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) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₁, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₂
t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, -X₄, -X₅, X₃, X₄, X₅) :|: X₄ < 0 ∧ X₅ < 0
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, -X₄, X₅, X₃, X₄, X₅) :|: X₄ < 0 ∧ 0 ≤ X₅
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₄, -X₅, X₃, X₄, X₅) :|: 0 ≤ X₄ ∧ X₅ < 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₄, X₅, X₃, X₄, X₅) :|: 0 ≤ X₄ ∧ 0 ≤ X₅
t₈: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₂, X₀, X₃, X₄, X₅) :|: X₀ < X₂
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀-X₂, X₁, X₂, X₃, X₄, X₅)

Preprocessing

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

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l6

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

Found invariant 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l1

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l4

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ X₁ 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
Transitions:
t₂₂: l0(X₀, X₁, X₂, X₄, X₅) → l2(X₀, X₁, X₂, X₄, X₅)
t₂₃: l1(X₀, X₁, X₂, X₄, X₅) → l3(X₁, X₁, X₂, X₄, X₅) :|: 0 < X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₂₄: l1(X₀, X₁, X₂, X₄, X₅) → l4(X₀, X₁, X₂, X₄, X₅) :|: X₂ ≤ 0 ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₂₅: l2(X₀, X₁, X₂, X₄, X₅) → l1(X₀, -X₄, -X₅, X₄, X₅) :|: X₄ < 0 ∧ X₅ < 0
t₂₆: l2(X₀, X₁, X₂, X₄, X₅) → l1(X₀, -X₄, X₅, X₄, X₅) :|: X₄ < 0 ∧ 0 ≤ X₅
t₂₇: l2(X₀, X₁, X₂, X₄, X₅) → l1(X₀, X₄, -X₅, X₄, X₅) :|: 0 ≤ X₄ ∧ X₅ < 0
t₂₈: l2(X₀, X₁, X₂, X₄, X₅) → l1(X₀, X₄, X₅, X₄, X₅) :|: 0 ≤ X₄ ∧ 0 ≤ X₅
t₃₀: l3(X₀, X₁, X₂, X₄, X₅) → l1(X₀, X₂, X₀, X₄, X₅) :|: X₀ < X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ X₁
t₂₉: l3(X₀, X₁, X₂, X₄, X₅) → l5(X₀, X₁, X₂, X₄, X₅) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ X₁
t₃₁: l4(X₀, X₁, X₂, X₄, X₅) → l6(X₀, X₁, X₂, X₄, X₅) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₃₂: l5(X₀, X₁, X₂, X₄, X₅) → l3(X₀-X₂, X₁, X₂, X₄, X₅) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

MPRF for transition t₂₃: l1(X₀, X₁, X₂, X₄, X₅) → l3(X₁, X₁, X₂, X₄, X₅) :|: 0 < X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

4⋅X₄+8⋅X₅ {O(n)}

MPRF:

l1 [X₁+2⋅X₂ ]
l5 [X₀+X₂ ]
l3 [X₀+2⋅X₂-1 ]

MPRF for transition t₂₉: l3(X₀, X₁, X₂, X₄, X₅) → l5(X₀, X₁, X₂, X₄, X₅) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ X₁ of depth 1:

new bound:

4⋅X₄+4⋅X₅+4 {O(n)}

MPRF:

l1 [X₁+X₂-1 ]
l5 [X₀+X₂-2 ]
l3 [X₀+X₂-1 ]

MPRF for transition t₃₀: l3(X₀, X₁, X₂, X₄, X₅) → l1(X₀, X₂, X₀, X₄, X₅) :|: X₀ < X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ X₁ of depth 1:

new bound:

8⋅X₅+4 {O(n)}

MPRF:

l1 [2⋅X₂-1 ]
l5 [2⋅X₂-1 ]
l3 [2⋅X₂-1 ]

MPRF for transition t₃₂: l5(X₀, X₁, X₂, X₄, X₅) → l3(X₀-X₂, X₁, X₂, X₄, X₅) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

4⋅X₄+4⋅X₅+4 {O(n)}

MPRF:

l1 [X₁+X₂-1 ]
l5 [X₀ ]
l3 [X₀+X₂-1 ]

