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)
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ < 0
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₃
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0 ∧ 0 ≤ X₃
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆)
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀+1, X₁+X₀+1, X₂, X₃, X₄, X₅, X₆)
t₁₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀-X₂, X₁+(X₂)², X₂-1, X₃, X₄, X₅, X₆)
t₂: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ X₀
t₃: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ < X₁
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₄, X₅, X₆, X₃, X₄, X₅, X₆)
t₁₂: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Found invariant X₂ ≤ X₆ ∧ X₁ ≤ X₀ for location l2

Found invariant X₂ ≤ X₆ for location l6

Found invariant X₂ ≤ X₆ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ for location l5

Found invariant X₂ ≤ X₆ ∧ 1+X₀ ≤ X₁ for location l8

Found invariant X₂ ≤ X₆ ∧ X₁ ≤ X₀ for location l1

Found invariant X₂ ≤ X₆ ∧ X₁ ≤ X₀ for location l4

Found invariant X₂ ≤ X₆ ∧ 1+X₀ ≤ X₁ for location l9

Found invariant X₂ ≤ X₆ ∧ X₁ ≤ X₀ for location l3

Problem after Preprocessing

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)
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ < 0 ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₀
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₃ ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₀
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₀
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ X₁ ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ X₁ ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀+1, X₁+X₀+1, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ X₁ ≤ X₀
t₁₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀-X₂, X₁+(X₂)², X₂-1, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀
t₂: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ X₀ ∧ X₂ ≤ X₆
t₃: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ < X₁ ∧ X₂ ≤ X₆
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₄, X₅, X₆, X₃, X₄, X₅, X₆)
t₁₂: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ 1+X₀ ≤ X₁

Chain transitions t₆: l3→l1 and t₉: l1→l5 to t₁₅₄: l3→l5

Chain transitions t₆: l3→l1 and t₈: l1→l4 to t₁₅₅: l3→l4

Chain transitions t₆: l3→l1 and t₇: l1→l4 to t₁₅₆: l3→l4

Chain transitions t₂: l6→l2 and t₄: l2→l3 to t₁₅₇: l6→l3

Chain transitions t₁₅₇: l6→l3 and t₁₅₄: l3→l5 to t₁₅₈: l6→l5

Chain transitions t₁₅₇: l6→l3 and t₁₅₆: l3→l4 to t₁₅₉: l6→l4

Chain transitions t₁₅₇: l6→l3 and t₁₅₅: l3→l4 to t₁₆₀: l6→l4

Chain transitions t₁₅₇: l6→l3 and t₆: l3→l1 to t₁₆₁: l6→l1

Chain transitions t₁₆₀: l6→l4 and t₁₀: l4→l6 to t₁₆₂: l6→l6

Chain transitions t₁₅₉: l6→l4 and t₁₀: l4→l6 to t₁₆₃: l6→l6

Chain transitions t₁₅₈: l6→l5 and t₁₁: l5→l6 to t₁₆₄: l6→l6

Analysing control-flow refined program

Eliminate variables {Temp_Int₁₀₃₄,X₃} that do not contribute to the problem

Found invariant X₂ ≤ X₅ ∧ X₁ ≤ X₀ for location l2

Found invariant X₂ ≤ X₅ for location l6

Found invariant X₂ ≤ X₅ ∧ X₁ ≤ X₀ for location l5

Found invariant X₂ ≤ X₅ ∧ 1+X₀ ≤ X₁ for location l8

Found invariant X₂ ≤ X₅ ∧ X₁ ≤ X₀ for location l1

Found invariant X₂ ≤ X₅ ∧ X₁ ≤ X₀ for location l4

Found invariant X₂ ≤ X₅ ∧ 1+X₀ ≤ X₁ for location l9

Found invariant X₂ ≤ X₅ ∧ X₁ ≤ 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 X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ for location n_l2___20

Found invariant 1+X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ for location n_l2___6

Found invariant 1+X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ for location n_l5___1

Found invariant X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₄ for location l6

Found invariant X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ 0 ∧ X₁ ≤ X₀ for location n_l4___17

Found invariant X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₁ ≤ X₀ for location n_l1___11

Found invariant X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ for location n_l1___18

Found invariant 1+X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₁ ≤ X₀ for location n_l1___4

Found invariant 1+X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1+X₃ ≤ 0 ∧ X₁ ≤ X₀ for location n_l4___3

Found invariant X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₁ ≤ X₀ for location n_l4___9

Found invariant X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ for location n_l3___19

Found invariant 1+X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₁ ≤ X₀ for location n_l4___2

Found invariant X₂ ≤ X₆ ∧ X₅ ≤ X₄ for location n_l6___14

Found invariant 1+X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ for location n_l3___5

Found invariant X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₁ ≤ X₀ for location n_l4___16

Found invariant X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ for location n_l5___8

Found invariant X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₁ ≤ X₀ for location n_l3___12

Found invariant X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ for location n_l5___15

Found invariant X₂ ≤ X₆ ∧ 1+X₀ ≤ X₁ for location l8

Found invariant 1+X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location n_l6___7

Found invariant X₂ ≤ X₆ ∧ 1+X₀ ≤ X₁ for location l9

Found invariant X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₁ ≤ X₀ for location n_l2___13

Found invariant X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 1+X₃ ≤ 0 ∧ X₁ ≤ X₀ for location n_l4___10

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: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₈: inf {Infinity}
t₉: inf {Infinity}
t₁₀: inf {Infinity}
t₁₁: inf {Infinity}
t₁₂: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₈: inf {Infinity}
t₉: inf {Infinity}
t₁₀: inf {Infinity}
t₁₁: inf {Infinity}
t₁₂: 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)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₅ {O(n)}
t₁, X₂: X₆ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₃, X₄: 3⋅X₄ {O(n)}
t₃, X₅: 3⋅X₅ {O(n)}
t₃, X₆: 3⋅X₆ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₇, X₆: X₆ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₉, X₃: 0 {O(1)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₅ {O(n)}
t₉, X₆: X₆ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₆ {O(n)}
t₁₁, X₃: 0 {O(1)}
t₁₁, X₄: X₄ {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₁, X₆: X₆ {O(n)}
t₁₂, X₄: 3⋅X₄ {O(n)}
t₁₂, X₅: 3⋅X₅ {O(n)}
t₁₂, X₆: 3⋅X₆ {O(n)}