Initial Problem

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

Preprocessing

Found invariant X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location l5

Found invariant X₂ ≤ X₀ for location l1

Found invariant X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location l4

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location l3

Problem after Preprocessing

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

Analysing control-flow refined program

Found invariant X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l3___3

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₀ for location n_l1___2

Found invariant X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location l5

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location l4

Found invariant X₄ ≤ X₁ ∧ 2+X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location n_l3___1

MPRF for transition t₃₈: n_l1___2(X₀, X₁, X₂, X₃, X₄) → n_l3___1(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ < X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₀ of depth 1:

new bound:

X₂+X₄+1 {O(n)}

MPRF:

n_l3___1 [X₁-X₀-1 ]
n_l1___2 [X₄-X₀ ]

MPRF for transition t₄₀: n_l3___1(X₀, X₁, X₂, X₃, X₄) → n_l1___2(X₀+1, X₄, X₂, X₃, X₄) :|: X₀ < X₄ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 2+X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ of depth 1:

new bound:

X₂+X₄+1 {O(n)}

MPRF:

n_l3___1 [X₄-X₀ ]
n_l1___2 [X₁-X₀ ]

CFR: Improvement to new bound with the following program:

new bound:

2⋅X₂+2⋅X₄+2 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l4, l5, n_l1___2, n_l3___1, n_l3___3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₃₉: l1(X₀, X₁, X₂, X₃, X₄) → n_l3___3(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ < X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₃, X₂, X₃, X₄)
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀
t₄₅: n_l1___2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₀
t₃₈: n_l1___2(X₀, X₁, X₂, X₃, X₄) → n_l3___1(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ < X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₀
t₄₀: n_l3___1(X₀, X₁, X₂, X₃, X₄) → n_l1___2(X₀+1, X₄, X₂, X₃, X₄) :|: X₀ < X₄ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 2+X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁
t₄₁: n_l3___3(X₀, X₁, X₂, X₃, X₄) → n_l1___2(X₀+1, X₄, X₂, X₃, X₄) :|: X₀ < X₁ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁

All Bounds

Timebounds

Overall timebound:2⋅X₂+2⋅X₄+9 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₃₉: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 1 {O(1)}
t₃₈: X₂+X₄+1 {O(n)}
t₄₅: 1 {O(1)}
t₄₀: X₂+X₄+1 {O(n)}
t₄₁: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₂+2⋅X₄+9 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₃₉: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 1 {O(1)}
t₃₈: X₂+X₄+1 {O(n)}
t₄₅: 1 {O(1)}
t₄₀: X₂+X₄+1 {O(n)}
t₄₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₃, X₀: X₂ {O(n)}
t₃, X₁: X₃ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃₉, X₀: X₂ {O(n)}
t₃₉, X₁: X₃ {O(n)}
t₃₉, X₂: X₂ {O(n)}
t₃₉, X₃: X₃ {O(n)}
t₃₉, X₄: X₄ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₅, X₀: 4⋅X₂+X₄+3 {O(n)}
t₅, X₁: X₃+X₄ {O(n)}
t₅, X₂: 3⋅X₂ {O(n)}
t₅, X₃: 3⋅X₃ {O(n)}
t₅, X₄: 3⋅X₄ {O(n)}
t₃₈, X₀: 2⋅X₂+X₄+2 {O(n)}
t₃₈, X₁: X₄ {O(n)}
t₃₈, X₂: X₂ {O(n)}
t₃₈, X₃: X₃ {O(n)}
t₃₈, X₄: X₄ {O(n)}
t₄₅, X₀: 3⋅X₂+X₄+3 {O(n)}
t₄₅, X₁: 2⋅X₄ {O(n)}
t₄₅, X₂: 2⋅X₂ {O(n)}
t₄₅, X₃: 2⋅X₃ {O(n)}
t₄₅, X₄: 2⋅X₄ {O(n)}
t₄₀, X₀: 2⋅X₂+X₄+2 {O(n)}
t₄₀, X₁: X₄ {O(n)}
t₄₀, X₂: X₂ {O(n)}
t₄₀, X₃: X₃ {O(n)}
t₄₀, X₄: X₄ {O(n)}
t₄₁, X₀: X₂+1 {O(n)}
t₄₁, X₁: X₄ {O(n)}
t₄₁, X₂: X₂ {O(n)}
t₄₁, X₃: X₃ {O(n)}
t₄₁, X₄: X₄ {O(n)}