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:
t₁₇: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₈: l1(X₀, X₁, X₂) → l3(X₀, X₀, X₂) :|: X₀ < 10 ∧ X₂ ≤ X₀
t₁₉: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 10 ≤ X₀ ∧ X₂ ≤ X₀
t₂₀: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₂₁: 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
t₂₃: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 10 ≤ X₀
t₂₄: 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
t₂₅: 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 t₁₈: l1(X₀, X₁, X₂) → l3(X₀, X₀, X₂) :|: X₀ < 10 ∧ X₂ ≤ X₀ of depth 1:

new bound:

X₂+10 {O(n)}

MPRF for transition t₂₁: 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 for transition t₂₄: 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)}

Chain transitions t₂₄: l5→l1 and t₁₉: l1→l4 to t₅₅: l5→l4

Chain transitions t₂₀: l2→l1 and t₁₉: l1→l4 to t₅₆: l2→l4

Chain transitions t₂₀: l2→l1 and t₁₈: l1→l3 to t₅₇: l2→l3

Chain transitions t₂₄: l5→l1 and t₁₈: l1→l3 to t₅₈: l5→l3

Chain transitions t₂₅: l6→l3 and t₂₂: l3→l6 to t₅₉: l6→l6

Chain transitions t₅₈: l5→l3 and t₂₂: l3→l6 to t₆₀: l5→l6

Chain transitions t₅₈: l5→l3 and t₂₁: l3→l5 to t₆₁: l5→l5

Chain transitions t₂₅: l6→l3 and t₂₁: l3→l5 to t₆₂: l6→l5

Chain transitions t₅₇: l2→l3 and t₂₁: l3→l5 to t₆₃: l2→l5

Chain transitions t₅₇: l2→l3 and t₂₂: l3→l6 to t₆₄: l2→l6

Analysing control-flow refined program

Cut unsatisfiable transition t₅₅: l5→l4

Cut unsatisfiable transition t₆₂: l6→l5

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 6 ≤ X₁ ∧ 12 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 ∧ 6 ≤ X₀ for location l6

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₂ ∧ 20 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 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 ≤ X₀ for location l1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₂ ∧ 20 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 10 ≤ X₀ for location l4

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

MPRF for transition t₆₁: l5(X₀, X₁, X₂) -{3}> l5(1+X₀, 1+X₀, X₂) :|: X₀ < 9 ∧ X₀ ≤ 4 ∧ X₂ ≤ 5 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 10 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 10 ∧ X₁ ≤ 5 ∧ X₀+X₁ ≤ 10 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 9 ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₀ ∧ X₀+X₂ ≤ 17 ∧ 0 ≤ 0 ∧ X₀ ≤ 8 ∧ X₂ ≤ 5 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 10 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 10 ∧ X₁ ≤ 5 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 10 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 of depth 1:

new bound:

X₂+6 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

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

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: X₂+10 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₂+10 {O(n)}
t₂₂: inf {Infinity}
t₂₃: 1 {O(1)}
t₂₄: X₂+6 {O(n)}
t₂₅: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: X₂+10 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₂+10 {O(n)}
t₂₂: inf {Infinity}
t₂₃: 1 {O(1)}
t₂₄: X₂+6 {O(n)}
t₂₅: inf {Infinity}

Sizebounds

t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₈, X₀: 2⋅X₂+6 {O(n)}
t₁₈, X₁: 3⋅X₂+6 {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₉, X₀: X₂ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₂₀, X₀: X₂ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₁, X₀: 2⋅X₂+6 {O(n)}
t₂₁, X₁: 3⋅X₂+6 {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: 2⋅X₂+6 {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₃, X₀: X₂ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₄, X₀: 2⋅X₂+6 {O(n)}
t₂₄, X₁: 3⋅X₂+6 {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₅, X₀: 2⋅X₂+6 {O(n)}
t₂₅, X₂: X₂ {O(n)}