Initial Problem

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

Preprocessing

Found invariant 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l2

Found invariant X₀ ≤ X₁ for location l6

Found invariant X₀ ≤ X₁ for location l8

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

Found invariant X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀ for location l4

Found invariant 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄+1 ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₄ ∧ X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: F+1 ≤ 0 ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ F ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₈: l2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₉: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄+1) :|: 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁+1, X₂, X₄, X₄) :|: X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀
t₂: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₃) :|: X₁+1 ≤ X₀
t₃: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₁₁: l6(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₁: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₁, X₀, X₃, X₂, X₄)

Analysing control-flow refined program

Found invariant X₀ ≤ X₁ for location l6

Found invariant X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___9

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___6

Found invariant X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l4___12

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___3

Found invariant X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ for location n_l5___2

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l4___5

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l5___4

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___11

Found invariant X₀ ≤ X₁ for location l8

Found invariant X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀ for location n_l1___14

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l2___8

Found invariant X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l1___1

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l2___13

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

Found invariant X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l4___7

Found invariant X₀ ≤ X₁ for location l6

Found invariant X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___9

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___6

Found invariant X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l4___12

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___3

Found invariant X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ for location n_l5___2

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l4___5

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l5___4

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___11

Found invariant X₀ ≤ X₁ for location l8

Found invariant X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀ for location n_l1___14

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l2___8

Found invariant X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l1___1

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l2___13

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

Found invariant X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l4___7

Found invariant X₀ ≤ X₁ for location l6

Found invariant X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___9

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___6

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l4___12

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___3

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ for location n_l5___2

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l4___5

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l5___4

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___11

Found invariant X₀ ≤ X₁ for location l8

Found invariant X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ 1+X₁ ≤ X₀ for location n_l1___14

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l2___8

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l1___1

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l2___13

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

Found invariant X₄ ≤ X₂ ∧ 1+X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l4___7

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₄: inf {Infinity}
t₅: inf {Infinity}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₈: inf {Infinity}
t₉: inf {Infinity}
t₁₀: inf {Infinity}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₄: inf {Infinity}
t₅: inf {Infinity}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₈: inf {Infinity}
t₉: inf {Infinity}
t₁₀: inf {Infinity}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁: 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)}
t₄, X₀: X₁ {O(n)}
t₄, X₂: X₃ {O(n)}
t₅, X₀: X₁ {O(n)}
t₅, X₂: X₃ {O(n)}
t₆, X₀: X₁ {O(n)}
t₆, X₂: X₃ {O(n)}
t₇, X₀: X₁ {O(n)}
t₇, X₂: X₃ {O(n)}
t₈, X₀: X₁ {O(n)}
t₈, X₂: X₃ {O(n)}
t₉, X₀: X₁ {O(n)}
t₉, X₂: X₃ {O(n)}
t₁₀, X₀: X₁ {O(n)}
t₁₀, X₂: X₃ {O(n)}
t₂, X₀: X₁ {O(n)}
t₂, X₂: X₃ {O(n)}
t₃, X₀: 2⋅X₁ {O(n)}
t₃, X₂: 2⋅X₃ {O(n)}
t₁₁, X₀: 2⋅X₁ {O(n)}
t₁₁, X₂: 2⋅X₃ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₃ {O(n)}
t₁, X₃: X₂ {O(n)}
t₁, X₄: X₄ {O(n)}