_bb1_in(1+X₀, X₁, X₂) :|: 1 ≤ X₁
t₁₂: eval_ex3_bb2_in(X₀, X₁, X₂) → eval_ex3_bb1_in(X₀-1, X₁, X₂) :|: 0 ≤ X₁ ∧ X₁ ≤ 0
t₁₃: eval_ex3_bb3_in(X₀, X₁, X₂) → eval_ex3_stop(X₀, X₁, X₂)
t₀: eval_ex3_start(X₀, X₁, X₂) → eval_ex3_bb0_in(X₀, X₁, X₂)

Preprocessing

Found invariant X₀ ≤ 254 ∧ 1 ≤ X₀ for location eval_ex3_bb2_in

Problem after Preprocessing

Start: eval_ex3_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_ex3_0, eval_ex3_1, eval_ex3_2, eval_ex3_3, eval_ex3_4, eval_ex3_bb0_in, eval_ex3_bb1_in, eval_ex3_bb2_in, eval_ex3_bb3_in, eval_ex3_start, eval_ex3_stop
Transitions:
t₂: eval_ex3_0(X₀, X₁, X₂) → eval_ex3_1(X₀, X₁, X₂)
t₃: eval_ex3_1(X₀, X₁, X₂) → eval_ex3_2(X₀, X₁, X₂)
t₄: eval_ex3_2(X₀, X₁, X₂) → eval_ex3_3(X₀, X₁, X₂)
t₅: eval_ex3_3(X₀, X₁, X₂) → eval_ex3_4(X₀, X₁, X₂)
t₆: eval_ex3_4(X₀, X₁, X₂) → eval_ex3_bb1_in(X₂, X₁, X₂)
t₁: eval_ex3_bb0_in(X₀, X₁, X₂) → eval_ex3_0(X₀, X₁, X₂)
t₇: eval_ex3_bb1_in(X₀, X₁, X₂) → eval_ex3_bb2_in(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ 1 ≤ X₀
t₈: eval_ex3_bb1_in(X₀, X₁, X₂) → eval_ex3_bb3_in(X₀, X₁, X₂) :|: X₀ ≤ 0
t₉: eval_ex3_bb1_in(X₀, X₁, X₂) → eval_ex3_bb3_in(X₀, X₁, X₂) :|: 255 ≤ X₀
t₁₀: eval_ex3_bb2_in(X₀, X₁, X₂) → eval_ex3_bb1_in(1+X₀, X₁, X₂) :|: 1+X₁ ≤ 0 ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₁₁: eval_ex3_bb2_in(X₀, X₁, X₂) → eval_ex3_bb1_in(1+X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₁₂: eval_ex3_bb2_in(X₀, X₁, X₂) → eval_ex3_bb1_in(X₀-1, X₁, X₂) :|: 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₁₃: eval_ex3_bb3_in(X₀, X₁, X₂) → eval_ex3_stop(X₀, X₁, X₂)
t₀: eval_ex3_start(X₀, X₁, X₂) → eval_ex3_bb0_in(X₀, X₁, X₂)

Found invariant X₂ ≤ 254 ∧ X₁+X₂ ≤ 253 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 509 ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 254+X₂ ∧ 1+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 254 ∧ X₀ ≤ 255 ∧ 2 ≤ X₀ for location eval_ex3_bb1_in_v3

Found invariant X₂ ≤ 253 ∧ X₂ ≤ 252+X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 507 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 253+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 253+X₁ ∧ X₀ ≤ 254 ∧ 2 ≤ X₀ for location eval_ex3_bb2_in_v3

Found invariant X₂ ≤ 254 ∧ X₂ ≤ 253+X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 509 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 254+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 254+X₁ ∧ X₀ ≤ 255 ∧ 2 ≤ X₀ for location eval_ex3_bb1_in_v2

