Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 2+X₁ ≤ X₂
t₄: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ X₁+1
t₅: l2(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂)
t₆: l3(X₀, X₁, X₂) → l4(X₀+1, X₁, X₂) :|: X₂ ≤ X₁+1 ∧ 3+X₀ ≤ X₂
t₇: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 2+X₁ ≤ X₂
t₈: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ X₀+2
t₂: l4(X₀, X₁, X₂) → l1(X₀, 0, X₂)
t₉: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₁: l6(X₀, X₁, X₂) → l4(0, X₁, X₂)

Preprocessing

Cut unsatisfiable transition t₇: l3→l5

Found invariant 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2

Found invariant X₂ ≤ 1+X₁ ∧ X₂ ≤ 2+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l7

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

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 0 ≤ X₀ for location l4

Found invariant X₂ ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 2+X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₄: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ X₁+1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₅: l2(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₆: l3(X₀, X₁, X₂) → l4(X₀+1, X₁, X₂) :|: X₂ ≤ X₁+1 ∧ 3+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₈: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ X₀+2 ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂: l4(X₀, X₁, X₂) → l1(X₀, 0, X₂) :|: 0 ≤ X₀
t₉: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ 1+X₁ ∧ X₂ ≤ 2+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁: l6(X₀, X₁, X₂) → l4(0, X₁, X₂)

Analysing control-flow refined program

Found invariant 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___7

Found invariant X₂ ≤ 1+X₁ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___2

Found invariant X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l3___3

Found invariant X₂ ≤ 1 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 1 ∧ X₂ ≤ 1+X₀ ∧ X₀+X₂ ≤ 1 ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l3___6

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___8

Found invariant X₂ ≤ 1+X₁ ∧ X₂ ≤ 2+X₀ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l7

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

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___5

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4

Found invariant 3 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___1

Found invariant 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___4

CFR did not improve the program. Rolling back

All Bounds

Timebounds

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

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₃: inf {Infinity}
t₄: inf {Infinity}
t₅: inf {Infinity}
t₆: inf {Infinity}
t₈: 1 {O(1)}
t₂: inf {Infinity}
t₉: 1 {O(1)}
t₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₃, X₂: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₅, X₂: X₂ {O(n)}
t₆, X₂: X₂ {O(n)}
t₈, X₂: X₂ {O(n)}
t₂, X₁: 0 {O(1)}
t₂, X₂: X₂ {O(n)}
t₉, X₂: X₂ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}