Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₀, X₂, X₃) :|: X₀ < 10
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 10 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ 5
t₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 5 < X₁
t₈: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l3(X₀, X₁+1, X₂, X₃)

Preprocessing

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

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 6 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location l6

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l7

Found invariant X₂ ≤ 5 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 10 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 10 ∧ X₁ ≤ 5 ∧ X₀+X₁ ≤ 10 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 for location l5

Found invariant X₂ ≤ X₀ for location l1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l4

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 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:
t₁₈: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₉: l1(X₀, X₁, X₂) → l3(X₀, X₀, X₂) :|: X₀ < 10 ∧ X₂ ≤ X₀
t₂₀: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 10 ≤ X₀ ∧ X₂ ≤ X₀
t₂₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₂₃: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 5 ∧ X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9
t₂₂: l3(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 5 < X₁ ∧ X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9
t₂₄: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 10 ≤ X₀
t₂₅: l5(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₂ ≤ 5 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 10 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 10 ∧ X₁ ≤ 5 ∧ X₀+X₁ ≤ 10 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5
t₂₆: l6(X₀, X₁, X₂) → l3(X₀, X₁+1, X₂) :|: X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 6 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9

MPRF for transition t₁₉: l1(X₀, X₁, X₂) → l3(X₀, X₀, X₂) :|: X₀ < 10 ∧ X₂ ≤ X₀ of depth 1:

new bound:

X₂+10 {O(n)}

MPRF:

l5 [9-X₀ ]
l1 [10-X₀ ]
l6 [9-X₀ ]
l3 [9-X₀ ]

MPRF for transition t₂₃: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 5 ∧ X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 of depth 1:

new bound:

X₂+10 {O(n)}

MPRF:

l5 [9-X₀ ]
l1 [10-X₀ ]
l6 [10-X₀ ]
l3 [10-X₀ ]

MPRF for transition t₂₅: l5(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₂ ≤ 5 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 10 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 10 ∧ X₁ ≤ 5 ∧ X₀+X₁ ≤ 10 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 of depth 1:

new bound:

X₂+6 {O(n)}

MPRF:

l5 [6-X₀ ]
l1 [6-X₀ ]
l6 [6-X₀ ]
l3 [6-X₀ ]

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 6 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location l6

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l7

Found invariant X₂ ≤ 5 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 10 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 10 ∧ X₁ ≤ 5 ∧ X₀+X₁ ≤ 10 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 for location l5

Found invariant X₂ ≤ X₀ for location l1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l4

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location l3

Analysing control-flow refined program

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 18 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ 6 ≤ X₁ ∧ 12 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 ∧ 6 ≤ X₀ for location n_l6___3

Found invariant X₂ ≤ 9 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 7 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 9 ∧ 6 ≤ X₀ for location n_l6___1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l7

Found invariant X₂ ≤ 5 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 10 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 10 ∧ X₁ ≤ 5 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 10 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 for location l5

Found invariant X₂ ≤ 9 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 7 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 9 ∧ 6 ≤ X₀ for location n_l3___2

Found invariant X₂ ≤ X₀ for location l1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l4

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 18 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location l3

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 18 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ 6 ≤ X₁ ∧ 12 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 ∧ 6 ≤ X₀ for location n_l6___3

Found invariant X₂ ≤ 9 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 7 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 9 ∧ 6 ≤ X₀ for location n_l6___1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l7

Found invariant X₂ ≤ 5 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 10 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 10 ∧ X₁ ≤ 5 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 10 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 for location l5

Found invariant X₂ ≤ 9 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 7 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 9 ∧ 6 ≤ X₀ for location n_l3___2

Found invariant X₂ ≤ X₀ for location l1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l4

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 18 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location l3

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: X₂+10 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₃: X₂+10 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₂+6 {O(n)}
t₂₆: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: X₂+10 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₃: X₂+10 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₂+6 {O(n)}
t₂₆: inf {Infinity}

Sizebounds

t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₉, X₀: 2⋅X₂+6 {O(n)}
t₁₉, X₁: 3⋅X₂+6 {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₂₀, X₀: X₂ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₁, X₀: X₂ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: 2⋅X₂+6 {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₃, X₀: 2⋅X₂+6 {O(n)}
t₂₃, X₁: 3⋅X₂+6 {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₄, X₀: X₂ {O(n)}
t₂₄, X₁: X₁ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₅, X₀: 2⋅X₂+6 {O(n)}
t₂₅, X₁: 3⋅X₂+6 {O(n)}
t₂₅, X₂: X₂ {O(n)}
t₂₆, X₀: 2⋅X₂+6 {O(n)}
t₂₆, X₂: X₂ {O(n)}