Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 100 < X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ < X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₄, X₅, X₆, X₃, X₄, X₅, X₆, X₇)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₁, X₀+1, X₂-1, X₃, X₄, X₅, X₆, X₇)
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

Preprocessing

Eliminate variables {X₃,X₇} that do not contribute to the problem

Found invariant X₂ ≤ X₆ for location l5

Found invariant X₂ ≤ X₆ for location l1

Found invariant X₂ ≤ X₆ for location l4

Found invariant X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 100 for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₄: l0(X₀, X₁, X₂, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₄, X₅, X₆)
t₁₅: l1(X₀, X₁, X₂, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₄, X₅, X₆) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₆
t₁₆: l1(X₀, X₁, X₂, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₄, X₅, X₆) :|: 100 < X₀ ∧ X₂ ≤ X₆
t₁₇: l1(X₀, X₁, X₂, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₄, X₅, X₆) :|: X₂ < X₁ ∧ X₂ ≤ X₆
t₁₈: l2(X₀, X₁, X₂, X₄, X₅, X₆) → l1(X₄, X₅, X₆, X₄, X₅, X₆)
t₁₉: l3(X₀, X₁, X₂, X₄, X₅, X₆) → l1(X₁, X₀+1, X₂-1, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 100
t₂₀: l4(X₀, X₁, X₂, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₄, X₅, X₆) :|: X₂ ≤ X₆

MPRF for transition t₁₅: l1(X₀, X₁, X₂, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₄, X₅, X₆) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₆ of depth 1:

new bound:

X₄+X₅+X₆+101 {O(n)}

MPRF:

l3 [X₆+100-X₀-X₁ ]
l1 [X₆+101-X₀-X₁ ]

MPRF for transition t₁₉: l3(X₀, X₁, X₂, X₄, X₅, X₆) → l1(X₁, X₀+1, X₂-1, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 100 of depth 1:

new bound:

X₄+X₅+X₆+101 {O(n)}

MPRF:

l3 [X₆+101-X₀-X₁ ]
l1 [X₆+101-X₀-X₁ ]

All Bounds

Timebounds

Overall timebound:2⋅X₄+2⋅X₅+2⋅X₆+207 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: X₄+X₅+X₆+101 {O(n)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: X₄+X₅+X₆+101 {O(n)}
t₂₀: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₄+2⋅X₅+2⋅X₆+207 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: X₄+X₅+X₆+101 {O(n)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: X₄+X₅+X₆+101 {O(n)}
t₂₀: 1 {O(1)}

Sizebounds

t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₄, X₆: X₆ {O(n)}
t₁₅, X₀: 2⋅X₄+2⋅X₅+X₆+101 {O(n)}
t₁₅, X₁: 2⋅X₄+2⋅X₅+X₆+101 {O(n)}
t₁₅, X₂: 2⋅X₆+X₄+X₅+101 {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₅, X₆: X₆ {O(n)}
t₁₆, X₀: 2⋅X₅+3⋅X₄+X₆+101 {O(n)}
t₁₆, X₁: 2⋅X₄+3⋅X₅+X₆+101 {O(n)}
t₁₆, X₂: 3⋅X₆+X₄+X₅+101 {O(n)}
t₁₆, X₄: 2⋅X₄ {O(n)}
t₁₆, X₅: 2⋅X₅ {O(n)}
t₁₆, X₆: 2⋅X₆ {O(n)}
t₁₇, X₀: 2⋅X₅+3⋅X₄+X₆+101 {O(n)}
t₁₇, X₁: 2⋅X₄+3⋅X₅+X₆+101 {O(n)}
t₁₇, X₂: 3⋅X₆+X₄+X₅+101 {O(n)}
t₁₇, X₄: 2⋅X₄ {O(n)}
t₁₇, X₅: 2⋅X₅ {O(n)}
t₁₇, X₆: 2⋅X₆ {O(n)}
t₁₈, X₀: X₄ {O(n)}
t₁₈, X₁: X₅ {O(n)}
t₁₈, X₂: X₆ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₈, X₆: X₆ {O(n)}
t₁₉, X₀: 2⋅X₄+2⋅X₅+X₆+101 {O(n)}
t₁₉, X₁: 2⋅X₄+2⋅X₅+X₆+101 {O(n)}
t₁₉, X₂: 2⋅X₆+X₄+X₅+101 {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₁₉, X₆: X₆ {O(n)}
t₂₀, X₀: 2⋅X₆+4⋅X₅+6⋅X₄+202 {O(n)}
t₂₀, X₁: 2⋅X₆+4⋅X₄+6⋅X₅+202 {O(n)}
t₂₀, X₂: 2⋅X₄+2⋅X₅+6⋅X₆+202 {O(n)}
t₂₀, X₄: 4⋅X₄ {O(n)}
t₂₀, X₅: 4⋅X₅ {O(n)}
t₂₀, X₆: 4⋅X₆ {O(n)}