Initial Problem

Start: eval_Loopus2011_ex3_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_Loopus2011_ex3_bb0_in, eval_Loopus2011_ex3_bb1_in, eval_Loopus2011_ex3_bb2_in, eval_Loopus2011_ex3_bb3_in, eval_Loopus2011_ex3_start, eval_Loopus2011_ex3_stop
Transitions:
t₁: eval_Loopus2011_ex3_bb0_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb1_in(X₂, X₁, X₂)
t₂: eval_Loopus2011_ex3_bb1_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb2_in(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ 1 ≤ X₀
t₃: eval_Loopus2011_ex3_bb1_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb3_in(X₀, X₁, X₂) :|: X₀ ≤ 0
t₄: eval_Loopus2011_ex3_bb1_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb3_in(X₀, X₁, X₂) :|: 255 ≤ X₀
t₅: eval_Loopus2011_ex3_bb2_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb1_in(1+X₀, X₁, X₂) :|: 1+X₁ ≤ 0
t₆: eval_Loopus2011_ex3_bb2_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb1_in(1+X₀, X₁, X₂) :|: 1 ≤ X₁
t₇: eval_Loopus2011_ex3_bb2_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb1_in(X₀-1, X₁, X₂) :|: 0 ≤ X₁ ∧ X₁ ≤ 0
t₈: eval_Loopus2011_ex3_bb3_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_stop(X₀, X₁, X₂)
t₀: eval_Loopus2011_ex3_start(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb0_in(X₀, X₁, X₂)

Preprocessing

Found invariant X₀ ≤ 254 ∧ 1 ≤ X₀ for location eval_Loopus2011_ex3_bb2_in

Problem after Preprocessing

Start: eval_Loopus2011_ex3_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_Loopus2011_ex3_bb0_in, eval_Loopus2011_ex3_bb1_in, eval_Loopus2011_ex3_bb2_in, eval_Loopus2011_ex3_bb3_in, eval_Loopus2011_ex3_start, eval_Loopus2011_ex3_stop
Transitions:
t₁: eval_Loopus2011_ex3_bb0_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb1_in(X₂, X₁, X₂)
t₂: eval_Loopus2011_ex3_bb1_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb2_in(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ 1 ≤ X₀
t₃: eval_Loopus2011_ex3_bb1_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb3_in(X₀, X₁, X₂) :|: X₀ ≤ 0
t₄: eval_Loopus2011_ex3_bb1_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb3_in(X₀, X₁, X₂) :|: 255 ≤ X₀
t₅: eval_Loopus2011_ex3_bb2_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb1_in(1+X₀, X₁, X₂) :|: 1+X₁ ≤ 0 ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₆: eval_Loopus2011_ex3_bb2_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb1_in(1+X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₇: eval_Loopus2011_ex3_bb2_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb1_in(X₀-1, X₁, X₂) :|: 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₈: eval_Loopus2011_ex3_bb3_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_stop(X₀, X₁, X₂)
t₀: eval_Loopus2011_ex3_start(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb0_in(X₀, X₁, X₂)

Found invariant X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ for location eval_Loopus2011_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_Loopus2011_ex3_bb2_in_v4

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_Loopus2011_ex3_bb1_in_v3

Found invariant X₂ ≤ 254+X₀ ∧ X₀ ≤ 254+X₂ for location eval_Loopus2011_ex3_stop

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_Loopus2011_ex3_bb2_in_v2

Found invariant X₂ ≤ 254+X₀ ∧ X₀ ≤ 254+X₂ for location eval_Loopus2011_ex3_bb3_in

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location eval_Loopus2011_ex3_bb1_in

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_Loopus2011_ex3_bb1_in_v1

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_Loopus2011_ex3_bb1_in_v2

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_Loopus2011_ex3_bb2_in_v3

Analysing control-flow refined program

MPRF for transition t₆₄: eval_Loopus2011_ex3_bb1_in_v1(X₀, X₁, X₂) → eval_Loopus2011_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_Loopus2011_ex3_bb1_in_v1: [1+X₀]
• eval_Loopus2011_ex3_bb2_in_v4: [X₀]

