Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₀, X₀, X₃) :|: X₀ < 64
t₅: l3(X₀, X₁, X₂, X₃) → l6(X₀, 64, 64, X₃) :|: 64 ≤ X₀
t₉: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₈: l5(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁, X₂, X₃)
t₇: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ 1
t₆: l6(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂-1, X₃) :|: 1 < X₂

Preprocessing

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 64 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 128 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 63+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 64 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6

Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l7

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5

Found invariant X₀ ≤ X₃ for location l1

Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l4

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₀ ≤ X₃
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ X₃
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₀, X₀, X₃) :|: X₀ < 64 ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃) → l6(X₀, 64, 64, X₃) :|: 64 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₉: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₀ ≤ 0
t₈: l5(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ 1 ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 64 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 128 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 63+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 64 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l6(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂-1, X₃) :|: 1 < X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 64 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 128 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 63+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 64 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

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

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₀, X₀, X₃) :|: X₀ < 64 ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

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

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃) → l6(X₀, 64, 64, X₃) :|: 64 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃+63 {O(n)}

MPRF:

l3 [X₀-63 ]
l1 [X₀-63 ]
l6 [X₀-X₁-63 ]
l5 [X₀-X₁-63 ]

MPRF for transition t₈: l5(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

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

MPRF for transition t₆: l6(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂-1, X₃) :|: 1 < X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 64 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 128 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 63+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 64 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

63⋅X₃+64 {O(n)}

MPRF:

l3 [63⋅X₀+64 ]
l1 [63⋅X₀+64 ]
l6 [63⋅X₀+X₂ ]
l5 [63⋅X₀+X₂+63-63⋅X₁ ]

MPRF for transition t₇: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ 1 ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 64 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 128 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 63+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 64 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l3 [X₀ ]
l1 [X₀ ]
l6 [X₀ ]
l5 [X₀-1 ]

All Bounds

Timebounds

Overall timebound:68⋅X₃+131 {O(n)}
t₀: 1 {O(1)}
t₂: X₃ {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₃ {O(n)}
t₅: X₃+63 {O(n)}
t₉: 1 {O(1)}
t₈: X₃ {O(n)}
t₆: 63⋅X₃+64 {O(n)}
t₇: X₃ {O(n)}

Costbounds

Overall costbound: 68⋅X₃+131 {O(n)}
t₀: 1 {O(1)}
t₂: X₃ {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₃ {O(n)}
t₅: X₃+63 {O(n)}
t₉: 1 {O(1)}
t₈: X₃ {O(n)}
t₆: 63⋅X₃+64 {O(n)}
t₇: X₃ {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₂, X₀: X₃+126 {O(n)}
t₂, X₁: X₁+64 {O(n)}
t₂, X₂: X₂+1 {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: 2⋅X₃+126 {O(n)}
t₃, X₁: X₁+64 {O(n)}
t₃, X₂: X₂+1 {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₄, X₀: 63 {O(1)}
t₄, X₁: 63 {O(1)}
t₄, X₂: 63 {O(1)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₃+126 {O(n)}
t₅, X₁: 64 {O(1)}
t₅, X₂: 64 {O(1)}
t₅, X₃: X₃ {O(n)}
t₉, X₀: 2⋅X₃+126 {O(n)}
t₉, X₁: X₁+64 {O(n)}
t₉, X₂: X₂+1 {O(n)}
t₉, X₃: 2⋅X₃ {O(n)}
t₈, X₀: X₃+126 {O(n)}
t₈, X₁: 64 {O(1)}
t₈, X₂: 1 {O(1)}
t₈, X₃: X₃ {O(n)}
t₆, X₀: X₃+126 {O(n)}
t₆, X₁: 64 {O(1)}
t₆, X₂: 63 {O(1)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₃+126 {O(n)}
t₇, X₁: 64 {O(1)}
t₇, X₂: 1 {O(1)}
t₇, X₃: X₃ {O(n)}