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

Preprocessing

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2

Found invariant X₁ ≤ X₄ ∧ 1 ≤ X₀ for location l6

Found invariant X₁ ≤ X₄ ∧ X₀ ≤ 0 for location l7

Found invariant X₁ ≤ X₄ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l8

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

Found invariant X₁ ≤ X₄ for location l4

Found invariant X₁ ≤ X₄ ∧ X₀ ≤ 0 for location l9

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 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, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₉: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₂, 0, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, nondef.0, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀ ∧ X₁ ≤ X₄
t₃: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ X₁ ≤ X₄
t₁: l5(X₀, X₁, X₂, X₃, X₄) → l4(X₃, X₄, X₂, X₃, X₄)
t₄: l6(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀
t₅: l6(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0 ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀
t₁₁: l7(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₄ ∧ X₀ ≤ 0
t₁₀: l8(X₀, X₁, X₂, X₃, X₄) → l4(X₀-1, X₁-1, X₂, X₃, X₄) :|: X₁ ≤ X₄ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀

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

new bound:

X₄ {O(n)}

MPRF:

l3 [1 ]
l1 [1 ]
l2 [1 ]
l6 [X₁ ]
l8 [X₁ ]
l4 [X₁ ]

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

new bound:

X₄ {O(n)}

MPRF:

l3 [0 ]
l1 [0 ]
l2 [1 ]
l6 [X₁ ]
l8 [X₁ ]
l4 [X₁ ]

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

new bound:

X₄ {O(n)}

MPRF:

l3 [1 ]
l1 [0 ]
l2 [1 ]
l6 [X₁ ]
l8 [X₁ ]
l4 [X₁ ]

MPRF for transition t₄: l6(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₁-1 ]
l1 [X₁-1 ]
l2 [X₁-1 ]
l6 [X₁ ]
l8 [X₁ ]
l4 [X₁ ]

Analysing control-flow refined program

Cut unsatisfiable transition t₉₀: n_l6___2→l2

Cut unsatisfiable transition t₉₁: n_l6___4→l2

Found invariant X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___2

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l8___1

Found invariant 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location n_l6___4

Found invariant 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location n_l8___3

Found invariant X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₁+X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location n_l8___6

Found invariant 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₀ for location n_l4___5

Found invariant X₁ ≤ X₄ ∧ X₀ ≤ 0 for location l7

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location n_l6___7

Found invariant X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

Found invariant X₁ ≤ X₄ for location l4

Found invariant X₁ ≤ X₄ ∧ X₀ ≤ 0 for location l9

Found invariant X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₇₇: l4(X₀, X₁, X₂, X₃, X₄) → n_l6___7(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 0 < X₀ ∧ X₁ ≤ X₄ ∧ X₁ ≤ X₄

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₉₂: n_l6___7(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₆: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₈: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, nondef.0, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₉: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₂, 0, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₉: X₄ {O(n)}
t₆: X₄ {O(n)}
t₈: X₄ {O(n)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: inf {Infinity}
t₁₁: 1 {O(1)}
t₁₀: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₉: X₄ {O(n)}
t₆: X₄ {O(n)}
t₈: X₄ {O(n)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: inf {Infinity}
t₁₁: 1 {O(1)}
t₁₀: inf {Infinity}

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, X₁: 0 {O(1)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: 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)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₁₁, X₃: 3⋅X₃ {O(n)}
t₁₁, X₄: 3⋅X₄ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}