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, X₀, X₂, X₃, X₄, X₅) :|: 1 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 1
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₁, X₂, X₃, X₄, X₅)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 1
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 < X₁
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₁, X₁, X₂, X₃, X₄, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁-2, X₂, X₃, X₄, X₅)

Preprocessing

Eliminate variables {X₂,X₃,X₅} that do not contribute to the problem

Found invariant 2 ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant X₀ ≤ X₄ ∧ X₀ ≤ 1 for location l7

Found invariant 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l5

Found invariant X₀ ≤ X₄ for location l1

Found invariant X₀ ≤ X₄ ∧ X₀ ≤ 1 for location l4

Found invariant 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₈: l0(X₀, X₁, X₄) → l2(X₀, X₁, X₄)
t₁₉: l1(X₀, X₁, X₄) → l3(X₀, X₀, X₄) :|: 1 < X₀ ∧ X₀ ≤ X₄
t₂₀: l1(X₀, X₁, X₄) → l4(X₀, X₁, X₄) :|: X₀ ≤ 1 ∧ X₀ ≤ X₄
t₂₁: l2(X₀, X₁, X₄) → l1(X₄, X₁, X₄)
t₂₃: l3(X₀, X₁, X₄) → l5(X₀, X₁, X₄) :|: X₁ ≤ 1 ∧ 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₂: l3(X₀, X₁, X₄) → l6(X₀, X₁, X₄) :|: 1 < X₁ ∧ 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₄: l4(X₀, X₁, X₄) → l7(X₀, X₁, X₄) :|: X₀ ≤ X₄ ∧ X₀ ≤ 1
t₂₅: l5(X₀, X₁, X₄) → l1(X₁, X₁, X₄) :|: 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₆: l6(X₀, X₁, X₄) → l3(X₀, X₁-2, X₄) :|: 2 ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₉: l1(X₀, X₁, X₄) → l3(X₀, X₀, X₄) :|: 1 < X₀ ∧ X₀ ≤ X₄

MPRF for transition t₂₂: l3(X₀, X₁, X₄) → l6(X₀, X₁, X₄) :|: 1 < X₁ ∧ 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l5 [X₁+1 ]
l1 [X₀+1 ]
l6 [X₁-1 ]
l3 [X₁+1 ]

MPRF for transition t₂₃: l3(X₀, X₁, X₄) → l5(X₀, X₁, X₄) :|: X₁ ≤ 1 ∧ 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

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

MPRF for transition t₂₅: l5(X₀, X₁, X₄) → l1(X₁, X₁, X₄) :|: 2 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l5 [2 ]
l1 [X₀ ]
l6 [X₀ ]
l3 [X₀ ]

MPRF for transition t₂₆: l6(X₀, X₁, X₄) → l3(X₀, X₁-2, X₄) :|: 2 ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l5 [X₁-1 ]
l1 [X₀-1 ]
l6 [X₁-1 ]
l3 [X₁-1 ]

All Bounds

Timebounds

Overall timebound:4⋅X₄+8 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: X₄+1 {O(n)}
t₂₃: X₄+1 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₄ {O(n)}
t₂₆: X₄+1 {O(n)}

Costbounds

Overall costbound: 4⋅X₄+8 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: X₄+1 {O(n)}
t₂₃: X₄+1 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₄ {O(n)}
t₂₆: X₄+1 {O(n)}

Sizebounds

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