Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₁, X₃, X₄, X₅, X₆) :|: X₆ < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ X₆
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₅, X₂, X₃, X₄, X₅, X₆)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₆
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ < X₂
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀-1, X₂, X₂, X₃, X₄, X₅, X₆)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂-1, X₃, X₄, X₅, X₆)

Preprocessing

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

Found invariant 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ for location l6

Found invariant X₀ ≤ X₆ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ for location l7

Found invariant 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₀ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ for location l5

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

Found invariant X₀ ≤ X₆ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ for location l4

Found invariant 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₀ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ 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, l6, l7
Transitions:
t₁₈: l0(X₀, X₁, X₂, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₄, X₅, X₆)
t₁₉: l1(X₀, X₁, X₂, X₄, X₅, X₆) → l3(X₀, X₁, X₁, X₄, X₅, X₆) :|: X₆ < X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₂₀: l1(X₀, X₁, X₂, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₄, X₅, X₆) :|: X₀ ≤ X₆ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₂₁: l2(X₀, X₁, X₂, X₄, X₅, X₆) → l1(X₄, X₅, X₂, X₄, X₅, X₆)
t₂₃: l3(X₀, X₁, X₂, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₀ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁
t₂₂: l3(X₀, X₁, X₂, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₄, X₅, X₆) :|: X₆ < X₂ ∧ 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₀ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁
t₂₄: l4(X₀, X₁, X₂, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₄, X₅, X₆) :|: X₀ ≤ X₆ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₂₅: l5(X₀, X₁, X₂, X₄, X₅, X₆) → l1(X₀-1, X₂, X₂, X₄, X₅, X₆) :|: 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₀ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀
t₂₆: l6(X₀, X₁, X₂, X₄, X₅, X₆) → l3(X₀, X₁, X₂-1, X₄, X₅, X₆) :|: 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁

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

new bound:

X₄+X₆ {O(n)}

MPRF:

l5 [X₀-X₆-1 ]
l1 [X₀-X₆ ]
l6 [X₀-X₆-1 ]
l3 [X₀-X₆-1 ]

MPRF for transition t₂₂: l3(X₀, X₁, X₂, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₄, X₅, X₆) :|: X₆ < X₂ ∧ 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₀ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF:

l5 [X₂-X₆ ]
l1 [X₁-X₆ ]
l6 [X₂-X₆-1 ]
l3 [X₂-X₆ ]

MPRF for transition t₂₃: l3(X₀, X₁, X₂, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₀ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₄+X₆ {O(n)}

MPRF:

l5 [X₀-X₆-1 ]
l1 [X₀-X₆ ]
l6 [X₀-X₆ ]
l3 [X₀-X₆ ]

MPRF for transition t₂₅: l5(X₀, X₁, X₂, X₄, X₅, X₆) → l1(X₀-1, X₂, X₂, X₄, X₅, X₆) :|: 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₀ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ of depth 1:

new bound:

X₄+X₆ {O(n)}

MPRF:

l5 [X₀-X₆ ]
l1 [X₀-X₆ ]
l6 [X₀-X₆ ]
l3 [X₀-X₆ ]

MPRF for transition t₂₆: l6(X₀, X₁, X₂, X₄, X₅, X₆) → l3(X₀, X₁, X₂-1, X₄, X₅, X₆) :|: 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF:

l5 [X₂-X₆ ]
l1 [X₁-X₆ ]
l6 [X₂-X₆ ]
l3 [X₂-X₆ ]

All Bounds

Timebounds

Overall timebound:2⋅X₅+3⋅X₄+5⋅X₆+4 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: X₄+X₆ {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: X₅+X₆ {O(n)}
t₂₃: X₄+X₆ {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₄+X₆ {O(n)}
t₂₆: X₅+X₆ {O(n)}

Costbounds

Overall costbound: 2⋅X₅+3⋅X₄+5⋅X₆+4 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: X₄+X₆ {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: X₅+X₆ {O(n)}
t₂₃: X₄+X₆ {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₄+X₆ {O(n)}
t₂₆: X₅+X₆ {O(n)}

Sizebounds

t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₈, X₆: X₆ {O(n)}
t₁₉, X₀: 2⋅X₄+X₆ {O(n)}
t₁₉, X₁: 3⋅X₅+X₆ {O(n)}
t₁₉, X₂: 2⋅X₅+X₆ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₁₉, X₆: X₆ {O(n)}
t₂₀, X₀: 3⋅X₄+X₆ {O(n)}
t₂₀, X₁: 3⋅X₅+X₆ {O(n)}
t₂₀, X₂: 2⋅X₅+X₂+X₆ {O(n)}
t₂₀, X₄: 2⋅X₄ {O(n)}
t₂₀, X₅: 2⋅X₅ {O(n)}
t₂₀, X₆: 2⋅X₆ {O(n)}
t₂₁, X₀: X₄ {O(n)}
t₂₁, X₁: X₅ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₁, X₆: X₆ {O(n)}
t₂₂, X₀: 2⋅X₄+X₆ {O(n)}
t₂₂, X₁: 3⋅X₅+X₆ {O(n)}
t₂₂, X₂: 2⋅X₅+X₆ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₂, X₆: X₆ {O(n)}
t₂₃, X₀: 2⋅X₄+X₆ {O(n)}
t₂₃, X₁: 2⋅X₆+6⋅X₅ {O(n)}
t₂₃, X₂: 2⋅X₅+X₆ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₃, X₆: X₆ {O(n)}
t₂₄, X₀: 3⋅X₄+X₆ {O(n)}
t₂₄, X₁: 3⋅X₅+X₆ {O(n)}
t₂₄, X₂: 2⋅X₅+X₂+X₆ {O(n)}
t₂₄, X₄: 2⋅X₄ {O(n)}
t₂₄, X₅: 2⋅X₅ {O(n)}
t₂₄, X₆: 2⋅X₆ {O(n)}
t₂₅, X₀: 2⋅X₄+X₆ {O(n)}
t₂₅, X₁: 2⋅X₅+X₆ {O(n)}
t₂₅, X₂: 2⋅X₅+X₆ {O(n)}
t₂₅, X₄: X₄ {O(n)}
t₂₅, X₅: X₅ {O(n)}
t₂₅, X₆: X₆ {O(n)}
t₂₆, X₀: 2⋅X₄+X₆ {O(n)}
t₂₆, X₁: 3⋅X₅+X₆ {O(n)}
t₂₆, X₂: 2⋅X₅+X₆ {O(n)}
t₂₆, X₄: X₄ {O(n)}
t₂₆, X₅: X₅ {O(n)}
t₂₆, X₆: X₆ {O(n)}