Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₄: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₅: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₆: l6(X₀, X₁, X₂) → l7(X₂, X₁, X₂)
t₇: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: 0 < X₀ ∧ X₀ < 255
t₈: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ ≤ 0
t₉: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: 255 ≤ X₀
t₁₀: l8(X₀, X₁, X₂) → l7(X₀+1, X₁, X₂) :|: X₁ < 0
t₁₁: l8(X₀, X₁, X₂) → l7(X₀+1, X₁, X₂) :|: 0 < X₁
t₁₂: l8(X₀, X₁, X₂) → l7(X₀-1, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₁₃: l9(X₀, X₁, X₂) → l10(X₀, X₁, X₂)
Preprocessing
Found invariant X₀ ≤ 254 ∧ 1 ≤ X₀ for location l8
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₄: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₅: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₆: l6(X₀, X₁, X₂) → l7(X₂, X₁, X₂)
t₇: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: 0 < X₀ ∧ X₀ < 255
t₈: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ ≤ 0
t₉: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: 255 ≤ X₀
t₁₀: l8(X₀, X₁, X₂) → l7(X₀+1, X₁, X₂) :|: X₁ < 0 ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₁₁: l8(X₀, X₁, X₂) → l7(X₀+1, X₁, X₂) :|: 0 < X₁ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₁₂: l8(X₀, X₁, X₂) → l7(X₀-1, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₁₃: l9(X₀, X₁, X₂) → l10(X₀, X₁, X₂)
Chain transitions t₁₂: l8→l7 and t₉: l7→l9 to t₁₀₆: l8→l9
Chain transitions t₁₁: l8→l7 and t₉: l7→l9 to t₁₀₇: l8→l9
Chain transitions t₁₁: l8→l7 and t₈: l7→l9 to t₁₀₈: l8→l9
Chain transitions t₁₂: l8→l7 and t₈: l7→l9 to t₁₀₉: l8→l9
Chain transitions t₁₀: l8→l7 and t₈: l7→l9 to t₁₁₀: l8→l9
Chain transitions t₁₀: l8→l7 and t₉: l7→l9 to t₁₁₁: l8→l9
Chain transitions t₁₀: l8→l7 and t₇: l7→l8 to t₁₁₂: l8→l8
Chain transitions t₁₁: l8→l7 and t₇: l7→l8 to t₁₁₃: l8→l8
Chain transitions t₁₂: l8→l7 and t₇: l7→l8 to t₁₁₄: l8→l8
Chain transitions t₆: l6→l7 and t₇: l7→l8 to t₁₁₅: l6→l8
Chain transitions t₆: l6→l7 and t₈: l7→l9 to t₁₁₆: l6→l9
Chain transitions t₆: l6→l7 and t₉: l7→l9 to t₁₁₇: l6→l9
Analysing control-flow refined program
Cut unsatisfiable transition t₁₀₆: l8→l9
Cut unsatisfiable transition t₁₀₈: l8→l9
Cut unsatisfiable transition t₁₁₀: l8→l9
Found invariant X₂ ≤ 254 ∧ X₂ ≤ 253+X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 253+X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ for location l8
Found invariant X₂ ≤ 254+X₀ ∧ X₀ ≤ 254+X₂ for location l10
Found invariant X₂ ≤ 254+X₀ ∧ X₀ ≤ 254+X₂ for location l9
MPRF for transition t₁₁₂: l8(X₀, X₁, X₂) -{2}> l8(1+X₀, X₁, X₂) :|: X₁ < 0 ∧ 0 < 1+X₀ ∧ X₀ < 254 ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ X₂ ≤ 254 ∧ X₂ ≤ 253+X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 253+X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ of depth 1:
new bound:
509 {O(1)}
MPRF for transition t₁₁₃: l8(X₀, X₁, X₂) -{2}> l8(1+X₀, X₁, X₂) :|: 0 < X₁ ∧ 0 < 1+X₀ ∧ X₀ < 254 ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ X₂ ≤ 254 ∧ X₂ ≤ 253+X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 253+X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ of depth 1:
new bound:
509 {O(1)}
MPRF for transition t₁₁₄: l8(X₀, X₁, X₂) -{2}> l8(X₀-1, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 < X₀ ∧ X₀ < 256 ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ X₂ ≤ 254 ∧ X₂ ≤ 253+X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 253+X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ of depth 1:
new bound:
254 {O(1)}
Analysing control-flow refined program
Cut unsatisfiable transition t₂₈₃: n_l7___5→l9
Cut unsatisfiable transition t₂₈₄: n_l7___6→l9
Cut unsatisfiable transition t₂₈₅: n_l7___4→l9
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 n_l8___1
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 n_l8___2
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 n_l8___3
Found invariant X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ for location n_l8___7
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 n_l7___6
Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l7
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 n_l7___5
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 n_l7___4
