Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀
t₉: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, 0, X₂, X₃, X₄, X₅) :|: 0 ≤ X₃ ∧ 0 < X₂
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < 0
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ 0
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, 0, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₁
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₂
t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₁+1, X₂, X₃, X₄, X₅)

Preprocessing

Eliminate variables {X₄,X₅} that do not contribute to the problem

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₂₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₁: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₃: l2(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₂₄: l3(X₀, X₁, X₂, X₃) → l1(X₃, 0, X₂, X₃) :|: 0 ≤ X₃ ∧ 0 < X₂
t₂₅: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ < 0
t₂₆: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂₈: l4(X₀, X₁, X₂, X₃) → l1(X₀, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₇: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ < X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₉: l5(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁+1, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₂₁: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

MPRF:

l4 [2⋅X₀+X₁ ]
l5 [2⋅X₀+X₁ ]
l1 [2⋅X₀+X₁+1 ]

MPRF for transition t₂₇: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ < X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l4 [X₀ ]
l5 [X₀-1 ]
l1 [X₀ ]

MPRF for transition t₂₈: l4(X₀, X₁, X₂, X₃) → l1(X₀, 0, X₂, X₃) :|: X₂ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l4 [X₀+X₁ ]
l5 [X₀+X₁ ]
l1 [X₀+X₁ ]

MPRF for transition t₂₉: l5(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁+1, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l4 [X₀ ]
l5 [X₀ ]
l1 [X₀ ]

All Bounds

Timebounds

Overall timebound:5⋅X₃+7 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 2⋅X₃+1 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: X₃ {O(n)}
t₂₈: X₃ {O(n)}
t₂₉: X₃ {O(n)}

Costbounds

Overall costbound: 5⋅X₃+7 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 2⋅X₃+1 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: X₃ {O(n)}
t₂₈: X₃ {O(n)}
t₂₉: X₃ {O(n)}

Sizebounds

t₂₀, X₀: X₀ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₁, X₀: X₃ {O(n)}
t₂₁, X₁: X₃ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₂, X₀: 0 {O(1)}
t₂₂, X₁: X₃ {O(n)}
t₂₂, X₂: 2⋅X₂ {O(n)}
t₂₂, X₃: 2⋅X₃ {O(n)}
t₂₃, X₀: 2⋅X₀ {O(n)}
t₂₃, X₁: 2⋅X₁+X₃ {O(n)}
t₂₃, X₂: 4⋅X₂ {O(n)}
t₂₃, X₃: 4⋅X₃ {O(n)}
t₂₄, X₀: X₃ {O(n)}
t₂₄, X₁: 0 {O(1)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₅, X₀: X₀ {O(n)}
t₂₅, X₁: X₁ {O(n)}
t₂₅, X₂: X₂ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₆, X₀: X₀ {O(n)}
t₂₆, X₁: X₁ {O(n)}
t₂₆, X₂: X₂ {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₇, X₀: X₃ {O(n)}
t₂₇, X₁: X₃ {O(n)}
t₂₇, X₂: X₂ {O(n)}
t₂₇, X₃: X₃ {O(n)}
t₂₈, X₀: X₃ {O(n)}
t₂₈, X₁: 0 {O(1)}
t₂₈, X₂: X₂ {O(n)}
t₂₈, X₃: X₃ {O(n)}
t₂₉, X₀: X₃ {O(n)}
t₂₉, X₁: X₃ {O(n)}
t₂₉, X₂: X₂ {O(n)}
t₂₉, X₃: X₃ {O(n)}