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location eval_ex3_bb1_in

Found invariant X₂ ≤ 254+X₀ ∧ X₀ ≤ 254+X₂ for location eval_ex3_stop

Found invariant X₂ ≤ 254 ∧ X₂ ≤ 254+X₁ ∧ X₁+X₂ ≤ 254 ∧ X₂ ≤ 254+X₀ ∧ X₀+X₂ ≤ 507 ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 253 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 253+X₁ ∧ X₀ ≤ 253 ∧ 0 ≤ X₀ for location eval_ex3_bb1_in_v1

Found invariant X₂ ≤ 253 ∧ X₁+X₂ ≤ 252 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 507 ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 253+X₂ ∧ 1+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 253 ∧ X₀ ≤ 254 ∧ 2 ≤ X₀ for location eval_ex3_bb2_in_v2

Found invariant X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ for location eval_ex3_bb2_in_v1

Found invariant X₂ ≤ 254 ∧ X₂ ≤ 254+X₁ ∧ X₁+X₂ ≤ 254 ∧ X₂ ≤ 253+X₀ ∧ X₀+X₂ ≤ 507 ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 253 ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 253+X₁ ∧ X₀ ≤ 253 ∧ 1 ≤ X₀ for location eval_ex3_bb2_in_v4

Found invariant X₂ ≤ 254+X₀ ∧ X₀ ≤ 254+X₂ for location eval_ex3_bb3_in

Analysing control-flow refined program

MPRF for transition t₈₉: eval_ex3_bb1_in_v1(X₀, X₁, X₂) → eval_ex3_bb2_in_v4(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ X₀+X₂ ≤ 507 ∧ X₀ ≤ 255 ∧ X₂ ≤ 254+X₀ ∧ X₂ ≤ 254+X₁ ∧ X₁+X₂ ≤ 254 ∧ X₂ ≤ 254 ∧ X₀ ≤ 253 ∧ X₀ ≤ 253+X₁ ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 of depth 1:

new bound:

254 {O(1)}

MPRF:

• eval_ex3_bb1_in_v1: [1+X₀]
• eval_ex3_bb2_in_v4: [X₀]

MPRF for transition t₉₀: eval_ex3_bb2_in_v4(X₀, X₁, X₂) → eval_ex3_bb1_in_v1(X₀-1, X₁, X₂) :|: 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₀+X₂ ≤ 507 ∧ X₀ ≤ 254 ∧ X₂ ≤ 254+X₁ ∧ X₁+X₂ ≤ 254 ∧ X₂ ≤ 254 ∧ X₂ ≤ 253+X₀ ∧ X₀ ≤ 253 ∧ X₀ ≤ 253+X₁ ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ of depth 1:

new bound:

253 {O(1)}

MPRF:

• eval_ex3_bb1_in_v1: [X₀]
• eval_ex3_bb2_in_v4: [X₀]

MPRF for transition t₈₆: eval_ex3_bb1_in_v2(X₀, X₁, X₂) → eval_ex3_bb2_in_v3(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ X₀+X₂ ≤ 509 ∧ X₀ ≤ 255 ∧ X₀ ≤ 254+X₁ ∧ X₀ ≤ 254+X₂ ∧ X₂ ≤ 254 ∧ X₂ ≤ 253+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

511 {O(1)}

MPRF:

• eval_ex3_bb1_in_v2: [256-X₀]
• eval_ex3_bb2_in_v3: [255-X₀]

MPRF for transition t₈₇: eval_ex3_bb2_in_v3(X₀, X₁, X₂) → eval_ex3_bb1_in_v2(1+X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀+X₂ ≤ 507 ∧ X₀ ≤ 254 ∧ X₀ ≤ 253+X₁ ∧ X₀ ≤ 253+X₂ ∧ X₂ ≤ 253 ∧ X₂ ≤ 252+X₁ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ of depth 1:

new bound:

510 {O(1)}

MPRF:

• eval_ex3_bb1_in_v2: [255-X₀]
• eval_ex3_bb2_in_v3: [255-X₀]

MPRF for transition t₈₃: eval_ex3_bb1_in_v3(X₀, X₁, X₂) → eval_ex3_bb2_in_v2(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ X₀+X₂ ≤ 509 ∧ X₀ ≤ 255 ∧ X₀+X₁ ≤ 254 ∧ X₀ ≤ 254+X₂ ∧ X₂ ≤ 254 ∧ X₁+X₂ ≤ 253 ∧ 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 3+X₁ ≤ X₀ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ 0 of depth 1:

new bound:

