Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 3 < X₀
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ ≤ 3
t₆: l4(X₀, X₁) → l5(X₀, X₁)

Preprocessing

Found invariant X₀ ≤ 0 for location l5

Found invariant X₀ ≤ 0 for location l4

Found invariant 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 3 < X₀ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ ≤ 3 ∧ 1 ≤ X₀
t₆: l4(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0

Analysing control-flow refined program

Cut unsatisfiable transition t₆₃: n_l1___4→l4

Found invariant 1+X₁ ≤ X₀ ∧ 4 ≤ X₁ ∧ 9 ≤ X₀+X₁ ∧ 5 ≤ X₀ for location n_l1___4

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___5

Found invariant X₁ ≤ 3 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 5 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 0 ≤ X₀ for location n_l1___3

Found invariant X₁ ≤ 3 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 3 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant 1+X₁ ≤ X₀ ∧ 4 ≤ X₁ ∧ 9 ≤ X₀+X₁ ∧ 5 ≤ X₀ for location n_l3___2

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

Found invariant X₁ ≤ 3 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 3 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4

Found invariant X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 5 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ for location n_l3___1

MPRF for transition t₄₉: n_l1___3(X₀, X₁) → n_l3___1(X₀, X₁) :|: X₀ ≤ 3 ∧ 0 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < X₀ ∧ X₁ ≤ 3 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 5 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 0 ≤ X₀ of depth 1:

new bound:

3 {O(1)}

MPRF:

n_l3___1 [X₀ ]
n_l1___3 [X₀+1 ]

MPRF for transition t₅₂: n_l3___1(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: X₀ ≤ 2 ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 5 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ of depth 1:

new bound:

2 {O(1)}

MPRF:

n_l3___1 [X₀ ]
n_l1___3 [X₀ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

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