MPRF for transition t₂₆₀: n_l7___4(X₀, X₁, X₂) → n_l8___1(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ X₀ < 255 ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 253 ∧ 0 < X₀ ∧ X₀ < 255 ∧ 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 of depth 1:
new bound:
254 {O(1)}
MPRF for transition t₂₆₄: n_l8___1(X₀, X₁, X₂) → n_l7___4(X₀-1, 0, X₂) :|: X₀ ≤ 253 ∧ 0 < X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ 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 of depth 1:
new bound:
253 {O(1)}
MPRF for transition t₂₆₁: n_l7___5(X₀, X₁, X₂) → n_l8___2(X₀, X₁, X₂) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ 0 < X₁ ∧ 0 < X₀ ∧ X₀ < 255 ∧ 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 of depth 1:
new bound:
511 {O(1)}
MPRF for transition t₂₆₅: n_l8___2(X₀, X₁, X₂) → n_l7___5(X₀+1, X₁, X₂) :|: X₀ < 255 ∧ 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 254 ∧ 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 of depth 1:
new bound:
510 {O(1)}
MPRF for transition t₂₆₂: n_l7___6(X₀, X₁, X₂) → n_l8___3(X₀, X₁, X₂) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ X₁ < 0 ∧ 0 < X₀ ∧ X₀ < 255 ∧ 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 of depth 1:
new bound:
511 {O(1)}
MPRF for transition t₂₆₆: n_l8___3(X₀, X₁, X₂) → n_l7___6(X₀+1, X₁, X₂) :|: X₀ < 255 ∧ X₁ < 0 ∧ X₁ < 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 254 ∧ 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 of depth 1:
new bound:
510 {O(1)}
CFR: Improvement to new bound with the following program:
new bound:
Infinite
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l9, n_l7___4, n_l7___5, n_l7___6, n_l8___1, n_l8___2, n_l8___3, n_l8___7
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₄: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₅: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₆: l6(X₀, X₁, X₂) → l7(X₂, X₁, X₂)
t₈: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₉: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₂₆₃: l7(X₀, X₁, X₂) → n_l8___7(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 < X₀ ∧ X₀ < 255 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁₃: l9(X₀, X₁, X₂) → l10(X₀, X₁, X₂)
t₂₈₂: n_l7___4(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 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
t₂₆₀: n_l7___4(X₀, X₁, X₂) → n_l8___1(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ X₀ < 255 ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 253 ∧ 0 < X₀ ∧ X₀ < 255 ∧ 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
t₂₈₆: n_l7___5(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ 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
t₂₆₁: n_l7___5(X₀, X₁, X₂) → n_l8___2(X₀, X₁, X₂) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ 0 < X₁ ∧ 0 < X₀ ∧ X₀ < 255 ∧ 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
t₂₈₇: n_l7___6(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ 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
t₂₆₂: n_l7___6(X₀, X₁, X₂) → n_l8___3(X₀, X₁, X₂) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ X₁ < 0 ∧ 0 < X₀ ∧ X₀ < 255 ∧ 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
t₂₆₄: n_l8___1(X₀, X₁, X₂) → n_l7___4(X₀-1, 0, X₂) :|: X₀ ≤ 253 ∧ 0 < X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ 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
t₂₆₅: n_l8___2(X₀, X₁, X₂) → n_l7___5(X₀+1, X₁, X₂) :|: X₀ < 255 ∧ 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 254 ∧ 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
t₂₆₆: n_l8___3(X₀, X₁, X₂) → n_l7___6(X₀+1, X₁, X₂) :|: X₀ < 255 ∧ X₁ < 0 ∧ X₁ < 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 254 ∧ 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
t₂₆₇: n_l8___7(X₀, X₁, X₂) → n_l7___4(X₀-1, 0, X₂) :|: X₂ < 255 ∧ 0 < X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₂₆₈: n_l8___7(X₀, X₁, X₂) → n_l7___5(X₀+1, X₁, X₂) :|: X₂ < 255 ∧ 0 < X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 254 ∧ X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₂₆₉: n_l8___7(X₀, X₁, X₂) → n_l7___6(X₀+1, X₁, X₂) :|: X₂ < 255 ∧ 0 < X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 254 ∧ X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
