Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < 2⋅X₁
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2⋅X₁ < X₀
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ X₀ ≤ 2⋅X₁ ∧ 2⋅X₁ ≤ X₀
t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₂, X₃, X₂, X₃, X₄, X₅)
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₀-1, X₃, X₄, X₅)
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, nondef.0, X₄, X₅)
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₅, X₄, X₂, X₃, X₄, X₅)

Preprocessing

Found invariant X₀ ≤ X₅ for location l2

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l5

Found invariant X₀ ≤ X₅ for location l1

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l4

Found invariant X₀ ≤ X₅ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ X₀ ≤ X₅
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < 2⋅X₁ ∧ X₀ ≤ X₅
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2⋅X₁ < X₀ ∧ X₀ ≤ X₅
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ X₀ ≤ 2⋅X₁ ∧ 2⋅X₁ ≤ X₀ ∧ X₀ ≤ X₅
t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₅
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₂, X₃, X₂, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₀-1, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, nondef.0, X₄, X₅) :|: 2 ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₅, X₄, X₂, X₃, X₄, X₅)

MPRF for transition t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ X₀ ≤ 2⋅X₁ ∧ 2⋅X₁ ≤ X₀ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

l2 [X₀ ]
l5 [X₀-1 ]
l6 [X₂ ]
l4 [X₂ ]

MPRF for transition t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₂, X₃, X₂, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

l2 [X₀-1 ]
l5 [X₀-1 ]
l6 [X₂ ]
l4 [X₀-1 ]

MPRF for transition t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₀-1, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

l2 [X₀-1 ]
l5 [X₀-1 ]
l6 [X₀-2 ]
l4 [X₂-1 ]

MPRF for transition t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, nondef.0, X₄, X₅) :|: 2 ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

l2 [X₀-1 ]
l5 [X₀-1 ]
l6 [X₂ ]
l4 [X₂-1 ]

All Bounds

Timebounds

Overall timebound:4⋅X₅+9 {O(n)}
t₀: 1 {O(1)}
t₂: X₅ {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁₀: 1 {O(1)}
t₉: X₅+1 {O(n)}
t₆: X₅+1 {O(n)}
t₈: X₅+1 {O(n)}
t₁: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₅+9 {O(n)}
t₀: 1 {O(1)}
t₂: X₅ {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁₀: 1 {O(1)}
t₉: X₅+1 {O(n)}
t₆: X₅+1 {O(n)}
t₈: X₅+1 {O(n)}
t₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₂, X₀: X₅ {O(n)}
t₂, X₂: X₂+X₅ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: X₅ {O(n)}
t₃, X₁: X₄ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₅ {O(n)}
t₄, X₀: 2⋅X₅ {O(n)}
t₄, X₂: X₂+X₅ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}
t₅, X₀: 2⋅X₅ {O(n)}
t₅, X₂: X₂+X₅ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₅, X₅: 2⋅X₅ {O(n)}
t₁₀, X₀: 5⋅X₅ {O(n)}
t₁₀, X₂: 2⋅X₅+3⋅X₂ {O(n)}
t₁₀, X₄: 5⋅X₄ {O(n)}
t₁₀, X₅: 5⋅X₅ {O(n)}
t₉, X₀: X₅ {O(n)}
t₉, X₂: X₅ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₅ {O(n)}
t₆, X₀: X₅ {O(n)}
t₆, X₂: X₅ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₈, X₀: X₅ {O(n)}
t₈, X₂: X₅ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₁, X₀: X₅ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}