Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
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, X₁, X₃, X₄, X₅) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ 0
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₂
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₂, X₂, X₃, X₄, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂-1, X₃, X₄, X₅)

Preprocessing

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

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6

Found invariant X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₀ ≤ 0 for location l7

Found invariant X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l5

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

Found invariant X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₀ ≤ 0 for location l4

Found invariant X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₈: l0(X₀, X₁, X₂, X₄, X₅) → l2(X₀, X₁, X₂, X₄, X₅)
t₁₉: l1(X₀, X₁, X₂, X₄, X₅) → l3(X₀, X₁, X₁, X₄, X₅) :|: 0 < X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₂₀: l1(X₀, X₁, X₂, X₄, X₅) → l4(X₀, X₁, X₂, X₄, X₅) :|: X₀ ≤ 0 ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₂₁: l2(X₀, X₁, X₂, X₄, X₅) → l1(X₄, X₅, X₂, X₄, X₅)
t₂₃: l3(X₀, X₁, X₂, X₄, X₅) → l5(X₀, X₁, X₂, X₄, X₅) :|: X₂ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀
t₂₂: l3(X₀, X₁, X₂, X₄, X₅) → l6(X₀, X₁, X₂, X₄, X₅) :|: 0 < X₂ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀
t₂₄: l4(X₀, X₁, X₂, X₄, X₅) → l7(X₀, X₁, X₂, X₄, X₅) :|: X₁ ≤ X₅ ∧ X₀ ≤ X₄ ∧ X₀ ≤ 0
t₂₅: l5(X₀, X₁, X₂, X₄, X₅) → l1(X₀-1, X₂, X₂, X₄, X₅) :|: X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀
t₂₆: l6(X₀, X₁, X₂, X₄, X₅) → l3(X₀, X₁, X₂-1, X₄, X₅) :|: 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₁₉: l1(X₀, X₁, X₂, X₄, X₅) → l3(X₀, X₁, X₁, X₄, X₅) :|: 0 < X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

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

MPRF for transition t₂₂: l3(X₀, X₁, X₂, X₄, X₅) → l6(X₀, X₁, X₂, X₄, X₅) :|: 0 < X₂ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

l5 [X₂ ]
l1 [X₁ ]
l6 [X₂-1 ]
l3 [X₂ ]

MPRF for transition t₂₃: l3(X₀, X₁, X₂, X₄, X₅) → l5(X₀, X₁, X₂, X₄, X₅) :|: X₂ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l5 [X₀-1 ]
l1 [X₀ ]
l6 [X₀ ]
l3 [X₀ ]

MPRF for transition t₂₅: l5(X₀, X₁, X₂, X₄, X₅) → l1(X₀-1, X₂, X₂, X₄, X₅) :|: X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l5 [X₀ ]
l1 [X₀ ]
l6 [X₀ ]
l3 [X₀ ]

MPRF for transition t₂₆: l6(X₀, X₁, X₂, X₄, X₅) → l3(X₀, X₁, X₂-1, X₄, X₅) :|: 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

l5 [X₂ ]
l1 [X₁ ]
l6 [X₂ ]
l3 [X₂ ]

All Bounds

Timebounds

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

Costbounds

Overall costbound: 2⋅X₅+3⋅X₄+4 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: X₄ {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: X₅ {O(n)}
t₂₃: X₄ {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₄ {O(n)}
t₂₆: X₅ {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)}
t₁₉, X₀: X₄ {O(n)}
t₁₉, X₁: 2⋅X₅ {O(n)}
t₁₉, X₂: X₅ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₂₀, X₀: 2⋅X₄ {O(n)}
t₂₀, X₁: 2⋅X₅ {O(n)}
t₂₀, X₂: X₂+X₅ {O(n)}
t₂₀, X₄: 2⋅X₄ {O(n)}
t₂₀, X₅: 2⋅X₅ {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)}
t₂₂, X₀: X₄ {O(n)}
t₂₂, X₁: 2⋅X₅ {O(n)}
t₂₂, X₂: X₅ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₃, X₀: X₄ {O(n)}
t₂₃, X₁: 4⋅X₅ {O(n)}
t₂₃, X₂: X₅ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₄, X₀: 2⋅X₄ {O(n)}
t₂₄, X₁: 2⋅X₅ {O(n)}
t₂₄, X₂: X₂+X₅ {O(n)}
t₂₄, X₄: 2⋅X₄ {O(n)}
t₂₄, X₅: 2⋅X₅ {O(n)}
t₂₅, X₀: X₄ {O(n)}
t₂₅, X₁: X₅ {O(n)}
t₂₅, X₂: X₅ {O(n)}
t₂₅, X₄: X₄ {O(n)}
t₂₅, X₅: X₅ {O(n)}
t₂₆, X₀: X₄ {O(n)}
t₂₆, X₁: 2⋅X₅ {O(n)}
t₂₆, X₂: X₅ {O(n)}
t₂₆, X₄: X₄ {O(n)}
t₂₆, X₅: X₅ {O(n)}