All Bounds

Timebounds

Overall timebound:12⋅X₄+24⋅X₅+19 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 4⋅X₄+8⋅X₅ {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 4⋅X₄+4⋅X₅+4 {O(n)}
t₃₀: 8⋅X₅+4 {O(n)}
t₃₁: 1 {O(1)}
t₃₂: 4⋅X₄+4⋅X₅+4 {O(n)}

Costbounds

Overall costbound: 12⋅X₄+24⋅X₅+19 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 4⋅X₄+8⋅X₅ {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 4⋅X₄+4⋅X₅+4 {O(n)}
t₃₀: 8⋅X₅+4 {O(n)}
t₃₁: 1 {O(1)}
t₃₂: 4⋅X₄+4⋅X₅+4 {O(n)}

Sizebounds

t₂₂, X₀: X₀ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₃, X₀: 4⋅X₄+4⋅X₅ {O(n)}
t₂₃, X₁: 4⋅X₅+8⋅X₄ {O(n)}
t₂₃, X₂: 4⋅X₄+4⋅X₅ {O(n)}
t₂₃, X₄: 4⋅X₄ {O(n)}
t₂₃, X₅: 4⋅X₅ {O(n)}
t₂₄, X₀: 2⋅X₀+8⋅X₄+8⋅X₅ {O(n)}
t₂₄, X₁: 4⋅X₅+6⋅X₄ {O(n)}
t₂₄, X₂: 4⋅X₄+6⋅X₅ {O(n)}
t₂₄, X₄: 6⋅X₄ {O(n)}
t₂₄, X₅: 6⋅X₅ {O(n)}
t₂₅, X₀: X₀ {O(n)}
t₂₅, X₁: X₄ {O(n)}
t₂₅, X₂: X₅ {O(n)}
t₂₅, X₄: X₄ {O(n)}
t₂₅, X₅: X₅ {O(n)}
t₂₆, X₀: X₀ {O(n)}
t₂₆, X₁: X₄ {O(n)}
t₂₆, X₂: X₅ {O(n)}
t₂₆, X₄: X₄ {O(n)}
t₂₆, X₅: X₅ {O(n)}
t₂₇, X₀: X₀ {O(n)}
t₂₇, X₁: X₄ {O(n)}
t₂₇, X₂: X₅ {O(n)}
t₂₇, X₄: X₄ {O(n)}
t₂₇, X₅: X₅ {O(n)}
t₂₈, X₀: X₀ {O(n)}
t₂₈, X₁: X₄ {O(n)}
t₂₈, X₂: X₅ {O(n)}
t₂₈, X₄: X₄ {O(n)}
t₂₈, X₅: X₅ {O(n)}
t₂₉, X₀: 4⋅X₄+4⋅X₅ {O(n)}
t₂₉, X₁: 4⋅X₅+8⋅X₄ {O(n)}
t₂₉, X₂: 4⋅X₄+4⋅X₅ {O(n)}
t₂₉, X₄: 4⋅X₄ {O(n)}
t₂₉, X₅: 4⋅X₅ {O(n)}
t₃₀, X₀: 8⋅X₄+8⋅X₅ {O(n)}
t₃₀, X₁: 4⋅X₄+4⋅X₅ {O(n)}
t₃₀, X₂: 4⋅X₄+4⋅X₅ {O(n)}
t₃₀, X₄: 4⋅X₄ {O(n)}
t₃₀, X₅: 4⋅X₅ {O(n)}
t₃₁, X₀: 2⋅X₀+8⋅X₄+8⋅X₅ {O(n)}
t₃₁, X₁: 4⋅X₅+6⋅X₄ {O(n)}
t₃₁, X₂: 4⋅X₄+6⋅X₅ {O(n)}
t₃₁, X₄: 6⋅X₄ {O(n)}
t₃₁, X₅: 6⋅X₅ {O(n)}
t₃₂, X₀: 4⋅X₄+4⋅X₅ {O(n)}
t₃₂, X₁: 4⋅X₅+8⋅X₄ {O(n)}
t₃₂, X₂: 4⋅X₄+4⋅X₅ {O(n)}
t₃₂, X₄: 4⋅X₄ {O(n)}
t₃₂, X₅: 4⋅X₅ {O(n)}