Initial Problem

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

Preprocessing

Found invariant X₅ ≤ X₂ ∧ X₀ ≤ X₁ for location l5

Found invariant X₅ ≤ X₂ for location l1

Found invariant X₅ ≤ X₂ ∧ X₀ ≤ X₁ for location l4

Found invariant X₅ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l3

Problem after Preprocessing

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

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₀ ∧ X₅ ≤ X₂ of depth 2:

new bound:

8⋅X₃+8⋅X₄+8⋅X₅+9 {O(n)}

MPRF:

l3 [-X₂-2 ; X₀-X₁-X₂-2 ]
l1 [-X₂-1 ; X₀-X₁ ]

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₁-X₀, X₂, X₂+1, X₃, X₄, X₅) :|: X₅ ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 2:

new bound:

8⋅X₃+8⋅X₄+8⋅X₅+17 {O(n)}

MPRF:

l3 [-X₂-1 ; 0 ]
l1 [-X₂-1 ; X₀-X₁-1 ]

All Bounds

Timebounds

Overall timebound:16⋅X₃+16⋅X₄+16⋅X₅+30 {O(n)}
t₀: 1 {O(1)}
t₂: 8⋅X₃+8⋅X₄+8⋅X₅+9 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 8⋅X₃+8⋅X₄+8⋅X₅+17 {O(n)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 16⋅X₃+16⋅X₄+16⋅X₅+30 {O(n)}
t₀: 1 {O(1)}
t₂: 8⋅X₃+8⋅X₄+8⋅X₅+9 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 8⋅X₃+8⋅X₄+8⋅X₅+17 {O(n)}
t₅: 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)}
t₀, X₅: X₅ {O(n)}
t₂, X₀: 136⋅X₃⋅X₄+136⋅X₃⋅X₅+144⋅X₄⋅X₅+64⋅X₃⋅X₃+72⋅X₄⋅X₄+72⋅X₅⋅X₅+281⋅X₃+298⋅X₄+298⋅X₅+306 {O(n^2)}
t₂, X₁: 8⋅X₃+9⋅X₄+9⋅X₅+17 {O(n)}
t₂, X₂: 8⋅X₃+8⋅X₄+9⋅X₅+17 {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 136⋅X₃⋅X₄+136⋅X₃⋅X₅+144⋅X₄⋅X₅+64⋅X₃⋅X₃+72⋅X₄⋅X₄+72⋅X₅⋅X₅+282⋅X₃+298⋅X₄+298⋅X₅+306 {O(n^2)}
t₃, X₁: 8⋅X₃+9⋅X₄+9⋅X₅+17 {O(n)}
t₃, X₂: 10⋅X₅+8⋅X₃+8⋅X₄+17 {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₅ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₄, X₀: 136⋅X₃⋅X₄+136⋅X₃⋅X₅+144⋅X₄⋅X₅+64⋅X₃⋅X₃+72⋅X₄⋅X₄+72⋅X₅⋅X₅+281⋅X₃+298⋅X₄+298⋅X₅+306 {O(n^2)}
t₄, X₁: 8⋅X₃+8⋅X₄+9⋅X₅+17 {O(n)}
t₄, X₂: 8⋅X₃+8⋅X₄+9⋅X₅+17 {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₅, X₀: 136⋅X₃⋅X₄+136⋅X₃⋅X₅+144⋅X₄⋅X₅+64⋅X₃⋅X₃+72⋅X₄⋅X₄+72⋅X₅⋅X₅+282⋅X₃+298⋅X₄+298⋅X₅+306 {O(n^2)}
t₅, X₁: 8⋅X₃+9⋅X₄+9⋅X₅+17 {O(n)}
t₅, X₂: 10⋅X₅+8⋅X₃+8⋅X₄+17 {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₅, X₅: 2⋅X₅ {O(n)}