510 {O(1)}

MPRF:

• eval_ex3_bb1_in_v3: [255-X₀]
• eval_ex3_bb2_in_v2: [254-X₀]

MPRF for transition t₈₄: eval_ex3_bb2_in_v2(X₀, X₁, X₂) → eval_ex3_bb1_in_v3(1+X₀, X₁, X₂) :|: 1+X₁ ≤ 0 ∧ X₀+X₂ ≤ 507 ∧ X₀ ≤ 254 ∧ X₀+X₁ ≤ 253 ∧ X₀ ≤ 253+X₂ ∧ X₂ ≤ 253 ∧ X₁+X₂ ≤ 252 ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 3+X₁ ≤ X₀ ∧ 3 ≤ X₀+X₂ of depth 1:

new bound:

510 {O(1)}

MPRF:

• eval_ex3_bb1_in_v3: [255-X₀]
• eval_ex3_bb2_in_v2: [255-X₀]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(1)

cfr-program:

Start: eval_ex3_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_ex3_0, eval_ex3_1, eval_ex3_2, eval_ex3_3, eval_ex3_4, eval_ex3_bb0_in, eval_ex3_bb1_in, eval_ex3_bb1_in_v1, eval_ex3_bb1_in_v2, eval_ex3_bb1_in_v3, eval_ex3_bb2_in_v1, eval_ex3_bb2_in_v2, eval_ex3_bb2_in_v3, eval_ex3_bb2_in_v4, eval_ex3_bb3_in, eval_ex3_start, eval_ex3_stop
Transitions:
t₂: eval_ex3_0(X₀, X₁, X₂) → eval_ex3_1(X₀, X₁, X₂)
t₃: eval_ex3_1(X₀, X₁, X₂) → eval_ex3_2(X₀, X₁, X₂)
t₄: eval_ex3_2(X₀, X₁, X₂) → eval_ex3_3(X₀, X₁, X₂)
t₅: eval_ex3_3(X₀, X₁, X₂) → eval_ex3_4(X₀, X₁, X₂)
t₆: eval_ex3_4(X₀, X₁, X₂) → eval_ex3_bb1_in(X₂, X₁, X₂)
t₁: eval_ex3_bb0_in(X₀, X₁, X₂) → eval_ex3_0(X₀, X₁, X₂)
t₇₈: eval_ex3_bb1_in(X₀, X₁, X₂) → eval_ex3_bb2_in_v1(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₈: eval_ex3_bb1_in(X₀, X₁, X₂) → eval_ex3_bb3_in(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₉: eval_ex3_bb1_in(X₀, X₁, X₂) → eval_ex3_bb3_in(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₇₆: eval_ex3_bb1_in(X₀, X₁, X₂) → eval_ex3_bb3_in(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₇₇: eval_ex3_bb1_in(X₀, X₁, X₂) → eval_ex3_bb3_in(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₈₉: eval_ex3_bb1_in_v1(X₀, X₁, X₂) → eval_ex3_bb2_in_v4(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ X₀+X₂ ≤ 507 ∧ X₀ ≤ 255 ∧ X₂ ≤ 254+X₀ ∧ X₂ ≤ 254+X₁ ∧ X₁+X₂ ≤ 254 ∧ X₂ ≤ 254 ∧ X₀ ≤ 253 ∧ X₀ ≤ 253+X₁ ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₈₈: eval_ex3_bb1_in_v1(X₀, X₁, X₂) → eval_ex3_bb3_in(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₀+X₂ ≤ 507 ∧ X₀ ≤ 255 ∧ X₂ ≤ 254+X₀ ∧ X₀ ≤ 254 ∧ X₂ ≤ 254+X₁ ∧ X₁+X₂ ≤ 254 ∧ X₂ ≤ 254 ∧ X₀ ≤ 253 ∧ X₀ ≤ 253+X₁ ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₈₆: eval_ex3_bb1_in_v2(X₀, X₁, X₂) → eval_ex3_bb2_in_v3(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ X₀+X₂ ≤ 509 ∧ X₀ ≤ 255 ∧ X₀ ≤ 254+X₁ ∧ X₀ ≤ 254+X₂ ∧ X₂ ≤ 254 ∧ X₂ ≤ 253+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁
