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+1, X₁) :|: X₀ < 3
t₅: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 3 < X₀
t₆: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 3 ∧ 3 ≤ X₀
t₇: l4(X₀, X₁) → l5(X₀, X₁)

Preprocessing

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₀ for location l5

Found invariant X₁ ≤ X₀ for location l1

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₀ for location l4

Found invariant X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9 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+1, X₁) :|: X₀ < 3 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9
t₅: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 3 < X₀ ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9
t₆: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9
t₇: l4(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀ ∧ 10 ≤ X₀

MPRF for transition t₄: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ < 3 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9 of depth 1:

new bound:

X₁+10 {O(n)}

MPRF for transition t₅: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 3 < X₀ ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9 of depth 1:

new bound:

X₁+10 {O(n)}

Chain transitions t₆: l3→l1 and t₃: l1→l4 to t₅₆: l3→l4

Chain transitions t₅: l3→l1 and t₃: l1→l4 to t₅₇: l3→l4

Chain transitions t₅: l3→l1 and t₂: l1→l3 to t₅₈: l3→l3

Chain transitions t₆: l3→l1 and t₂: l1→l3 to t₅₉: l3→l3

Chain transitions t₄: l3→l1 and t₂: l1→l3 to t₆₀: l3→l3

Chain transitions t₄: l3→l1 and t₃: l1→l4 to t₆₁: l3→l4

Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₆₂: l2→l3

Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₆₃: l2→l4

Analysing control-flow refined program

Cut unsatisfiable transition t₅₆: l3→l4

Cut unsatisfiable transition t₆₁: l3→l4

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₀ for location l5

Found invariant X₁ ≤ X₀ for location l1

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₀ for location l4

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

MPRF for transition t₅₈: l3(X₀, X₁) -{2}> l3(1+X₀, X₁) :|: 3 < X₀ ∧ X₀ < 9 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9 ∧ X₁ ≤ 1+X₀ ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9 of depth 1:

new bound:

X₁+10 {O(n)}

MPRF for transition t₆₀: l3(X₀, X₁) -{2}> l3(1+X₀, X₁) :|: X₀ < 3 ∧ X₀ < 9 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9 ∧ X₁ ≤ 1+X₀ ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9 of depth 1:

new bound:

X₁+10 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Cut unsatisfiable transition t₁₉₄: n_l1___10→l4

Cut unsatisfiable transition t₁₉₅: n_l1___5→l4

Cut unsatisfiable transition t₁₉₇: n_l1___8→l4

Found invariant 1 ≤ 0 for location n_l1___6

Found invariant 1 ≤ 0 for location n_l3___4

Found invariant X₁ ≤ 9 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 19 ∧ 4 ≤ X₁ ∧ 9 ≤ X₀+X₁ ∧ X₀ ≤ 6+X₁ ∧ X₀ ≤ 10 ∧ 5 ≤ X₀ for location n_l1___9

Found invariant X₁ ≤ 2 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 5 ∧ X₀ ≤ 3 ∧ 3 ≤ X₀ for location n_l3___3

Found invariant X₁ ≤ 2 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 5 ∧ X₀ ≤ 3 for location n_l1___10

Found invariant X₁ ≤ 3 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 6 ∧ 3 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 3 ∧ 3 ≤ X₀ for location n_l1___8

Found invariant X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location n_l3___11

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₀ for location l5

Found invariant X₁ ≤ 2 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 5 ∧ X₀ ≤ 3 ∧ 3 ≤ X₀ for location n_l1___5

Found invariant X₁ ≤ 8 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 17 ∧ 4 ≤ X₁ ∧ 9 ≤ X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 9 ∧ 5 ≤ X₀ for location n_l3___2

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

Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₀ for location l4

Found invariant X₁ ≤ 3 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 6 ∧ 3 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 3 ∧ 3 ≤ X₀ for location n_l3___1

Found invariant X₁ ≤ 2 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 5 ∧ X₀ ≤ 3 for location n_l3___7

Cut unsatisfiable transition t₁₇₂: n_l1___6→n_l3___4

Cut unsatisfiable transition t₁₈₁: n_l3___4→n_l1___6

Cut unsatisfiable transition t₁₈₄: n_l3___7→n_l1___6

Cut unsatisfiable transition t₁₉₆: n_l1___6→l4

Cut unreachable locations [n_l1___6; n_l3___4] from the program graph

MPRF for transition t₁₆₉: n_l1___10(X₀, X₁) → n_l3___7(X₀, X₁) :|: X₀ < 10 ∧ X₀ ≤ 9 ∧ X₁ ≤ 3 ∧ X₀ ≤ 9 ∧ X₀ < 10 ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 2 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 5 ∧ X₀ ≤ 3 of depth 1:

new bound:

X₁+11 {O(n)}

MPRF for transition t₁₈₂: n_l3___7(X₀, X₁) → n_l1___10(X₀+1, X₁) :|: X₁ ≤ 3 ∧ X₀ < 3 ∧ X₀ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 2 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 5 ∧ X₀ ≤ 3 of depth 1:

new bound:

X₁+5 {O(n)}

MPRF for transition t₁₇₄: n_l1___9(X₀, X₁) → n_l3___2(X₀, X₁) :|: 3 < X₀ ∧ X₀ < 10 ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 9 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 19 ∧ 4 ≤ X₁ ∧ 9 ≤ X₀+X₁ ∧ X₀ ≤ 6+X₁ ∧ X₀ ≤ 10 ∧ 5 ≤ X₀ of depth 1:

new bound:

20 {O(1)}

MPRF for transition t₁₇₉: n_l3___2(X₀, X₁) → n_l1___9(X₀+1, X₁) :|: X₀ < 10 ∧ 3 < X₀ ∧ 3 < X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ 9 ∧ X₁ ≤ 8 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 17 ∧ 4 ≤ X₁ ∧ 9 ≤ X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 9 ∧ 5 ≤ X₀ of depth 1:

new bound:

20 {O(1)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: X₁+10 {O(n)}
t₅: X₁+10 {O(n)}
t₆: inf {Infinity}
t₇: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: X₁+10 {O(n)}
t₅: X₁+10 {O(n)}
t₆: inf {Infinity}
t₇: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: 2⋅X₁+23 {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+10 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₄, X₀: 2⋅X₁+23 {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 10 {O(1)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: 3 {O(1)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: X₁+10 {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}