Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l3(X₀, X₁)
t₅: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ < 0
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: 0 < X₀
t₇: l2(X₀, X₁) → l5(X₀, X₁)
t₁: l3(X₀, X₁) → l1(X₁, X₁) :|: 0 < X₁
t₂: l3(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ 0
t₆: l4(X₀, X₁) → l1(X₀-2, X₁)

Preprocessing

Found invariant 1 ≤ X₁ ∧ X₀ ≤ X₁ for location l1

Found invariant 1 ≤ X₁ ∧ X₀ ≤ X₁ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l3(X₀, X₁)
t₅: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ < 0 ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: 0 < X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
t₇: l2(X₀, X₁) → l5(X₀, X₁)
t₁: l3(X₀, X₁) → l1(X₁, X₁) :|: 0 < X₁
t₂: l3(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ 0
t₆: l4(X₀, X₁) → l1(X₀-2, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ X₁

MPRF for transition t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: 0 < X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l4 [X₀-2 ]
l1 [X₀ ]

Found invariant 1 ≤ X₁ ∧ X₀ ≤ X₁ for location l1

Found invariant 1 ≤ X₁ ∧ X₀ ≤ X₁ for location l4

Analysing control-flow refined program

Cut unsatisfiable transition t₅: l1→l2

Cut unsatisfiable transition t₈₄: n_l1___2→l2

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___6

Found invariant 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___3

Found invariant 1 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location n_l4___4

Found invariant 1 ≤ X₁ ∧ 4+X₀ ≤ X₁ ∧ 3+X₀ ≤ 0 for location n_l1___2

Found invariant 1 ≤ X₁ ∧ 4+X₀ ≤ X₁ ∧ 3+X₀ ≤ 0 for location n_l4___1

Found invariant 1 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ for location n_l1___5

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1

MPRF for transition t₇₂: n_l1___5(X₀, X₁) → n_l4___3(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF:

n_l4___3 [X₀ ]
n_l1___5 [X₀+2 ]

MPRF for transition t₇₆: n_l4___3(X₀, X₁) → n_l1___5(X₀-2, X₁) :|: 2+X₀ ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

n_l4___3 [X₀ ]
n_l1___5 [X₀ ]

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___6

Found invariant 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___3

Found invariant 1 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location n_l4___4

Found invariant 1 ≤ X₁ ∧ 4+X₀ ≤ X₁ ∧ 3+X₀ ≤ 0 for location n_l1___2

Found invariant 1 ≤ X₁ ∧ 4+X₀ ≤ X₁ ∧ 3+X₀ ≤ 0 for location n_l4___1

Found invariant 1 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ for location n_l1___5

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₃: inf {Infinity}
t₄: X₁ {O(n)}
t₅: 1 {O(1)}
t₇: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₆: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₃: inf {Infinity}
t₄: X₁ {O(n)}
t₅: 1 {O(1)}
t₇: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₆: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₃, X₁: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 0 {O(1)}
t₅, X₁: X₁ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₆, X₁: X₁ {O(n)}