CFR: Improvement to new bound with the following program:
new bound:
2549 {O(1)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l9, n_l7___4, n_l7___5, n_l7___6, n_l8___1, n_l8___2, n_l8___3, n_l8___7
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₄: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₅: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₆: l6(X₀, X₁, X₂) → l7(X₂, X₁, X₂)
t₈: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₉: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₂₆₃: l7(X₀, X₁, X₂) → n_l8___7(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 < X₀ ∧ X₀ < 255 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁₃: l9(X₀, X₁, X₂) → l10(X₀, X₁, X₂)
t₂₈₂: n_l7___4(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 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
t₂₆₀: n_l7___4(X₀, X₁, X₂) → n_l8___1(X₀, X₁, X₂) :|: X₀ ≤ 254 ∧ X₀ < 255 ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 253 ∧ 0 < X₀ ∧ X₀ < 255 ∧ 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
t₂₈₆: n_l7___5(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ 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
t₂₆₁: n_l7___5(X₀, X₁, X₂) → n_l8___2(X₀, X₁, X₂) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ 0 < X₁ ∧ 0 < X₀ ∧ X₀ < 255 ∧ 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
t₂₈₇: n_l7___6(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ 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
t₂₆₂: n_l7___6(X₀, X₁, X₂) → n_l8___3(X₀, X₁, X₂) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ X₁ < 0 ∧ 0 < X₀ ∧ X₀ < 255 ∧ 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
t₂₆₄: n_l8___1(X₀, X₁, X₂) → n_l7___4(X₀-1, 0, X₂) :|: X₀ ≤ 253 ∧ 0 < X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ 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
t₂₆₅: n_l8___2(X₀, X₁, X₂) → n_l7___5(X₀+1, X₁, X₂) :|: X₀ < 255 ∧ 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 254 ∧ 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
t₂₆₆: n_l8___3(X₀, X₁, X₂) → n_l7___6(X₀+1, X₁, X₂) :|: X₀ < 255 ∧ X₁ < 0 ∧ X₁ < 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 254 ∧ 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
t₂₆₇: n_l8___7(X₀, X₁, X₂) → n_l7___4(X₀-1, 0, X₂) :|: X₂ < 255 ∧ 0 < X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ ∧ X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₂₆₈: n_l8___7(X₀, X₁, X₂) → n_l7___5(X₀+1, X₁, X₂) :|: X₂ < 255 ∧ 0 < X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 254 ∧ X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₂₆₉: n_l8___7(X₀, X₁, X₂) → n_l7___6(X₀+1, X₁, X₂) :|: X₂ < 255 ∧ 0 < X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ < 0 ∧ 1 ≤ X₀ ∧ X₀ ≤ 254 ∧ X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:2566 {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)}
t₂₆₀: 254 {O(1)}
t₂₆₁: 511 {O(1)}
t₂₆₂: 511 {O(1)}
t₂₆₃: 1 {O(1)}
t₂₆₄: 253 {O(1)}
t₂₆₅: 510 {O(1)}
t₂₆₆: 510 {O(1)}
t₂₆₇: 1 {O(1)}
t₂₆₈: 1 {O(1)}
t₂₆₉: 1 {O(1)}
t₂₈₂: 1 {O(1)}
t₂₈₆: 1 {O(1)}
t₂₈₇: 1 {O(1)}
Costbounds
Overall costbound: 2566 {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)}
t₂₆₀: 254 {O(1)}
t₂₆₁: 511 {O(1)}
t₂₆₂: 511 {O(1)}
t₂₆₃: 1 {O(1)}
t₂₆₄: 253 {O(1)}
t₂₆₅: 510 {O(1)}
t₂₆₆: 510 {O(1)}
t₂₆₇: 1 {O(1)}
t₂₆₈: 1 {O(1)}
t₂₆₉: 1 {O(1)}
t₂₈₂: 1 {O(1)}
t₂₈₆: 1 {O(1)}
t₂₈₇: 1 {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: 2⋅X₂+510 {O(n)}
t₁₃, X₁: 6⋅X₁ {O(n)}
t₁₃, X₂: 5⋅X₂ {O(n)}
t₂₆₀, X₀: 253 {O(1)}
t₂₆₀, X₁: 0 {O(1)}
t₂₆₀, X₂: 254 {O(1)}
t₂₆₁, X₀: 254 {O(1)}
t₂₆₁, X₁: X₁ {O(n)}
t₂₆₁, X₂: 253 {O(1)}
t₂₆₂, X₀: 254 {O(1)}
t₂₆₂, X₁: X₁ {O(n)}
t₂₆₂, X₂: 253 {O(1)}
t₂₆₃, X₀: 254 {O(1)}
t₂₆₃, X₁: X₁ {O(n)}
t₂₆₃, X₂: 254 {O(1)}
t₂₆₄, X₀: 252 {O(1)}
t₂₆₄, X₁: 0 {O(1)}
t₂₆₄, X₂: 254 {O(1)}
t₂₆₅, X₀: 255 {O(1)}
t₂₆₅, X₁: X₁ {O(n)}
t₂₆₅, X₂: 253 {O(1)}
t₂₆₆, X₀: 255 {O(1)}
t₂₆₆, X₁: X₁ {O(n)}
t₂₆₆, X₂: 253 {O(1)}
t₂₆₇, X₀: 253 {O(1)}
t₂₆₇, X₁: 0 {O(1)}
t₂₆₇, X₂: 254 {O(1)}
t₂₆₈, X₀: 255 {O(1)}
t₂₆₈, X₁: X₁ {O(n)}
t₂₆₈, X₂: 254 {O(1)}
t₂₆₉, X₀: 255 {O(1)}
t₂₆₉, X₁: X₁ {O(n)}
t₂₆₉, X₂: 254 {O(1)}
t₂₈₂, X₀: 0 {O(1)}
t₂₈₂, X₁: 0 {O(1)}
t₂₈₂, X₂: 254 {O(1)}
t₂₈₆, X₀: 255 {O(1)}
t₂₈₆, X₁: 2⋅X₁ {O(n)}
t₂₈₆, X₂: 254 {O(1)}
t₂₈₇, X₀: 255 {O(1)}
t₂₈₇, X₁: 2⋅X₁ {O(n)}
t₂₈₇, X₂: 254 {O(1)}