Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₁₃: l10(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄)
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₄, X₃, X₄)
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₂, X₄) :|: 0 < X₂
t₁₁: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₀, X₃, X₄) :|: 0 < X₁
t₁₂: l6(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ 0
t₉: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₁₀: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, nondef_0, X₂, X₃, X₄)
t₈: l9(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₃-1, X₃, X₄) :|: X₃ ≤ 1
t₇: l9(X₀, X₁, X₂, X₃, X₄) → l7(X₃-1, X₁, X₂, X₃, X₄) :|: 1 < X₃

Preprocessing

Found invariant X₂ ≤ X₄ ∧ X₂ ≤ 0 for location l11

Found invariant 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l6

Found invariant 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l7

Found invariant X₂ ≤ X₄ for location l5

Found invariant 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l8

Found invariant X₂ ≤ X₄ ∧ X₂ ≤ 0 for location l10

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₁₃: l10(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₄ ∧ X₂ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₄, X₃, X₄)
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ X₂ ≤ X₄
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₂, X₄) :|: 0 < X₂ ∧ X₂ ≤ X₄
t₁₁: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₀, X₃, X₄) :|: 0 < X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₂: l6(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ 0 ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₉: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₀: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, nondef_0, X₂, X₃, X₄) :|: 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₈: l9(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₃-1, X₃, X₄) :|: X₃ ≤ 1 ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂
t₇: l9(X₀, X₁, X₂, X₃, X₄) → l7(X₃-1, X₁, X₂, X₃, X₄) :|: 1 < X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂

MPRF for transition t₅: l5(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₂, X₄) :|: 0 < X₂ ∧ X₂ ≤ X₄ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l8 [2⋅X₀+1-X₃ ]
l6 [2⋅X₀+1-X₃ ]
l7 [2⋅X₀+1-X₃ ]
l9 [X₃-1 ]
l5 [X₂ ]

MPRF for transition t₁₁: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₀, X₃, X₄) :|: 0 < X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l8 [X₃ ]
l6 [X₀+1 ]
l7 [X₃ ]
l9 [X₃ ]
l5 [X₂ ]

MPRF for transition t₁₂: l6(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ 0 ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l8 [X₃-1 ]
l6 [X₃-1 ]
l7 [X₃-1 ]
l9 [X₃-1 ]
l5 [X₂-1 ]

MPRF for transition t₉: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l8 [X₃-1 ]
l6 [X₃-1 ]
l7 [X₃ ]
l9 [X₃ ]
l5 [X₂ ]

MPRF for transition t₁₀: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, nondef_0, X₂, X₃, X₄) :|: 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l8 [X₃-1 ]
l6 [X₀-1 ]
l7 [X₃-1 ]
l9 [X₃-1 ]
l5 [X₂-1 ]

MPRF for transition t₇: l9(X₀, X₁, X₂, X₃, X₄) → l7(X₃-1, X₁, X₂, X₃, X₄) :|: 1 < X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l8 [X₀ ]
l6 [X₀ ]
l7 [X₃-1 ]
l9 [X₃ ]
l5 [X₂ ]

MPRF for transition t₈: l9(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₃-1, X₃, X₄) :|: X₃ ≤ 1 ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l8 [X₀ ]
l6 [X₀ ]
l7 [X₀ ]
l9 [X₃ ]
l5 [X₂ ]

All Bounds

Timebounds

Overall timebound:7⋅X₄+9 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₄ {O(n)}
t₆: 1 {O(1)}
t₁₁: X₄ {O(n)}
t₁₂: X₄+1 {O(n)}
t₉: X₄ {O(n)}
t₁₀: X₄+1 {O(n)}
t₇: X₄ {O(n)}
t₈: X₄ {O(n)}

Costbounds

Overall costbound: 7⋅X₄+9 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₄ {O(n)}
t₆: 1 {O(1)}
t₁₁: X₄ {O(n)}
t₁₂: X₄+1 {O(n)}
t₉: X₄ {O(n)}
t₁₀: X₄+1 {O(n)}
t₇: X₄ {O(n)}
t₈: X₄ {O(n)}

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)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₁₃, X₀: 2⋅X₀+2⋅X₄ {O(n)}
t₁₃, X₂: X₄ {O(n)}
t₁₃, X₃: X₃+1 {O(n)}
t₁₃, X₄: 3⋅X₄ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {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)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₄ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₀+X₄ {O(n)}
t₅, X₂: 2⋅X₄ {O(n)}
t₅, X₃: X₄ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: 2⋅X₀+2⋅X₄ {O(n)}
t₆, X₂: X₄ {O(n)}
t₆, X₃: X₃+1 {O(n)}
t₆, X₄: 3⋅X₄ {O(n)}
t₁₁, X₀: X₄ {O(n)}
t₁₁, X₂: X₄ {O(n)}
t₁₁, X₃: 2⋅X₄ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₂, X₀: X₄ {O(n)}
t₁₂, X₂: 2⋅X₄ {O(n)}
t₁₂, X₃: X₄ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₉, X₀: X₄ {O(n)}
t₉, X₂: 2⋅X₄ {O(n)}
t₉, X₃: 2⋅X₄ {O(n)}
t₉, X₄: X₄ {O(n)}
t₁₀, X₀: X₄ {O(n)}
t₁₀, X₂: 2⋅X₄ {O(n)}
t₁₀, X₃: 2⋅X₄ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₇, X₀: X₄ {O(n)}
t₇, X₂: 2⋅X₄ {O(n)}
t₇, X₃: 2⋅X₄ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: 2⋅X₄+X₀ {O(n)}
t₈, X₂: 0 {O(1)}
t₈, X₃: 1 {O(1)}
t₈, X₄: 2⋅X₄ {O(n)}