Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₁, X₃, X₆, X₇, X₈, X₉) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₆, X₇, X₈, X₉, X₄, X₅, X₆, X₇, X₈, X₉)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀-1, 3⋅X₁+X₂, -6⋅X₁-2⋅X₂, X₃+2⋅(X₀)²+2-4⋅X₀, X₄, X₅, X₆, X₇, X₈, X₉)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₄+X₅
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₄+X₅ ≤ 0
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₄-1, X₅-1, X₆, X₇, X₈, X₉)
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)

Preprocessing

Found invariant X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l6

Found invariant X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l7

Found invariant X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0 for location l5

Found invariant X₀ ≤ X₆ for location l1

Found invariant X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l4

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₀ ∧ X₀ ≤ X₆
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₁, X₃, X₆, X₇, X₈, X₉) :|: X₀ ≤ 0 ∧ X₀ ≤ X₆
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₆, X₇, X₈, X₉, X₄, X₅, X₆, X₇, X₈, X₉)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀-1, 3⋅X₁+X₂, -6⋅X₁-2⋅X₂, X₃+2⋅(X₀)²+2-4⋅X₀, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₄+X₅ ∧ X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₄+X₅ ≤ 0 ∧ X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₄-1, X₅-1, X₆, X₇, X₈, X₉) :|: X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₀ ∧ X₀ ≤ X₆ of depth 1:

new bound:

X₆ {O(n)}

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀-1, 3⋅X₁+X₂, -6⋅X₁-2⋅X₂, X₃+2⋅Temp_Int₃₆₃+2⋅Temp_Int₃₆₄-4⋅X₀, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < Temp_Int₃₆₃ ∧ X₀ ≤ Temp_Int₃₆₃ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₆ {O(n)}

Chain transitions t₇: l5→l4 and t₆: l4→l6 to t₅₇: l5→l6

Chain transitions t₃: l1→l4 and t₆: l4→l6 to t₅₈: l1→l6

Chain transitions t₃: l1→l4 and t₅: l4→l5 to t₅₉: l1→l5

Chain transitions t₇: l5→l4 and t₅: l4→l5 to t₆₀: l5→l5

Analysing control-flow refined program

Found invariant X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l6

Found invariant X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l7

Found invariant X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0 for location l5

Found invariant X₀ ≤ X₆ for location l1

Found invariant X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l4

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₀ for location l3

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₀ ≤ X₆ ∧ 1+X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₄ ≤ X₁ ∧ 2 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₃ ∧ X₀ ≤ 0 for location n_l5___1

Found invariant X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l6

Found invariant X₀ ≤ X₆ ∧ 1+X₅ ≤ X₃ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ X₁+X₅ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0 for location n_l4___2

Found invariant X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l7

Found invariant X₀ ≤ X₆ for location l1

Found invariant X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₃ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₀ ≤ 0 for location l4

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₀ for location l3

Found invariant X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₃+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0 for location n_l5___3

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₆ {O(n)}
t₃: 1 {O(1)}
t₄: X₆ {O(n)}
t₅: inf {Infinity}
t₆: 1 {O(1)}
t₇: inf {Infinity}
t₈: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₆ {O(n)}
t₃: 1 {O(1)}
t₄: X₆ {O(n)}
t₅: inf {Infinity}
t₆: 1 {O(1)}
t₇: inf {Infinity}
t₈: 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)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₀, X₇: X₇ {O(n)}
t₀, X₈: X₈ {O(n)}
t₀, X₉: X₉ {O(n)}
t₁, X₀: X₆ {O(n)}
t₁, X₁: X₇ {O(n)}
t₁, X₂: X₈ {O(n)}
t₁, X₃: X₉ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₁, X₇: X₇ {O(n)}
t₁, X₈: X₈ {O(n)}
t₁, X₉: X₉ {O(n)}
t₂, X₀: X₆ {O(n)}
t₂, X₁: 12^(X₆)⋅X₇+12^(X₆)⋅X₈ {O(EXP)}
t₂, X₂: 12^(X₆)⋅X₇+12^(X₆)⋅X₈ {O(EXP)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₂, X₇: X₇ {O(n)}
t₂, X₈: X₈ {O(n)}
t₂, X₉: X₉ {O(n)}
t₃, X₀: 2⋅X₆ {O(n)}
t₃, X₁: 12^(X₆)⋅X₇+12^(X₆)⋅X₈+X₇ {O(EXP)}
t₃, X₂: 12^(X₆)⋅X₇+12^(X₆)⋅X₈+X₈ {O(EXP)}
t₃, X₄: 12^(X₆)⋅X₇+12^(X₆)⋅X₈+X₇ {O(EXP)}
t₃, X₆: 2⋅X₆ {O(n)}
t₃, X₇: 2⋅X₇ {O(n)}
t₃, X₈: 2⋅X₈ {O(n)}
t₃, X₉: 2⋅X₉ {O(n)}
t₄, X₀: X₆ {O(n)}
t₄, X₁: 12^(X₆)⋅X₇+12^(X₆)⋅X₈ {O(EXP)}
t₄, X₂: 12^(X₆)⋅X₇+12^(X₆)⋅X₈ {O(EXP)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₄, X₇: X₇ {O(n)}
t₄, X₈: X₈ {O(n)}
t₄, X₉: X₉ {O(n)}
t₅, X₀: 2⋅X₆ {O(n)}
t₅, X₁: 12^(X₆)⋅X₇+12^(X₆)⋅X₈+X₇ {O(EXP)}
t₅, X₂: 12^(X₆)⋅X₇+12^(X₆)⋅X₈+X₈ {O(EXP)}
t₅, X₆: 2⋅X₆ {O(n)}
t₅, X₇: 2⋅X₇ {O(n)}
t₅, X₈: 2⋅X₈ {O(n)}
t₅, X₉: 2⋅X₉ {O(n)}
t₆, X₀: 4⋅X₆ {O(n)}
t₆, X₁: 12^(X₆)⋅2⋅X₇+12^(X₆)⋅2⋅X₈+2⋅X₇ {O(EXP)}
t₆, X₂: 12^(X₆)⋅2⋅X₇+12^(X₆)⋅2⋅X₈+2⋅X₈ {O(EXP)}
t₆, X₆: 4⋅X₆ {O(n)}
t₆, X₇: 4⋅X₇ {O(n)}
t₆, X₈: 4⋅X₈ {O(n)}
t₆, X₉: 4⋅X₉ {O(n)}
t₇, X₀: 2⋅X₆ {O(n)}
t₇, X₁: 12^(X₆)⋅X₇+12^(X₆)⋅X₈+X₇ {O(EXP)}
t₇, X₂: 12^(X₆)⋅X₇+12^(X₆)⋅X₈+X₈ {O(EXP)}
t₇, X₆: 2⋅X₆ {O(n)}
t₇, X₇: 2⋅X₇ {O(n)}
t₇, X₈: 2⋅X₈ {O(n)}
t₇, X₉: 2⋅X₉ {O(n)}
t₈, X₀: 4⋅X₆ {O(n)}
t₈, X₁: 12^(X₆)⋅2⋅X₇+12^(X₆)⋅2⋅X₈+2⋅X₇ {O(EXP)}
t₈, X₂: 12^(X₆)⋅2⋅X₇+12^(X₆)⋅2⋅X₈+2⋅X₈ {O(EXP)}
t₈, X₆: 4⋅X₆ {O(n)}
t₈, X₇: 4⋅X₇ {O(n)}
t₈, X₈: 4⋅X₈ {O(n)}
t₈, X₉: 4⋅X₉ {O(n)}