Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l11, 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)
t₁₂: l10(X₀, X₁, X₂) → l11(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(X₀, X₁, X₂)
t₇: l7(X₀, X₁, X₂) → l8(X₀, X₁, 0)
t₉: l8(X₀, X₁, X₂) → l10(X₀, X₁, X₂) :|: X₁ < X₂
t₈: l8(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₁₀: l9(X₀, X₁, X₂) → l8(X₀, X₁, X₂+1) :|: X₂ ≤ X₀
t₁₁: l9(X₀, X₁, X₂) → l8(X₀, X₁, X₂-1) :|: X₀ < X₂

Preprocessing

Found invariant 1+X₁ ≤ X₂ for location l11

Found invariant 1+X₁ ≤ X₂ for location l10

Found invariant X₂ ≤ X₁ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l11, 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)
t₁₂: l10(X₀, X₁, X₂) → l11(X₀, X₁, X₂) :|: 1+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(X₀, X₁, X₂)
t₇: l7(X₀, X₁, X₂) → l8(X₀, X₁, 0)
t₉: l8(X₀, X₁, X₂) → l10(X₀, X₁, X₂) :|: X₁ < X₂
t₈: l8(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₁₀: l9(X₀, X₁, X₂) → l8(X₀, X₁, X₂+1) :|: X₂ ≤ X₀ ∧ X₂ ≤ X₁
t₁₁: l9(X₀, X₁, X₂) → l8(X₀, X₁, X₂-1) :|: X₀ < X₂ ∧ X₂ ≤ X₁

Analysing control-flow refined program

Cut unsatisfiable transition t₁₆₉: n_l8___3→l10

Cut unsatisfiable transition t₁₇₀: n_l8___5→l10

Found invariant 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ for location l11

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location n_l8___3

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₁ for location n_l9___4

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location n_l9___7

Found invariant 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l9___1

Found invariant 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l8___5

Found invariant X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₁ for location n_l8___6

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location n_l9___2

Found invariant X₂ ≤ 0 ∧ 0 ≤ X₂ for location l8

Found invariant 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ for location l10

MPRF for transition t₁₅₃: n_l8___5(X₀, X₁, X₂) → n_l9___1(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:

new bound:

X₀+2 {O(n)}

MPRF:

n_l9___1 [X₂-X₀ ]
n_l8___5 [X₂+1-X₀ ]

MPRF for transition t₁₅₆: n_l9___1(X₀, X₁, X₂) → n_l8___5(X₀, X₁, X₂-1) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₀ < X₂ ∧ 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:

new bound:

X₀+2 {O(n)}

MPRF:

n_l9___1 [X₂+1-X₀ ]
n_l8___5 [X₂+1-X₀ ]

MPRF for transition t₁₆₀: n_l9___4(X₀, X₁, X₂) → n_l8___6(X₀, X₁, X₂+1) :|: X₂ ≤ 1+X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

3⋅X₀+6 {O(n)}

MPRF:

n_l9___2 [0 ]
n_l8___3 [X₀-X₂ ]
n_l9___4 [X₀+1-X₂ ]
n_l8___6 [X₀+1-X₂ ]

Found invariant X₂ ≤ 1 ∧ X₁+X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l11

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l8___3

Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l9___4

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location n_l9___7

Found invariant 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l9___1

Found invariant 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l8___5

Found invariant X₂ ≤ 1 ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l8___6

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l9___2

Found invariant X₂ ≤ 0 ∧ 0 ≤ X₂ for location l8

Found invariant X₂ ≤ 1 ∧ X₁+X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ 0 for location l10

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: inf {Infinity}

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)}
t₁₂, X₀: 2⋅X₀ {O(n)}
t₁₂, X₁: 2⋅X₁ {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: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 0 {O(1)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: 2⋅X₀ {O(n)}
t₉, X₁: 2⋅X₁ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}