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)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₀
t₅: 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(X₅, X₄, X₂, X₃, X₄, X₅) :|: X₄ < X₅
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₅, X₅, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₄
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+1, X₄, X₂, X₃, X₄, X₅) :|: X₄ < X₀+1
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+1, X₀+1, X₂, X₃, X₄, X₅) :|: X₀+1 ≤ X₄
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Cut unsatisfiable transition t₅: l1→l4

Eliminate variables {X₂,X₃} that do not contribute to the problem

Found invariant X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ 1+X₁ ≤ X₀ for location l5

Found invariant X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₁ ≤ X₀ for location l1

Found invariant X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ 1+X₁ ≤ X₀ for location l4

Found invariant X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₂₂: l0(X₀, X₁, X₄, X₅) → l2(X₀, X₁, X₄, X₅)
t₂₃: l1(X₀, X₁, X₄, X₅) → l3(X₀, X₁, X₄, X₅) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₁ ≤ X₀
t₂₄: l1(X₀, X₁, X₄, X₅) → l4(X₀, X₁, X₄, X₅) :|: X₁ < X₀ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₁ ≤ X₀
t₂₅: l2(X₀, X₁, X₄, X₅) → l1(X₅, X₄, X₄, X₅) :|: X₄ < X₅
t₂₆: l2(X₀, X₁, X₄, X₅) → l1(X₅, X₅, X₄, X₅) :|: X₅ ≤ X₄
t₂₇: l3(X₀, X₁, X₄, X₅) → l1(X₀+1, X₄, X₄, X₅) :|: X₄ < X₀+1 ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₂₈: l3(X₀, X₁, X₄, X₅) → l1(X₀+1, X₀+1, X₄, X₅) :|: X₀+1 ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₂₉: l4(X₀, X₁, X₄, X₅) → l5(X₀, X₁, X₄, X₅) :|: X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ 1+X₁ ≤ X₀

MPRF for transition t₂₃: l1(X₀, X₁, X₄, X₅) → l3(X₀, X₁, X₄, X₅) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₄+X₅+1 {O(n)}

MPRF:

l3 [X₄-X₁ ]
l1 [X₄+1-X₀ ]

MPRF for transition t₂₇: l3(X₀, X₁, X₄, X₅) → l1(X₀+1, X₄, X₄, X₅) :|: X₄ < X₀+1 ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₅+1 {O(n)}

MPRF:

l3 [1 ]
l1 [X₁+1-X₀ ]

MPRF for transition t₂₈: l3(X₀, X₁, X₄, X₅) → l1(X₀+1, X₀+1, X₄, X₅) :|: X₀+1 ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₄+X₅+1 {O(n)}

MPRF:

l3 [X₄+1-X₁ ]
l1 [X₄+1-X₀ ]

All Bounds

Timebounds

Overall timebound:2⋅X₄+4⋅X₅+8 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: X₄+X₅+1 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 2⋅X₅+1 {O(n)}
t₂₈: X₄+X₅+1 {O(n)}
t₂₉: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₄+4⋅X₅+8 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: X₄+X₅+1 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 2⋅X₅+1 {O(n)}
t₂₈: X₄+X₅+1 {O(n)}
t₂₉: 1 {O(1)}

Sizebounds

t₂₂, X₀: X₀ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₃, X₀: 2⋅X₅+X₄+1 {O(n)}
t₂₃, X₁: 3⋅X₅+X₄+2 {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₄, X₀: 3⋅X₅+X₄+2 {O(n)}
t₂₄, X₁: 2⋅X₄+3⋅X₅+2 {O(n)}
t₂₄, X₄: 2⋅X₄ {O(n)}
t₂₄, X₅: 2⋅X₅ {O(n)}
t₂₅, X₀: X₅ {O(n)}
t₂₅, X₁: X₄ {O(n)}
t₂₅, X₄: X₄ {O(n)}
t₂₅, X₅: X₅ {O(n)}
t₂₆, X₀: X₅ {O(n)}
t₂₆, X₁: X₅ {O(n)}
t₂₆, X₄: X₄ {O(n)}
t₂₆, X₅: X₅ {O(n)}
t₂₇, X₀: 2⋅X₅+X₄+2 {O(n)}
t₂₇, X₁: 3⋅X₅+X₄+2 {O(n)}
t₂₇, X₄: X₄ {O(n)}
t₂₇, X₅: X₅ {O(n)}
t₂₈, X₀: 2⋅X₅+X₄+1 {O(n)}
t₂₈, X₁: 2⋅X₅+X₄+2 {O(n)}
t₂₈, X₄: X₄ {O(n)}
t₂₈, X₅: X₅ {O(n)}
t₂₉, X₀: 3⋅X₅+X₄+2 {O(n)}
t₂₉, X₁: 2⋅X₄+3⋅X₅+2 {O(n)}
t₂₉, X₄: 2⋅X₄ {O(n)}
t₂₉, X₅: 2⋅X₅ {O(n)}