Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₉: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₀, X₄) :|: 0 < X₁
t₁₀: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₀) :|: X₁ ≤ 0
t₆: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₈: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, nondef.0, X₂, X₃, X₄)
t₂: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₃) :|: X₃ < X₂
t₃: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃
t₄: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₄+1, X₁, X₂, X₃, X₄) :|: X₄+1 < X₂
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₄+1, X₄) :|: X₂ ≤ X₄+1
t₁: l6(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, 0, X₄)
t₁₁: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Found invariant 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l2

Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l7

Found invariant 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l5

Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l8

Found invariant 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l1

Found invariant 0 ≤ X₃ for location l4

Found invariant 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₉: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₀, X₄) :|: 0 < X₁ ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₀: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₀) :|: X₁ ≤ 0 ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₈: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, nondef.0, X₂, X₃, X₄) :|: 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₂: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₃) :|: X₃ < X₂ ∧ 0 ≤ X₃
t₃: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃ ∧ 0 ≤ X₃
t₄: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₄+1, X₁, X₂, X₃, X₄) :|: X₄+1 < X₂ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₄+1, X₄) :|: X₂ ≤ X₄+1 ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂
t₁: l6(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, 0, X₄)
t₁₁: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ X₂ ≤ X₃

MPRF for transition t₉: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₀, X₄) :|: 0 < X₁ ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l3 [X₂-X₄-1 ]
l1 [X₂-X₀ ]
l2 [X₂-X₄-1 ]
l5 [X₂-X₄-1 ]
l4 [X₂-X₃-1 ]

MPRF for transition t₁₀: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₀) :|: X₁ ≤ 0 ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l3 [X₂+X₄+1-2⋅X₀ ]
l1 [X₂-X₄-1 ]
l2 [X₂-X₄-1 ]
l5 [X₂-X₄-1 ]
l4 [X₂-X₃-1 ]

MPRF for transition t₆: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l3 [X₂-X₀-1 ]
l1 [X₂+X₄-2⋅X₀ ]
l2 [X₂-X₀ ]
l5 [X₂-X₄-1 ]
l4 [X₂-X₃-1 ]

MPRF for transition t₈: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, nondef.0, X₂, X₃, X₄) :|: 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l3 [X₂-X₄-1 ]
l1 [X₂-X₄-2 ]
l2 [X₂-X₄-1 ]
l5 [X₂-X₄-1 ]
l4 [X₂-X₃-1 ]

MPRF for transition t₂: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₃) :|: X₃ < X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l3 [X₂+X₄-X₀-X₃ ]
l1 [X₂-X₃-1 ]
l2 [X₂+X₄-X₀-X₃ ]
l5 [X₂-X₃-1 ]
l4 [X₂-X₃ ]

MPRF for transition t₄: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₄+1, X₁, X₂, X₃, X₄) :|: X₄+1 < X₂ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l3 [X₂-X₄ ]
l1 [X₂-X₄ ]
l2 [X₂-X₄ ]
l5 [X₂+1-X₄ ]
l4 [X₂+1-X₃ ]

MPRF for transition t₅: l5(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₄+1, X₄) :|: X₂ ≤ X₄+1 ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:

new bound:

X₂+2 {O(n)}

MPRF:

l3 [X₂+2-X₄ ]
l1 [X₂+2-X₄ ]
l2 [2⋅X₀+X₂-3⋅X₄ ]
l5 [X₂+2-X₄ ]
l4 [X₂+2-X₃ ]

All Bounds

Timebounds

Overall timebound:7⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₉: X₂+1 {O(n)}
t₁₀: X₂+1 {O(n)}
t₆: X₂+1 {O(n)}
t₈: X₂+1 {O(n)}
t₂: X₂ {O(n)}
t₃: 1 {O(1)}
t₄: X₂+1 {O(n)}
t₅: X₂+2 {O(n)}
t₁: 1 {O(1)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 7⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₉: X₂+1 {O(n)}
t₁₀: X₂+1 {O(n)}
t₆: X₂+1 {O(n)}
t₈: X₂+1 {O(n)}
t₂: X₂ {O(n)}
t₃: 1 {O(1)}
t₄: X₂+1 {O(n)}
t₅: X₂+2 {O(n)}
t₁: 1 {O(1)}
t₁₁: 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)}
t₉, X₀: X₂+1 {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₂+1 {O(n)}
t₉, X₄: 2⋅X₂+2 {O(n)}
t₁₀, X₀: X₂+1 {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₂+1 {O(n)}
t₁₀, X₄: X₂+1 {O(n)}
t₆, X₀: X₂+1 {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₂+1 {O(n)}
t₆, X₄: 2⋅X₂+2 {O(n)}
t₈, X₀: X₂+1 {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₂+1 {O(n)}
t₈, X₄: 2⋅X₂+2 {O(n)}
t₂, X₀: X₀+X₂+1 {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₂+1 {O(n)}
t₂, X₄: X₂+1 {O(n)}
t₃, X₀: 2⋅X₀+2⋅X₂+2 {O(n)}
t₃, X₂: 3⋅X₂ {O(n)}
t₃, X₃: 2⋅X₂+4 {O(n)}
t₃, X₄: 2⋅X₂+X₄+2 {O(n)}
t₄, X₀: X₂+1 {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₂+1 {O(n)}
t₄, X₄: 2⋅X₂+2 {O(n)}
t₅, X₀: 2⋅X₂+X₀+2 {O(n)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₂+4 {O(n)}
t₅, X₄: 2⋅X₂+2 {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: 0 {O(1)}
t₁, X₄: X₄ {O(n)}
t₁₁, X₀: 2⋅X₀+2⋅X₂+2 {O(n)}
t₁₁, X₂: 3⋅X₂ {O(n)}
t₁₁, X₃: 2⋅X₂+4 {O(n)}
t₁₁, X₄: 2⋅X₂+X₄+2 {O(n)}