MPRF for transition t₆₅: eval_Loopus2011_ex3_bb2_in_v4(X₀, X₁, X₂) → eval_Loopus2011_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_Loopus2011_ex3_bb1_in_v1: [X₀]
• eval_Loopus2011_ex3_bb2_in_v4: [X₀]

MPRF for transition t₆₁: eval_Loopus2011_ex3_bb1_in_v2(X₀, X₁, X₂) → eval_Loopus2011_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:

510 {O(1)}

MPRF:

• eval_Loopus2011_ex3_bb1_in_v2: [255-X₀]
• eval_Loopus2011_ex3_bb2_in_v3: [254-X₀]

MPRF for transition t₆₂: eval_Loopus2011_ex3_bb2_in_v3(X₀, X₁, X₂) → eval_Loopus2011_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_Loopus2011_ex3_bb1_in_v2: [255-X₀]
• eval_Loopus2011_ex3_bb2_in_v3: [255-X₀]

MPRF for transition t₅₈: eval_Loopus2011_ex3_bb1_in_v3(X₀, X₁, X₂) → eval_Loopus2011_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_Loopus2011_ex3_bb1_in_v3: [255-X₀]
• eval_Loopus2011_ex3_bb2_in_v2: [254-X₀]

MPRF for transition t₅₉: eval_Loopus2011_ex3_bb2_in_v2(X₀, X₁, X₂) → eval_Loopus2011_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_Loopus2011_ex3_bb1_in_v3: [255-X₀]
• eval_Loopus2011_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_Loopus2011_ex3_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_Loopus2011_ex3_bb0_in, eval_Loopus2011_ex3_bb1_in, eval_Loopus2011_ex3_bb1_in_v1, eval_Loopus2011_ex3_bb1_in_v2, eval_Loopus2011_ex3_bb1_in_v3, eval_Loopus2011_ex3_bb2_in_v1, eval_Loopus2011_ex3_bb2_in_v2, eval_Loopus2011_ex3_bb2_in_v3, eval_Loopus2011_ex3_bb2_in_v4, eval_Loopus2011_ex3_bb3_in, eval_Loopus2011_ex3_start, eval_Loopus2011_ex3_stop
Transitions:
t₁: eval_Loopus2011_ex3_bb0_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb1_in(X₂, X₁, X₂)
t₅₃: eval_Loopus2011_ex3_bb1_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb2_in_v1(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₃: eval_Loopus2011_ex3_bb1_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb3_in(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₄: eval_Loopus2011_ex3_bb1_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb3_in(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₅₁: eval_Loopus2011_ex3_bb1_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb3_in(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₅₂: eval_Loopus2011_ex3_bb1_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb3_in(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₆₄: eval_Loopus2011_ex3_bb1_in_v1(X₀, X₁, X₂) → eval_Loopus2011_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
t₆₃: eval_Loopus2011_ex3_bb1_in_v1(X₀, X₁, X₂) → eval_Loopus2011_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
t₆₁: eval_Loopus2011_ex3_bb1_in_v2(X₀, X₁, X₂) → eval_Loopus2011_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
t₆₀: eval_Loopus2011_ex3_bb1_in_v2(X₀, X₁, X₂) → eval_Loopus2011_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
t₅₈: eval_Loopus2011_ex3_bb1_in_v3(X₀, X₁, X₂) → eval_Loopus2011_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
t₅₇: eval_Loopus2011_ex3_bb1_in_v3(X₀, X₁, X₂) → eval_Loopus2011_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
t₅₄: eval_Loopus2011_ex3_bb2_in_v1(X₀, X₁, X₂) → eval_Loopus2011_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
t₅₅: eval_Loopus2011_ex3_bb2_in_v1(X₀, X₁, X₂) → eval_Loopus2011_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
t₅₆: eval_Loopus2011_ex3_bb2_in_v1(X₀, X₁, X₂) → eval_Loopus2011_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
t₅₉: eval_Loopus2011_ex3_bb2_in_v2(X₀, X₁, X₂) → eval_Loopus2011_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
t₆₂: eval_Loopus2011_ex3_bb2_in_v3(X₀, X₁, X₂) → eval_Loopus2011_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
t₆₅: eval_Loopus2011_ex3_bb2_in_v4(X₀, X₁, X₂) → eval_Loopus2011_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
t₈: eval_Loopus2011_ex3_bb3_in(X₀, X₁, X₂) → eval_Loopus2011_ex3_stop(X₀, X₁, X₂) :|: X₂ ≤ 254+X₀ ∧ X₀ ≤ 254+X₂
t₀: eval_Loopus2011_ex3_start(X₀, X₁, X₂) → eval_Loopus2011_ex3_bb0_in(X₀, X₁, X₂)