t₈₅: eval_ex3_bb1_in_v2(X₀, X₁, X₂) → eval_ex3_bb3_in(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ X₀+X₂ ≤ 509 ∧ X₀ ≤ 255 ∧ X₀ ≤ 254+X₁ ∧ X₀ ≤ 254+X₂ ∧ X₂ ≤ 254 ∧ X₂ ≤ 253+X₁ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁
t₈₃: eval_ex3_bb1_in_v3(X₀, X₁, X₂) → eval_ex3_bb2_in_v2(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ X₀+X₂ ≤ 509 ∧ X₀ ≤ 255 ∧ X₀+X₁ ≤ 254 ∧ X₀ ≤ 254+X₂ ∧ X₂ ≤ 254 ∧ X₁+X₂ ≤ 253 ∧ 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 3+X₁ ≤ X₀ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ 0
t₈₂: eval_ex3_bb1_in_v3(X₀, X₁, X₂) → eval_ex3_bb3_in(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ X₀+X₂ ≤ 509 ∧ X₀ ≤ 255 ∧ X₀+X₁ ≤ 254 ∧ X₀ ≤ 254+X₂ ∧ X₂ ≤ 254 ∧ X₁+X₂ ≤ 253 ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 3+X₁ ≤ X₀ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ 0
t₇₉: eval_ex3_bb2_in_v1(X₀, X₁, X₂) → eval_ex3_bb1_in_v1(X₀-1, X₁, X₂) :|: 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254 ∧ X₂ ≤ 254 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₈₀: eval_ex3_bb2_in_v1(X₀, X₁, X₂) → eval_ex3_bb1_in_v2(1+X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254 ∧ X₂ ≤ 254 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₈₁: eval_ex3_bb2_in_v1(X₀, X₁, X₂) → eval_ex3_bb1_in_v3(1+X₀, X₁, X₂) :|: 1+X₁ ≤ 0 ∧ X₀+X₂ ≤ 508 ∧ X₀ ≤ 254 ∧ X₂ ≤ 254 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₈₄: eval_ex3_bb2_in_v2(X₀, X₁, X₂) → eval_ex3_bb1_in_v3(1+X₀, X₁, X₂) :|: 1+X₁ ≤ 0 ∧ X₀+X₂ ≤ 507 ∧ X₀ ≤ 254 ∧ X₀+X₁ ≤ 253 ∧ X₀ ≤ 253+X₂ ∧ X₂ ≤ 253 ∧ X₁+X₂ ≤ 252 ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 3+X₁ ≤ X₀ ∧ 3 ≤ X₀+X₂
t₈₇: eval_ex3_bb2_in_v3(X₀, X₁, X₂) → eval_ex3_bb1_in_v2(1+X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀+X₂ ≤ 507 ∧ X₀ ≤ 254 ∧ X₀ ≤ 253+X₁ ∧ X₀ ≤ 253+X₂ ∧ X₂ ≤ 253 ∧ X₂ ≤ 252+X₁ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂
t₉₀: eval_ex3_bb2_in_v4(X₀, X₁, X₂) → eval_ex3_bb1_in_v1(X₀-1, X₁, X₂) :|: 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₀+X₂ ≤ 507 ∧ X₀ ≤ 254 ∧ X₂ ≤ 254+X₁ ∧ X₁+X₂ ≤ 254 ∧ X₂ ≤ 254 ∧ X₂ ≤ 253+X₀ ∧ X₀ ≤ 253 ∧ X₀ ≤ 253+X₁ ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂
t₁₃: eval_ex3_bb3_in(X₀, X₁, X₂) → eval_ex3_stop(X₀, X₁, X₂) :|: X₂ ≤ 254+X₀ ∧ X₀ ≤ 254+X₂
t₀: eval_ex3_start(X₀, X₁, X₂) → eval_ex3_bb0_in(X₀, X₁, X₂)

