Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 0 < X₀ ∧ X₀ < 255
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 255 ≤ X₀
t₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₅: l3(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₁ < 0
t₆: l3(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: 0 < X₁
t₇: l3(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₈: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)

Preprocessing

Found invariant X₀ ≤ 254 ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 0 < X₀ ∧ X₀ < 255
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 255 ≤ X₀
t₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₅: l3(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₁ < 0 ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₆: l3(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: 0 < X₁ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₇: l3(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀
t₈: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)

Chain transitions t₇: l3→l1 and t₄: l1→l4 to t₈₁: l3→l4

Chain transitions t₆: l3→l1 and t₄: l1→l4 to t₈₂: l3→l4

Chain transitions t₆: l3→l1 and t₃: l1→l4 to t₈₃: l3→l4

Chain transitions t₇: l3→l1 and t₃: l1→l4 to t₈₄: l3→l4

Chain transitions t₅: l3→l1 and t₃: l1→l4 to t₈₅: l3→l4

Chain transitions t₅: l3→l1 and t₄: l1→l4 to t₈₆: l3→l4

Chain transitions t₅: l3→l1 and t₂: l1→l3 to t₈₇: l3→l3

Chain transitions t₆: l3→l1 and t₂: l1→l3 to t₈₈: l3→l3

Chain transitions t₇: l3→l1 and t₂: l1→l3 to t₈₉: l3→l3

Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₉₀: l2→l3

Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₉₁: l2→l4

Chain transitions t₁: l2→l1 and t₄: l1→l4 to t₉₂: l2→l4

Analysing control-flow refined program

Cut unsatisfiable transition t₈₁: l3→l4

Cut unsatisfiable transition t₈₃: l3→l4

Cut unsatisfiable transition t₈₅: l3→l4

Found invariant X₂ ≤ 254+X₀ ∧ X₀ ≤ 254+X₂ for location l5

Found invariant X₂ ≤ 254+X₀ ∧ X₀ ≤ 254+X₂ for location l4

Found invariant X₂ ≤ 254 ∧ X₂ ≤ 253+X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 253+X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ for location l3

MPRF for transition t₈₇: l3(X₀, X₁, X₂) -{2}> l3(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 t₈₈: l3(X₀, X₁, X₂) -{2}> l3(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 t₈₉: l3(X₀, X₁, X₂) -{2}> l3(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 t₂₄₃: n_l1___5→l4

Cut unsatisfiable transition t₂₄₄: n_l1___6→l4

Cut unsatisfiable transition t₂₄₅: n_l1___4→l4

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_l1___6

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_l1___4

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_l3___3

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_l1___5

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_l3___2

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

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_l3___1

Found invariant X₂ ≤ 254 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 508 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 254 ∧ 1 ≤ X₀ for location n_l3___7

