Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ X₄
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ < X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(1, X₆, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₂
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(-1, X₆, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 1
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁+X₀, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₂
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁-X₀, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 1
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Eliminate variables {X₃,X₅} that do not contribute to the problem

Found invariant 1+X₄ ≤ X₁ ∧ X₀ ≤ 1 for location l5

Found invariant X₀ ≤ 1 for location l1

Found invariant 1+X₄ ≤ X₁ ∧ X₀ ≤ 1 for location l4

Found invariant X₁ ≤ X₄ ∧ X₀ ≤ 1 for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₄, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₆: l0(X₀, X₁, X₂, X₄, X₆) → l2(X₀, X₁, X₂, X₄, X₆)
t₁₇: l1(X₀, X₁, X₂, X₄, X₆) → l3(X₀, X₁, X₂, X₄, X₆) :|: X₁ ≤ X₄ ∧ X₀ ≤ 1
t₁₈: l1(X₀, X₁, X₂, X₄, X₆) → l4(X₀, X₁, X₂, X₄, X₆) :|: X₄ < X₁ ∧ X₀ ≤ 1
t₁₉: l2(X₀, X₁, X₂, X₄, X₆) → l1(1, X₆, X₂, X₄, X₆) :|: 1 ≤ X₂
t₂₀: l2(X₀, X₁, X₂, X₄, X₆) → l1(-1, X₆, X₂, X₄, X₆) :|: X₂ < 1
t₂₁: l3(X₀, X₁, X₂, X₄, X₆) → l1(X₀, X₁+X₀, X₂, X₄, X₆) :|: 1 ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₀ ≤ 1
t₂₂: l3(X₀, X₁, X₂, X₄, X₆) → l1(X₀, X₁-X₀, X₂, X₄, X₆) :|: X₂ < 1 ∧ X₁ ≤ X₄ ∧ X₀ ≤ 1
t₂₃: l4(X₀, X₁, X₂, X₄, X₆) → l5(X₀, X₁, X₂, X₄, X₆) :|: 1+X₄ ≤ X₁ ∧ X₀ ≤ 1

Analysing control-flow refined program

Found invariant X₆ ≤ X₄ ∧ X₆ ≤ X₁ ∧ X₁ ≤ X₆ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___4

Found invariant X₆ ≤ X₄ ∧ 1+X₆ ≤ X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___3

Found invariant 1+X₄ ≤ X₁ ∧ X₀ ≤ 1 for location l5

Found invariant 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___2

Found invariant X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l1

Found invariant 1+X₄ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l4

Found invariant X₁ ≤ X₄ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ X₀+X₂ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location n_l3___1

MPRF for transition t₅₉: n_l1___3(X₀, X₁, X₂, X₄, X₆) → n_l3___2(X₀, X₁, X₂, X₄, X₆) :|: X₀ ≤ 1 ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀+X₄ ∧ X₀ ≤ 1 ∧ X₁ ≤ X₄ ∧ X₀ ≤ 1 ∧ X₆ ≤ X₄ ∧ 1+X₆ ≤ X₁ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄+X₆+2 {O(n)}

MPRF:

n_l3___2 [X₄-X₁ ]
n_l1___3 [X₄+1-X₁ ]

MPRF for transition t₆₃: n_l3___2(X₀, X₁, X₂, X₄, X₆) → n_l1___3(X₀, X₀+X₁, X₂, X₄, X₆) :|: X₀ ≤ 1 ∧ X₁ ≤ X₀+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₀ ≤ 1 ∧ 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄+X₆+2 {O(n)}

MPRF:

n_l3___2 [X₄+1-X₁ ]
n_l1___3 [X₀+X₄-X₁ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: 1 {O(1)}

Sizebounds

t₁₆, X₀: X₀ {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁₆, X₆: X₆ {O(n)}
t₁₇, X₀: 2 {O(1)}
t₁₇, X₂: 2⋅X₂ {O(n)}
t₁₇, X₄: 2⋅X₄ {O(n)}
t₁₇, X₆: 2⋅X₆ {O(n)}
t₁₈, X₀: 6 {O(1)}
t₁₈, X₂: 6⋅X₂ {O(n)}
t₁₈, X₄: 6⋅X₄ {O(n)}
t₁₈, X₆: 6⋅X₆ {O(n)}
t₁₉, X₀: 1 {O(1)}
t₁₉, X₁: X₆ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₆: X₆ {O(n)}
t₂₀, X₀: 1 {O(1)}
t₂₀, X₁: X₆ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₀, X₆: X₆ {O(n)}
t₂₁, X₀: 2 {O(1)}
t₂₁, X₂: 2⋅X₂ {O(n)}
t₂₁, X₄: 2⋅X₄ {O(n)}
t₂₁, X₆: 2⋅X₆ {O(n)}
t₂₂, X₀: 2 {O(1)}
t₂₂, X₂: 2⋅X₂ {O(n)}
t₂₂, X₄: 2⋅X₄ {O(n)}
t₂₂, X₆: 2⋅X₆ {O(n)}
t₂₃, X₀: 6 {O(1)}
t₂₃, X₂: 6⋅X₂ {O(n)}
t₂₃, X₄: 6⋅X₄ {O(n)}
t₂₃, X₆: 6⋅X₆ {O(n)}