All Bounds

Timebounds

Overall timebound:2561 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₈: 1 {O(1)}
t₅₁: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₇: 1 {O(1)}
t₅₈: 510 {O(1)}
t₅₉: 510 {O(1)}
t₆₀: 1 {O(1)}
t₆₁: 510 {O(1)}
t₆₂: 510 {O(1)}
t₆₃: 1 {O(1)}
t₆₄: 254 {O(1)}
t₆₅: 253 {O(1)}

Costbounds

Overall costbound: 2561 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₈: 1 {O(1)}
t₅₁: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₇: 1 {O(1)}
t₅₈: 510 {O(1)}
t₅₉: 510 {O(1)}
t₆₀: 1 {O(1)}
t₆₁: 510 {O(1)}
t₆₂: 510 {O(1)}
t₆₃: 1 {O(1)}
t₆₄: 254 {O(1)}
t₆₅: 253 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₃, X₀: X₂ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₈, X₀: 4⋅X₂+510 {O(n)}
t₈, X₁: 8⋅X₁ {O(n)}
t₈, X₂: 4⋅X₂+762 {O(n)}
t₅₁, X₀: X₂ {O(n)}
t₅₁, X₁: X₁ {O(n)}
t₅₁, X₂: X₂ {O(n)}
t₅₂, X₀: X₂ {O(n)}
t₅₂, X₁: X₁ {O(n)}
t₅₂, X₂: X₂ {O(n)}
t₅₃, X₀: 254 {O(1)}
t₅₃, X₁: X₁ {O(n)}
t₅₃, X₂: 254 {O(1)}
t₅₄, X₀: 253 {O(1)}
t₅₄, X₁: 0 {O(1)}
t₅₄, X₂: 254 {O(1)}
t₅₅, X₀: 255 {O(1)}
t₅₅, X₁: X₁ {O(n)}
t₅₅, X₂: 254 {O(1)}
t₅₆, X₀: 255 {O(1)}
t₅₆, X₁: X₁ {O(n)}
t₅₆, X₂: 254 {O(1)}
t₅₇, X₀: 255 {O(1)}
t₅₇, X₁: 2⋅X₁ {O(n)}
t₅₇, X₂: 254 {O(1)}
t₅₈, X₀: 254 {O(1)}
t₅₈, X₁: X₁ {O(n)}
t₅₈, X₂: 253 {O(1)}
t₅₉, X₀: 255 {O(1)}
t₅₉, X₁: X₁ {O(n)}
t₅₉, X₂: 253 {O(1)}
t₆₀, X₀: 255 {O(1)}
t₆₀, X₁: 2⋅X₁ {O(n)}
t₆₀, X₂: 254 {O(1)}
t₆₁, X₀: 254 {O(1)}
t₆₁, X₁: X₁ {O(n)}
t₆₁, X₂: 253 {O(1)}
t₆₂, X₀: 255 {O(1)}
t₆₂, X₁: X₁ {O(n)}
t₆₂, X₂: 253 {O(1)}
t₆₃, X₀: 0 {O(1)}
t₆₃, X₁: 0 {O(1)}
t₆₃, X₂: 254 {O(1)}
t₆₄, X₀: 253 {O(1)}
t₆₄, X₁: 0 {O(1)}
t₆₄, X₂: 254 {O(1)}
t₆₅, X₀: 252 {O(1)}
t₆₅, X₁: 0 {O(1)}
t₆₅, X₂: 254 {O(1)}