Initial Problem

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

Preprocessing

Cut unsatisfiable transition t₂: l1→l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₃: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 0 < X₀ ∧ 1 ≤ X₀
t₄: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 0 ∧ X₀ < 0
t₅: l1(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)

MPRF for transition t₃: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 0 < X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l1 [X₀ ]

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

new bound:

X₁+1 {O(n)}

MPRF:

l1 [1-X₀ ]

Analysing control-flow refined program

Cut unsatisfiable transition t₆₆: n_l1___3→n_l1___4

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___4

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___2

Found invariant 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location n_l1___3

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

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1

MPRF for transition t₆₅: n_l1___3(X₀, X₁) → n_l1___3(X₀+1, X₁) :|: X₀ < 0 ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

n_l1___3 [1-X₀ ]

MPRF for transition t₆₈: n_l1___4(X₀, X₁) → n_l1___4(X₀-1, X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

n_l1___4 [X₀+1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₃, X₀: X₁ {O(n)}
t₃, X₁: X₁ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 0 {O(1)}
t₅, X₁: 3⋅X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}