Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₇: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁+1, X₂, X₃, X₄) :|: 0 < X₂ ∧ 0 < X₂
t₈: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀-1, X₁+1, X₂, X₃, X₄) :|: 0 < X₂ ∧ X₂ ≤ 0
t₉: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ 0 < X₂
t₁₀: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀-1, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ X₂ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, nondef.0, X₃, X₄)
t₂: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ < X₀
t₃: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₁: l5(X₀, X₁, X₂, X₃, X₄) → l4(X₃, X₄, X₂, X₃, X₄)
t₁₁: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Cut unsatisfiable transition t₈: l1→l4

Cut unsatisfiable transition t₉: l1→l4

Found invariant 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location l2

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

Found invariant X₄ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₁ for location l7

Found invariant 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location l1

Found invariant X₄ ≤ X₁ ∧ X₀ ≤ X₃ for location l4

Found invariant 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ 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
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₇: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁+1, X₂, X₃, X₄) :|: 0 < X₂ ∧ 0 < X₂ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₁₀: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀-1, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ X₂ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₄: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, nondef.0, X₃, X₄) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₂: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ < X₀ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃
t₃: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃
t₁: l5(X₀, X₁, X₂, X₃, X₄) → l4(X₃, X₄, X₂, X₃, X₄)
t₁₁: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₁

MPRF for transition t₇: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁+1, X₂, X₃, X₄) :|: 0 < X₂ ∧ 0 < X₂ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF:

l3 [X₃-X₁ ]
l1 [X₃-X₁ ]
l4 [X₃-X₁ ]
l2 [X₃-X₁ ]

MPRF for transition t₁₀: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀-1, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ X₂ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF:

l3 [X₀-X₁ ]
l1 [X₀-X₁ ]
l4 [X₀-X₁ ]
l2 [X₀-X₁ ]

MPRF for transition t₄: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF:

l3 [X₀-X₁-1 ]
l1 [X₀-X₁-1 ]
l4 [X₀-X₁ ]
l2 [X₀-X₁ ]

MPRF for transition t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, nondef.0, X₃, X₄) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF:

l3 [X₀-X₁ ]
l1 [X₀-X₁-1 ]
l4 [X₀-X₁ ]
l2 [X₀-X₁ ]

MPRF for transition t₂: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ < X₀ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF:

l3 [X₀-X₁-1 ]
l1 [X₀-X₁-1 ]
l4 [X₀-X₁ ]
l2 [X₀-X₁-1 ]

All Bounds

Timebounds

Overall timebound:5⋅X₃+5⋅X₄+4 {O(n)}
t₀: 1 {O(1)}
t₇: X₃+X₄ {O(n)}
t₁₀: X₃+X₄ {O(n)}
t₄: X₃+X₄ {O(n)}
t₆: X₃+X₄ {O(n)}
t₂: X₃+X₄ {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 5⋅X₃+5⋅X₄+4 {O(n)}
t₀: 1 {O(1)}
t₇: X₃+X₄ {O(n)}
t₁₀: X₃+X₄ {O(n)}
t₄: X₃+X₄ {O(n)}
t₆: X₃+X₄ {O(n)}
t₂: X₃+X₄ {O(n)}
t₃: 1 {O(1)}
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)}
t₇, X₀: 2⋅X₃+X₄ {O(n)}
t₇, X₁: 2⋅X₄+X₃ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₁₀, X₀: 2⋅X₃+X₄ {O(n)}
t₁₀, X₁: 2⋅X₄+X₃ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₄, X₀: 2⋅X₃+X₄ {O(n)}
t₄, X₁: 2⋅X₄+X₃ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₆, X₀: 2⋅X₃+X₄ {O(n)}
t₆, X₁: 2⋅X₄+X₃ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₂, X₀: 2⋅X₃+X₄ {O(n)}
t₂, X₁: 2⋅X₄+X₃ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: 2⋅X₄+5⋅X₃ {O(n)}
t₃, X₁: 2⋅X₃+5⋅X₄ {O(n)}
t₃, X₃: 3⋅X₃ {O(n)}
t₃, X₄: 3⋅X₄ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁₁, X₀: 2⋅X₄+5⋅X₃ {O(n)}
t₁₁, X₁: 2⋅X₃+5⋅X₄ {O(n)}
t₁₁, X₃: 3⋅X₃ {O(n)}
t₁₁, X₄: 3⋅X₄ {O(n)}