MPRF for transition t₂₂₀: n_l1___4(X₀, X₁, X₂) → n_l3___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 t₂₂₄: n_l3___1(X₀, X₁, X₂) → n_l1___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 t₂₂₁: n_l1___5(X₀, X₁, X₂) → n_l3___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 t₂₂₅: n_l3___2(X₀, X₁, X₂) → n_l1___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 t₂₂₂: n_l1___6(X₀, X₁, X₂) → n_l3___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 t₂₂₆: n_l3___3(X₀, X₁, X₂) → n_l1___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, l2, l4, l5, n_l1___4, n_l1___5, n_l1___6, n_l3___1, n_l3___2, n_l3___3, n_l3___7
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₂₂₃: l1(X₀, X₁, X₂) → n_l3___7(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 < X₀ ∧ X₀ < 255 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₈: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₂₄₂: n_l1___4(X₀, X₁, X₂) → l4(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
t₂₂₀: n_l1___4(X₀, X₁, X₂) → n_l3___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
t₂₄₆: n_l1___5(X₀, X₁, X₂) → l4(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
t₂₂₁: n_l1___5(X₀, X₁, X₂) → n_l3___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
t₂₄₇: n_l1___6(X₀, X₁, X₂) → l4(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
t₂₂₂: n_l1___6(X₀, X₁, X₂) → n_l3___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
t₂₂₄: n_l3___1(X₀, X₁, X₂) → n_l1___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
t₂₂₅: n_l3___2(X₀, X₁, X₂) → n_l1___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
t₂₂₆: n_l3___3(X₀, X₁, X₂) → n_l1___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
t₂₂₇: n_l3___7(X₀, X₁, X₂) → n_l1___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
t₂₂₈: n_l3___7(X₀, X₁, X₂) → n_l1___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
t₂₂₉: n_l3___7(X₀, X₁, X₂) → n_l1___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, l2, l4, l5, n_l1___4, n_l1___5, n_l1___6, n_l3___1, n_l3___2, n_l3___3, n_l3___7
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 255 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₂₂₃: l1(X₀, X₁, X₂) → n_l3___7(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 < X₀ ∧ X₀ < 255 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₈: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₂₄₂: n_l1___4(X₀, X₁, X₂) → l4(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
t₂₂₀: n_l1___4(X₀, X₁, X₂) → n_l3___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
t₂₄₆: n_l1___5(X₀, X₁, X₂) → l4(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
t₂₂₁: n_l1___5(X₀, X₁, X₂) → n_l3___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
t₂₄₇: n_l1___6(X₀, X₁, X₂) → l4(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
t₂₂₂: n_l1___6(X₀, X₁, X₂) → n_l3___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
t₂₂₄: n_l3___1(X₀, X₁, X₂) → n_l1___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
t₂₂₅: n_l3___2(X₀, X₁, X₂) → n_l1___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
t₂₂₆: n_l3___3(X₀, X₁, X₂) → n_l1___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
t₂₂₇: n_l3___7(X₀, X₁, X₂) → n_l1___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
t₂₂₈: n_l3___7(X₀, X₁, X₂) → n_l1___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
t₂₂₉: n_l3___7(X₀, X₁, X₂) → n_l1___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:2561 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₈: 1 {O(1)}
t₂₂₀: 254 {O(1)}
t₂₂₁: 511 {O(1)}
t₂₂₂: 511 {O(1)}
t₂₂₃: 1 {O(1)}
t₂₂₄: 253 {O(1)}
t₂₂₅: 510 {O(1)}
t₂₂₆: 510 {O(1)}
t₂₂₇: 1 {O(1)}
t₂₂₈: 1 {O(1)}
t₂₂₉: 1 {O(1)}
t₂₄₂: 1 {O(1)}
t₂₄₆: 1 {O(1)}
t₂₄₇: 1 {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)}
t₂₂₀: 254 {O(1)}
t₂₂₁: 511 {O(1)}
t₂₂₂: 511 {O(1)}
t₂₂₃: 1 {O(1)}
t₂₂₄: 253 {O(1)}
t₂₂₅: 510 {O(1)}
t₂₂₆: 510 {O(1)}
t₂₂₇: 1 {O(1)}
t₂₂₈: 1 {O(1)}
t₂₂₉: 1 {O(1)}
t₂₄₂: 1 {O(1)}
t₂₄₆: 1 {O(1)}
t₂₄₇: 1 {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: 2⋅X₂+510 {O(n)}
t₈, X₁: 6⋅X₁ {O(n)}
t₈, X₂: 5⋅X₂ {O(n)}
t₂₂₀, X₀: 253 {O(1)}
t₂₂₀, X₁: 0 {O(1)}
t₂₂₀, X₂: 254 {O(1)}
t₂₂₁, X₀: 254 {O(1)}
t₂₂₁, X₁: X₁ {O(n)}
t₂₂₁, X₂: 253 {O(1)}
t₂₂₂, X₀: 254 {O(1)}
t₂₂₂, X₁: X₁ {O(n)}
t₂₂₂, X₂: 253 {O(1)}
t₂₂₃, X₀: 254 {O(1)}
t₂₂₃, X₁: X₁ {O(n)}
t₂₂₃, X₂: 254 {O(1)}
t₂₂₄, X₀: 252 {O(1)}
t₂₂₄, X₁: 0 {O(1)}
t₂₂₄, X₂: 254 {O(1)}
t₂₂₅, X₀: 255 {O(1)}
t₂₂₅, X₁: X₁ {O(n)}
t₂₂₅, X₂: 253 {O(1)}
t₂₂₆, X₀: 255 {O(1)}
t₂₂₆, X₁: X₁ {O(n)}
t₂₂₆, X₂: 253 {O(1)}
t₂₂₇, X₀: 253 {O(1)}
t₂₂₇, X₁: 0 {O(1)}
t₂₂₇, X₂: 254 {O(1)}
t₂₂₈, X₀: 255 {O(1)}
t₂₂₈, X₁: X₁ {O(n)}
t₂₂₈, X₂: 254 {O(1)}
t₂₂₉, X₀: 255 {O(1)}
t₂₂₉, X₁: X₁ {O(n)}
t₂₂₉, X₂: 254 {O(1)}
t₂₄₂, X₀: 0 {O(1)}
t₂₄₂, X₁: 0 {O(1)}
t₂₄₂, X₂: 254 {O(1)}
t₂₄₆, X₀: 255 {O(1)}
t₂₄₆, X₁: 2⋅X₁ {O(n)}
t₂₄₆, X₂: 254 {O(1)}
t₂₄₇, X₀: 255 {O(1)}
t₂₄₇, X₁: 2⋅X₁ {O(n)}
t₂₄₇, X₂: 254 {O(1)}