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) :|: 0 < X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 5
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 5 < X₀
t₆: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 5 ∧ 5 ≤ X₀
t₇: l4(X₀, X₁) → l5(X₀, X₁)

Preprocessing

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant X₀ ≤ X₁ for location l1

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ 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) :|: 0 < X₀ ∧ X₀ ≤ X₁
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0 ∧ X₀ ≤ X₁
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 5 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 5 < X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 5 ∧ 5 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₇: l4(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₀ ≤ 0

MPRF for transition t₄: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 5 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 5 < X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+5 {O(n)}

Chain transitions t₆: l3→l1 and t₃: l1→l4 to t₅₈: l3→l4

Chain transitions t₅: l3→l1 and t₃: l1→l4 to t₅₉: l3→l4

Chain transitions t₅: l3→l1 and t₂: l1→l3 to t₆₀: l3→l3

Chain transitions t₆: l3→l1 and t₂: l1→l3 to t₆₁: l3→l3

Chain transitions t₄: l3→l1 and t₂: l1→l3 to t₆₂: l3→l3

Chain transitions t₄: l3→l1 and t₃: l1→l4 to t₆₃: l3→l4

Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₆₄: l2→l3

Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₆₅: l2→l4

Analysing control-flow refined program

Cut unsatisfiable transition t₅₈: l3→l4

Cut unsatisfiable transition t₅₉: l3→l4

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant X₀ ≤ X₁ for location l1

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3

MPRF for transition t₆₀: l3(X₀, X₁) -{2}> l3(X₀-1, X₁) :|: 5 < X₀ ∧ 1 < X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₆₂: l3(X₀, X₁) -{2}> l3(X₀-1, X₁) :|: X₀ < 5 ∧ 1 < X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {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 t₁₉₈: n_l1___4→l4

Cut unsatisfiable transition t₂₀₀: n_l1___8→l4

Cut unsatisfiable transition t₂₀₁: n_l1___9→l4

Found invariant 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 5 ≤ X₀ for location n_l1___9

Found invariant 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ for location n_l1___4

Found invariant 1 ≤ 0 for location n_l3___3

Found invariant 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 5 ≤ X₀ for location n_l3___6

Found invariant X₁ ≤ 4 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 7 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 3 ∧ 0 ≤ X₀ for location n_l1___10

Found invariant X₁ ≤ 5 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 10 ∧ 5 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ for location n_l1___8

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___11

Found invariant X₁ ≤ 4 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant 1 ≤ 0 for location n_l1___5

Found invariant 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ for location n_l3___2

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

Found invariant X₁ ≤ 4 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4

Found invariant X₁ ≤ 5 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 10 ∧ 5 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ for location n_l3___1

Found invariant X₁ ≤ 4 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 7 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 3 ∧ 1 ≤ X₀ for location n_l3___7

Cut unsatisfiable transition t₁₇₅: n_l1___5→n_l3___3

Cut unsatisfiable transition t₁₈₃: n_l3___3→n_l1___5

Cut unsatisfiable transition t₁₈₅: n_l3___6→n_l1___5

Cut unsatisfiable transition t₁₉₉: n_l1___5→l4

Cut unreachable locations [n_l1___5; n_l3___3] from the program graph

MPRF for transition t₁₇₂: n_l1___10(X₀, X₁) → n_l3___7(X₀, X₁) :|: X₀ < 5 ∧ 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ 4 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 7 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 3 ∧ 0 ≤ X₀ of depth 1:

new bound:

4 {O(1)}

MPRF for transition t₁₈₇: n_l3___7(X₀, X₁) → n_l1___10(X₀-1, X₁) :|: X₀ < 5 ∧ 0 < X₀ ∧ X₀ < 5 ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ 4 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 7 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 3 ∧ 1 ≤ X₀ of depth 1:

new bound:

3 {O(1)}

MPRF for transition t₁₇₇: n_l1___9(X₀, X₁) → n_l3___6(X₀, X₁) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ 5 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 5 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₁₈₆: n_l3___6(X₀, X₁) → n_l1___9(X₀-1, X₁) :|: 5 ≤ X₁ ∧ 5 < X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 5 ≤ X₀ of depth 1:

new bound:

X₁+5 {O(n)}

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 {O(n)}
t₅: X₁+5 {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 {O(n)}
t₅: X₁+5 {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: X₁+8 {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+3 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₄, X₀: 3 {O(1)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: X₁+8 {O(n)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: 5 {O(1)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: X₁+3 {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}