Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 10
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: 10 < X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀+2, X₁) :|: 6 < X₀
t₅: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 6
t₆: l4(X₀, X₁) → l5(X₀, X₁)

Preprocessing

Found invariant X₁ ≤ X₀ ∧ 11 ≤ X₀ for location l5

Found invariant X₁ ≤ X₀ for location l1

Found invariant X₁ ≤ X₀ ∧ 11 ≤ X₀ for location l4

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10 for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 10 ∧ X₁ ≤ X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: 10 < X₀ ∧ X₁ ≤ X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀+2, X₁) :|: 6 < X₀ ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10
t₅: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 6 ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10
t₆: l4(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀ ∧ 11 ≤ X₀

Analysing control-flow refined program

Cut unsatisfiable transition t₁₃₆: n_l1___3→l4

Found invariant X₁ ≤ 10 ∧ 2+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 22 ∧ 7 ≤ X₁ ∧ 16 ≤ X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 12 ∧ 9 ≤ X₀ for location n_l1___4

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 10 for location n_l3___5

Found invariant X₁ ≤ 6 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 12 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 6 for location n_l1___3

Found invariant X₁ ≤ X₀ ∧ 7 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ 11 ≤ X₀ for location l5

Found invariant X₁ ≤ 8 ∧ 2+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ 7 ≤ X₁ ∧ 16 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 10 ∧ 9 ≤ X₀ for location n_l3___2

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

Found invariant X₁ ≤ X₀ ∧ 7 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ 11 ≤ X₀ for location l4

Found invariant X₁ ≤ 6 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 12 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 6 for location n_l3___1

Found invariant X₁ ≤ 10 ∧ 2+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 22 ∧ 7 ≤ X₁ ∧ 16 ≤ X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 12 ∧ 9 ≤ X₀ for location n_l1___4

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 10 for location n_l3___5

Found invariant X₁ ≤ 6 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 12 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 6 for location n_l1___3

Found invariant X₁ ≤ X₀ ∧ 7 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ 11 ≤ X₀ for location l5

Found invariant X₁ ≤ 8 ∧ 2+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ 7 ≤ X₁ ∧ 16 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 10 ∧ 9 ≤ X₀ for location n_l3___2

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

Found invariant X₁ ≤ X₀ ∧ 7 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ 11 ≤ X₀ for location l4

Found invariant X₁ ≤ 6 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 12 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 6 for location n_l3___1

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₂₄: n_l1___4(X₀, X₁) → n_l3___2(X₀, X₁) :|: X₁ ≤ X₀ ∧ 6 < X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ 10 ∧ X₁ ≤ 10 ∧ 2+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 22 ∧ 7 ≤ X₁ ∧ 16 ≤ X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 12 ∧ 9 ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₂₇: n_l3___2(X₀, X₁) → n_l1___4(X₀+2, X₁) :|: X₀ ≤ 10 ∧ 6 < X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ 10 ∧ 6 < X₀ ∧ X₁ ≤ 8 ∧ 2+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ 7 ≤ X₁ ∧ 16 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 10 ∧ 9 ≤ X₀

CFR did not improve the program. Rolling back

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₂, X₀: X₁+12 {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+12 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₄, X₀: 12 {O(1)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: X₁+12 {O(n)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: X₁+12 {O(n)}
t₆, X₁: 2⋅X₁ {O(n)}