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)

MPRF for transition 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 of depth 1:

new bound:

X₂+2 {O(n)}

knowledge_propagation leads to new time bound X₂+3 {O(n)} for transition t₂: l4(X₀, X₁, X₂) → l1(X₀, 0, X₂) :|: 0 ≤ X₀

MPRF for transition t₃: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 2+X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+3⋅X₂ {O(n^2)}

MPRF for transition t₄: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ X₁+1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+3 {O(n)}

MPRF for transition 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 of depth 1:

new bound:

X₂⋅X₂+3⋅X₂ {O(n^2)}

Chain transitions t₂: l4→l1 and t₄: l1→l3 to t₆₃: l4→l3

Chain transitions t₅: l2→l1 and t₄: l1→l3 to t₆₄: l2→l3

Chain transitions t₅: l2→l1 and t₃: l1→l2 to t₆₅: l2→l2

Chain transitions t₂: l4→l1 and t₃: l1→l2 to t₆₆: l4→l2

Chain transitions t₆₃: l4→l3 and t₈: l3→l5 to t₆₇: l4→l5

Chain transitions t₆₄: l2→l3 and t₈: l3→l5 to t₆₈: l2→l5

Chain transitions t₆₄: l2→l3 and t₆: l3→l4 to t₆₉: l2→l4

Chain transitions t₆₃: l4→l3 and t₆: l3→l4 to t₇₀: l4→l4

Analysing control-flow refined program

Cut unsatisfiable transition t₇₀: l4→l4

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 ∧ 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 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

MPRF for transition t₆₉: l2(X₀, X₁, X₂) -{3}> l4(X₀+1, 1+X₁, X₂) :|: X₂ ≤ X₁+2 ∧ X₂ ≤ 2+X₁ ∧ 3+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₀+X₁+1 ∧ 0 ≤ X₀ ∧ X₂ ≤ 2+X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₀+1+X₁ ∧ 0 ≤ X₀ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+2 {O(n)}

knowledge_propagation leads to new time bound X₂+3 {O(n)} for transition t₆₆: l4(X₀, X₁, X₂) -{2}> l2(X₀, 0, X₂) :|: 2 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀

MPRF for transition t₆₅: l2(X₀, X₁, X₂) -{2}> l2(X₀, 1+X₁, X₂) :|: 3+X₁ ≤ X₂ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₀+X₁+1 ∧ 0 ≤ X₀ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+3⋅X₂ {O(n^2)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___2

Found invariant 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___1

Found invariant 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___3

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 X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 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

knowledge_propagation leads to new time bound X₂+3 {O(n)} for transition t₁₃₈: l1(X₀, X₁, X₂) → n_l2___3(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ 2+X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₂+3 {O(n)} for transition t₁₄₀: n_l2___3(X₀, X₁, X₂) → n_l1___2(X₀, X₁+1, X₂) :|: X₁ ≤ 0 ∧ 2 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

MPRF for transition t₁₃₇: n_l1___2(X₀, X₁, X₂) → n_l2___1(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+4⋅X₂+3 {O(n^2)}

MPRF for transition t₁₃₉: n_l2___1(X₀, X₁, X₂) → n_l1___2(X₀, X₁+1, X₂) :|: 1 ≤ X₁ ∧ 2+X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+5⋅X₂+6 {O(n^2)}

MPRF for transition t₁₄₄: n_l1___2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ X₁+1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+4⋅X₂+4 {O(n^2)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:2⋅X₂⋅X₂+9⋅X₂+12 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+3 {O(n)}
t₃: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₄: X₂+3 {O(n)}
t₅: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₆: X₂+2 {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₂⋅X₂+9⋅X₂+12 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+3 {O(n)}
t₃: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₄: X₂+3 {O(n)}
t₅: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₆: X₂+2 {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₂+2 {O(n)}
t₂, X₁: 0 {O(1)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: X₂+2 {O(n)}
t₃, X₁: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₃, X₂: X₂ {O(n)}
t₄, X₀: X₂+2 {O(n)}
t₄, X₁: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₄, X₂: X₂ {O(n)}
t₅, X₀: X₂+2 {O(n)}
t₅, X₁: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₅, X₂: X₂ {O(n)}
t₆, X₀: X₂+2 {O(n)}
t₆, X₁: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₆, X₂: X₂ {O(n)}
t₈, X₀: X₂+2 {O(n)}
t₈, X₁: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₈, X₂: X₂ {O(n)}
t₉, X₀: X₂+2 {O(n)}
t₉, X₁: X₂⋅X₂+3⋅X₂ {O(n^2)}
t₉, X₂: X₂ {O(n)}