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) :|: X₀ < X₁
t₈: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₁ < X₀
t₉: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₀: l8(X₀, X₁, X₂) → l7(X₀+1, X₁, X₂)
t₁₁: l9(X₀, X₁, X₂) → l10(X₀, X₁, X₂)

Preprocessing

Found invariant X₂ ≤ X₀ for location l7

Found invariant X₂ ≤ X₀ for location l8

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l10

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l9

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) :|: X₀ < X₁ ∧ X₂ ≤ X₀
t₈: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₂ ≤ X₀
t₉: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀
t₁₀: l8(X₀, X₁, X₂) → l7(X₀+1, X₁, X₂) :|: X₂ ≤ X₀
t₁₁: l9(X₀, X₁, X₂) → l10(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁

MPRF for transition t₇: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₂ ≤ X₀ of depth 1:

new bound:

X₁+X₂ {O(n)}

MPRF:

l8 [X₁-X₀-1 ]
l7 [X₁-X₀ ]

Analysing control-flow refined program

Cut unsatisfiable transition t₉₂: n_l7___2→l9

Cut unsatisfiable transition t₇₈: n_l7___5→n_l8___3

Cut unreachable locations [n_l8___3] from the program graph

Found invariant 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ for location n_l8___1

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l8___7

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l8___6

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l7

Found invariant 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ for location n_l7___2

Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location n_l8___4

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l10

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l9

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l7___5

MPRF for transition t₇₉: n_l7___5(X₀, X₁, X₂) → n_l8___4(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ < X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

n_l8___4 [X₁-X₀-1 ]
n_l7___5 [X₁-X₀ ]

MPRF for transition t₈₄: n_l8___4(X₀, X₁, X₂) → n_l7___5(X₀+1, X₁, X₂) :|: X₀ < X₁ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

n_l8___4 [X₁-X₀ ]
n_l7___5 [X₁-X₀ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₁+X₂ {O(n)}
t₈: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₁+X₂ {O(n)}
t₈: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, 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)}
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)}
t₇, X₁: 2⋅X₁ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₉, X₁: 3⋅X₁ {O(n)}
t₉, X₂: 3⋅X₂ {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₁, X₁: 3⋅X₁ {O(n)}
t₁₁, X₂: 3⋅X₂ {O(n)}