Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < 0
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ 0 ≤ X₂
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, nondef.0, X₃, X₄, X₅, X₆)
t₁₁: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀-1, X₀, X₂, X₃, X₄, X₅, X₆)
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₁-2, X₀+1, X₂, X₃, X₄, X₅, X₆)
t₂: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀ ∧ 0 < X₁
t₃: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0
t₄: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ 0
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₅, X₆, X₂, X₃, X₄, X₅, X₆)
t₁₃: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Eliminate variables {X₃,X₄} that do not contribute to the problem

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

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5

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

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₅, X₆
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₂₇: l0(X₀, X₁, X₂, X₅, X₆) → l7(X₀, X₁, X₂, X₅, X₆)
t₂₈: l1(X₀, X₁, X₂, X₅, X₆) → l4(X₀, X₁, X₂, X₅, X₆) :|: X₂ < 0 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₉: l1(X₀, X₁, X₂, X₅, X₆) → l4(X₀, X₁, X₂, X₅, X₆) :|: 0 < X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₀: l1(X₀, X₁, X₂, X₅, X₆) → l5(X₀, X₁, X₂, X₅, X₆) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₁: l2(X₀, X₁, X₂, X₅, X₆) → l3(X₀, X₁, X₂, X₅, X₆) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₂: l3(X₀, X₁, X₂, X₅, X₆) → l1(X₀, X₁, nondef.0, X₅, X₆) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₃: l4(X₀, X₁, X₂, X₅, X₆) → l6(X₀-1, X₀, X₂, X₅, X₆) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₄: l5(X₀, X₁, X₂, X₅, X₆) → l6(X₁-2, X₀+1, X₂, X₅, X₆) :|: X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₅: l6(X₀, X₁, X₂, X₅, X₆) → l2(X₀, X₁, X₂, X₅, X₆) :|: 0 < X₀ ∧ 0 < X₁
t₃₆: l6(X₀, X₁, X₂, X₅, X₆) → l8(X₀, X₁, X₂, X₅, X₆) :|: X₀ ≤ 0
t₃₇: l6(X₀, X₁, X₂, X₅, X₆) → l8(X₀, X₁, X₂, X₅, X₆) :|: X₁ ≤ 0
t₃₈: l7(X₀, X₁, X₂, X₅, X₆) → l6(X₅, X₆, X₂, X₅, X₆)
t₃₉: l8(X₀, X₁, X₂, X₅, X₆) → l9(X₀, X₁, X₂, X₅, X₆)

Analysing control-flow refined program

Found invariant X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___20

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 3 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___6

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 3 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___1

Found invariant X₆ ≤ X₁ ∧ X₁ ≤ X₆ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ for location l6

Found invariant X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2+X₂ ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___17

Found invariant 1 ≤ X₆ ∧ 3 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___11

Found invariant X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___18

Found invariant 1 ≤ X₆ ∧ 3 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___4

Found invariant 1 ≤ X₆ ∧ 2+X₂ ≤ X₆ ∧ 3 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1+X₂ ≤ 0 ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___3

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₂+X₆ ∧ 3 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___9

Found invariant X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___19

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₂+X₆ ∧ 3 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___2

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l6___14

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 3 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___5

Found invariant X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___16

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 3 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___8

Found invariant 1 ≤ X₆ ∧ 3 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___12

Found invariant X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___15

Found invariant 1 ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 3 ≤ X₁+X₆ ∧ 0 ≤ X₀+X₆ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 2 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ 1+X₀ for location n_l6___7

Found invariant 1 ≤ X₆ ∧ 3 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l2___13

Found invariant 1 ≤ X₆ ∧ 2+X₂ ≤ X₆ ∧ 3 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1+X₂ ≤ 0 ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___10

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂₇: 1 {O(1)}
t₂₈: inf {Infinity}
t₂₉: inf {Infinity}
t₃₀: inf {Infinity}
t₃₁: inf {Infinity}
t₃₂: inf {Infinity}
t₃₃: inf {Infinity}
t₃₄: inf {Infinity}
t₃₅: inf {Infinity}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₂₇: 1 {O(1)}
t₂₈: inf {Infinity}
t₂₉: inf {Infinity}
t₃₀: inf {Infinity}
t₃₁: inf {Infinity}
t₃₂: inf {Infinity}
t₃₃: inf {Infinity}
t₃₄: inf {Infinity}
t₃₅: inf {Infinity}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}

Sizebounds

t₂₇, X₀: X₀ {O(n)}
t₂₇, X₁: X₁ {O(n)}
t₂₇, X₂: X₂ {O(n)}
t₂₇, X₅: X₅ {O(n)}
t₂₇, X₆: X₆ {O(n)}
t₂₈, X₅: X₅ {O(n)}
t₂₈, X₆: X₆ {O(n)}
t₂₉, X₅: X₅ {O(n)}
t₂₉, X₆: X₆ {O(n)}
t₃₀, X₂: 0 {O(1)}
t₃₀, X₅: X₅ {O(n)}
t₃₀, X₆: X₆ {O(n)}
t₃₁, X₅: X₅ {O(n)}
t₃₁, X₆: X₆ {O(n)}
t₃₂, X₅: X₅ {O(n)}
t₃₂, X₆: X₆ {O(n)}
t₃₃, X₅: X₅ {O(n)}
t₃₃, X₆: X₆ {O(n)}
t₃₄, X₂: 0 {O(1)}
t₃₄, X₅: X₅ {O(n)}
t₃₄, X₆: X₆ {O(n)}
t₃₅, X₅: X₅ {O(n)}
t₃₅, X₆: X₆ {O(n)}
t₃₆, X₅: 3⋅X₅ {O(n)}
t₃₆, X₆: 3⋅X₆ {O(n)}
t₃₇, X₀: X₅ {O(n)}
t₃₇, X₁: X₆ {O(n)}
t₃₇, X₂: X₂ {O(n)}
t₃₇, X₅: X₅ {O(n)}
t₃₇, X₆: X₆ {O(n)}
t₃₈, X₀: X₅ {O(n)}
t₃₈, X₁: X₆ {O(n)}
t₃₈, X₂: X₂ {O(n)}
t₃₈, X₅: X₅ {O(n)}
t₃₈, X₆: X₆ {O(n)}
t₃₉, X₅: 4⋅X₅ {O(n)}
t₃₉, X₆: 4⋅X₆ {O(n)}