All Bounds

Timebounds

Overall timebound:2567 {O(1)}
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)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₃: 1 {O(1)}
t₇₆: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₇₉: 1 {O(1)}
t₈₀: 1 {O(1)}
t₈₁: 1 {O(1)}
t₈₂: 1 {O(1)}
t₈₃: 510 {O(1)}
t₈₄: 510 {O(1)}
t₈₅: 1 {O(1)}
t₈₆: 511 {O(1)}
t₈₇: 510 {O(1)}
t₈₈: 1 {O(1)}
t₈₉: 254 {O(1)}
t₉₀: 253 {O(1)}

Costbounds

Overall costbound: 2567 {O(1)}
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)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₃: 1 {O(1)}
t₇₆: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₇₉: 1 {O(1)}
t₈₀: 1 {O(1)}
t₈₁: 1 {O(1)}
t₈₂: 1 {O(1)}
t₈₃: 510 {O(1)}
t₈₄: 510 {O(1)}
t₈₅: 1 {O(1)}
t₈₆: 511 {O(1)}
t₈₇: 510 {O(1)}
t₈₈: 1 {O(1)}
t₈₉: 254 {O(1)}
t₉₀: 253 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₆, X₀: X₂ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₈, X₀: X₂ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₉, X₀: X₂ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₁₃, X₀: 4⋅X₂+510 {O(n)}
t₁₃, X₁: 8⋅X₁ {O(n)}
t₁₃, X₂: 4⋅X₂+762 {O(n)}
t₇₆, X₀: X₂ {O(n)}
t₇₆, X₁: X₁ {O(n)}
t₇₆, X₂: X₂ {O(n)}
t₇₇, X₀: X₂ {O(n)}
t₇₇, X₁: X₁ {O(n)}
t₇₇, X₂: X₂ {O(n)}
t₇₈, X₀: 254 {O(1)}
t₇₈, X₁: X₁ {O(n)}
t₇₈, X₂: 254 {O(1)}
t₇₉, X₀: 253 {O(1)}
t₇₉, X₁: 0 {O(1)}
t₇₉, X₂: 254 {O(1)}
t₈₀, X₀: 255 {O(1)}
t₈₀, X₁: X₁ {O(n)}
t₈₀, X₂: 254 {O(1)}
t₈₁, X₀: 255 {O(1)}
t₈₁, X₁: X₁ {O(n)}
t₈₁, X₂: 254 {O(1)}
t₈₂, X₀: 255 {O(1)}
t₈₂, X₁: 2⋅X₁ {O(n)}
t₈₂, X₂: 254 {O(1)}
t₈₃, X₀: 254 {O(1)}
t₈₃, X₁: X₁ {O(n)}
t₈₃, X₂: 253 {O(1)}
t₈₄, X₀: 255 {O(1)}
t₈₄, X₁: X₁ {O(n)}
t₈₄, X₂: 253 {O(1)}
t₈₅, X₀: 255 {O(1)}
t₈₅, X₁: 2⋅X₁ {O(n)}
t₈₅, X₂: 254 {O(1)}
t₈₆, X₀: 254 {O(1)}
t₈₆, X₁: X₁ {O(n)}
t₈₆, X₂: 253 {O(1)}
t₈₇, X₀: 255 {O(1)}
t₈₇, X₁: X₁ {O(n)}
t₈₇, X₂: 253 {O(1)}
t₈₈, X₀: 0 {O(1)}
t₈₈, X₁: 0 {O(1)}
t₈₈, X₂: 254 {O(1)}
t₈₉, X₀: 253 {O(1)}
t₈₉, X₁: 0 {O(1)}
t₈₉, X₂: 254 {O(1)}
t₉₀, X₀: 252 {O(1)}
t₉₀, X₁: 0 {O(1)}
t₉₀, X₂: 254 {O(1)}