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, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₂
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ 0
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, nondef.0, X₃, X₄, X₅)
t₁₁: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀-X₃-1, X₁, X₂, X₃, X₄, X₅)
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁+X₃+1, X₂, X₃, X₄, X₅)
t₅: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₀ ∧ 0 ≤ X₃
t₃: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < X₁
t₄: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < 0
t₁₃: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₄, X₅, X₂, X₃, X₄, X₅) :|: 0 ≤ X₃
t₂: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < 0

Preprocessing

Found invariant X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ for location l2

Found invariant X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ for location l6

Found invariant X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₁ ≤ X₀ for location l5

Found invariant X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ for location l1

Found invariant X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ for location l4

Found invariant X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ for location l3

Cut unsatisfiable transition t₄: l6→l7

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, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₂ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ 0 ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀
t₈: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, nondef.0, X₃, X₄, X₅) :|: X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀
t₁₁: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀-X₃-1, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁+X₃+1, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₁ ≤ X₀
t₅: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃
t₃: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < X₁ ∧ X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃
t₁₃: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₄, X₅, X₂, X₃, X₄, X₅) :|: 0 ≤ X₃
t₂: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < 0

MPRF for transition t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₂ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₄+X₅+1 {O(n)}

MPRF:

l3 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
l4 [X₀-X₁ ]
l5 [X₀-X₁ ]
l6 [X₀+1-X₁ ]
l2 [X₀+1-X₁ ]

MPRF for transition t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ 0 ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₄+X₅+1 {O(n)}

MPRF:

l3 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
l4 [X₀-X₁ ]
l5 [X₀-X₁ ]
l6 [X₀+1-X₁ ]
l2 [X₀+1-X₁ ]

MPRF for transition t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₄+X₅+1 {O(n)}

MPRF:

l3 [X₀-X₁ ]
l1 [X₀-X₁ ]
l4 [X₀-X₁ ]
l5 [X₀-X₁ ]
l6 [X₀+1-X₁ ]
l2 [X₀+1-X₁ ]

MPRF for transition t₈: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, nondef.0, X₃, X₄, X₅) :|: X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₄+X₅+1 {O(n)}

MPRF:

l3 [X₀+1-X₁ ]
l1 [X₀-X₁ ]
l4 [X₀-X₁ ]
l5 [X₀-X₁ ]
l6 [X₀+1-X₁ ]
l2 [X₀+1-X₁ ]

MPRF for transition t₁₁: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀-X₃-1, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₄+X₅+1 {O(n)}

MPRF:

l3 [X₀+1-X₅ ]
l1 [X₀+1-X₅ ]
l4 [X₀+1-X₅ ]
l5 [X₀+1-X₅ ]
l6 [X₀+1-X₅ ]
l2 [X₀+1-X₅ ]

MPRF for transition t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁+X₃+1, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₄+X₅+1 {O(n)}

MPRF:

l3 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
l4 [X₀-X₁ ]
l5 [X₀+1-X₁ ]
l6 [X₀+1-X₁ ]
l2 [X₀+1-X₁ ]

MPRF for transition t₅: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₄+X₅+1 {O(n)}

MPRF:

l3 [X₀-X₁ ]
l1 [X₀-X₁ ]
l4 [X₀-X₁ ]
l5 [X₀-X₁ ]
l6 [X₀+1-X₁ ]
l2 [X₀-X₁ ]

All Bounds

Timebounds

Overall timebound:7⋅X₄+7⋅X₅+12 {O(n)}
t₀: 1 {O(1)}
t₉: X₄+X₅+1 {O(n)}
t₁₀: X₄+X₅+1 {O(n)}
t₆: X₄+X₅+1 {O(n)}
t₈: X₄+X₅+1 {O(n)}
t₁₁: X₄+X₅+1 {O(n)}
t₁₂: X₄+X₅+1 {O(n)}
t₃: 1 {O(1)}
t₅: X₄+X₅+1 {O(n)}
t₁₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}

Costbounds

Overall costbound: 7⋅X₄+7⋅X₅+12 {O(n)}
t₀: 1 {O(1)}
t₉: X₄+X₅+1 {O(n)}
t₁₀: X₄+X₅+1 {O(n)}
t₆: X₄+X₅+1 {O(n)}
t₈: X₄+X₅+1 {O(n)}
t₁₁: X₄+X₅+1 {O(n)}
t₁₂: X₄+X₅+1 {O(n)}
t₃: 1 {O(1)}
t₅: X₄+X₅+1 {O(n)}
t₁₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 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)}
t₉, X₀: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₄+X₅+1 {O(n^2)}
t₉, X₁: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₅+X₄+1 {O(n^2)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₅ {O(n)}
t₁₀, X₀: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₄+X₅+1 {O(n^2)}
t₁₀, X₁: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₅+X₄+1 {O(n^2)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₆, X₀: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₄+X₅+1 {O(n^2)}
t₆, X₁: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₅+X₄+1 {O(n^2)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₈, X₀: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₄+X₅+1 {O(n^2)}
t₈, X₁: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₅+X₄+1 {O(n^2)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₁₁, X₀: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₄+X₅+1 {O(n^2)}
t₁₁, X₁: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₅+X₄+1 {O(n^2)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₂, X₀: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₄+X₅+1 {O(n^2)}
t₁₂, X₁: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₅+X₄+1 {O(n^2)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₃, X₀: 2⋅X₃⋅X₄+2⋅X₃⋅X₅+2⋅X₅+4⋅X₃+5⋅X₄+2 {O(n^2)}
t₃, X₁: 2⋅X₃⋅X₄+2⋅X₃⋅X₅+2⋅X₄+4⋅X₃+5⋅X₅+2 {O(n^2)}
t₃, X₃: 3⋅X₃ {O(n)}
t₃, X₄: 3⋅X₄ {O(n)}
t₃, X₅: 3⋅X₅ {O(n)}
t₅, X₀: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₄+X₅+1 {O(n^2)}
t₅, X₁: X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₅+X₄+1 {O(n^2)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₁₃, X₀: 2⋅X₃⋅X₄+2⋅X₃⋅X₅+2⋅X₅+4⋅X₃+5⋅X₄+X₀+2 {O(n^2)}
t₁₃, X₁: 2⋅X₃⋅X₄+2⋅X₃⋅X₅+2⋅X₄+4⋅X₃+5⋅X₅+X₁+2 {O(n^2)}
t₁₃, X₃: 4⋅X₃ {O(n)}
t₁₃, X₄: 4⋅X₄ {O(n)}
t₁₃, X₅: 4⋅X₅ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₅ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}