Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₂, X₃, X₄) :|: 1 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₁, X₂, X₃, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1 < X₁
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1
t₁₄: l4(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄)
t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₁, X₂, X₃, X₄) :|: X₀ ≤ 2⋅X₂
t₁₀: l5(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: 2⋅X₂ < X₀
t₁₃: l6(X₀, X₁, X₂, X₃, X₄) → l1(3⋅X₀+1, X₁, X₂, X₃, X₄)
t₆: l7(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁-2, X₂, X₃, X₄)
t₇: l8(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₁, X₃, X₄) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₈: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₁ < 0
t₉: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₁
t₁₂: l9(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂+1, X₃, X₄)

Preprocessing

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

Found invariant X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l7

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

Found invariant X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l8

Found invariant X₀ ≤ 1 for location l10

Found invariant X₀ ≤ 1 for location l4

Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l9

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l3

Cut unsatisfiable transition t₄₂: l8→l6

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₃₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃₁: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₀, X₂, X₃) :|: 1 < X₀
t₃₂: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1
t₃₃: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃)
t₃₄: l3(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1 < X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₅: l3(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₆: l4(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1
t₃₈: l5(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃) :|: X₀ ≤ 2⋅X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₇: l5(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: 2⋅X₂ < X₀ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₉: l6(X₀, X₁, X₂, X₃) → l1(3⋅X₀+1, X₁, X₂, X₃) :|: X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₄₀: l7(X₀, X₁, X₂, X₃) → l3(X₀, X₁-2, X₂, X₃) :|: X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₄₁: l8(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₁, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₄₃: l8(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₄₄: l9(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂+1, X₃) :|: 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀

Analysing control-flow refined program

Cut unsatisfiable transition t₇₀₄: n_l1___3→l4

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l5___9

Found invariant 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l9___4

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l9___7

Found invariant X₁ ≤ 1 ∧ 9+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 10 ≤ X₀ for location n_l1___3

Found invariant 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l5___6

Found invariant 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___12

Found invariant X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l3___14

Found invariant X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l7___13

Found invariant 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_l1___5

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 10 ≤ X₀ for location n_l3___2

Found invariant X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l6___8

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l1

Found invariant X₀ ≤ 1 for location l10

Found invariant X₀ ≤ 1 for location l4

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 10 ≤ X₀ for location n_l7___1

Found invariant 2+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location n_l7___11

Found invariant X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l8___10

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₃₀: 1 {O(1)}
t₃₁: inf {Infinity}
t₃₂: 1 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: inf {Infinity}
t₃₅: inf {Infinity}
t₃₆: 1 {O(1)}
t₃₇: inf {Infinity}
t₃₈: inf {Infinity}
t₃₉: inf {Infinity}
t₄₀: inf {Infinity}
t₄₁: inf {Infinity}
t₄₃: inf {Infinity}
t₄₄: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₃₀: 1 {O(1)}
t₃₁: inf {Infinity}
t₃₂: 1 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: inf {Infinity}
t₃₅: inf {Infinity}
t₃₆: 1 {O(1)}
t₃₇: inf {Infinity}
t₃₈: inf {Infinity}
t₃₉: inf {Infinity}
t₄₀: inf {Infinity}
t₄₁: inf {Infinity}
t₄₃: inf {Infinity}
t₄₄: inf {Infinity}

Sizebounds

t₃₀, X₀: X₀ {O(n)}
t₃₀, X₁: X₁ {O(n)}
t₃₀, X₂: X₂ {O(n)}
t₃₀, X₃: X₃ {O(n)}
t₃₁, X₃: X₃ {O(n)}
t₃₂, X₁: X₁ {O(n)}
t₃₂, X₃: 2⋅X₃ {O(n)}
t₃₃, X₀: X₃ {O(n)}
t₃₃, X₁: X₁ {O(n)}
t₃₃, X₂: X₂ {O(n)}
t₃₃, X₃: X₃ {O(n)}
t₃₄, X₃: X₃ {O(n)}
t₃₅, X₁: 1 {O(1)}
t₃₅, X₃: X₃ {O(n)}
t₃₆, X₁: X₁ {O(n)}
t₃₆, X₃: 2⋅X₃ {O(n)}
t₃₇, X₁: 0 {O(1)}
t₃₇, X₃: X₃ {O(n)}
t₃₈, X₁: 0 {O(1)}
t₃₈, X₃: X₃ {O(n)}
t₃₉, X₁: 1 {O(1)}
t₃₉, X₃: X₃ {O(n)}
t₄₀, X₃: X₃ {O(n)}
t₄₁, X₁: 0 {O(1)}
t₄₁, X₂: 0 {O(1)}
t₄₁, X₃: X₃ {O(n)}
t₄₃, X₁: 1 {O(1)}
t₄₃, X₃: X₃ {O(n)}
t₄₄, X₁: 0 {O(1)}
t₄₄, X₃: X₃ {O(n)}