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

Preprocessing

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

Found invariant X₁ ≤ X₀ for location l1

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

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

MPRF for transition t₄: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₀+5 < 0 ∧ 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 of depth 1:

new bound:

X₁+5 {O(n)}

MPRF for transition t₅: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 0 < 5+X₀ ∧ 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 of depth 1:

new bound:

X₁ {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 ∧ 0 ≤ X₀ for location l5

Found invariant X₁ ≤ X₀ for location l1

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

Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l3

MPRF for transition t₅₈: l3(X₀, X₁) -{2}> l3(1+X₀, X₁) :|: 0 < 5+X₀ ∧ 1+X₀ < 0 ∧ 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₁ ≤ 1+X₀ ∧ 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₆₀: l3(X₀, X₁) -{2}> l3(1+X₀, X₁) :|: X₀+5 < 0 ∧ 1+X₀ < 0 ∧ 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₁ ≤ 1+X₀ ∧ 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 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 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 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 0 ≤ 4+X₁ ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ 3+X₀ for location n_l1___9

Found invariant 6+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 11+X₀+X₁ ≤ 0 ∧ 5+X₀ ≤ 0 ∧ 0 ≤ 5+X₀ for location n_l3___3

Found invariant 6+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 11+X₀+X₁ ≤ 0 ∧ 5+X₀ ≤ 0 for location n_l1___10

Found invariant 5+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 10+X₀+X₁ ≤ 0 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 10+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 5+X₀ ≤ 0 ∧ 0 ≤ 5+X₀ for location n_l1___8

Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l3___11

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

Found invariant 6+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 11+X₀+X₁ ≤ 0 ∧ 5+X₀ ≤ 0 ∧ 0 ≤ 5+X₀ for location n_l1___5

Found invariant 2+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 3+X₀+X₁ ≤ 0 ∧ 0 ≤ 4+X₁ ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 3+X₀ for location n_l3___2

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

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

Found invariant 5+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 10+X₀+X₁ ≤ 0 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 10+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 5+X₀ ≤ 0 ∧ 0 ≤ 5+X₀ for location n_l3___1

Found invariant 6+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 11+X₀+X₁ ≤ 0 ∧ 5+X₀ ≤ 0 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 < 0 ∧ 1+X₀ ≤ 0 ∧ 5+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₀ < 0 ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 6+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 11+X₀+X₁ ≤ 0 ∧ 5+X₀ ≤ 0 of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₁₈₂: n_l3___7(X₀, X₁) → n_l1___10(X₀+1, X₁) :|: 5+X₁ ≤ 0 ∧ 5+X₀ < 0 ∧ 1+X₀ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 6+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 11+X₀+X₁ ≤ 0 ∧ 5+X₀ ≤ 0 of depth 1:

new bound:

X₁+5 {O(n)}

MPRF for transition t₁₇₄: n_l1___9(X₀, X₁) → n_l3___2(X₀, X₁) :|: 0 < 5+X₀ ∧ X₀ < 0 ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 0 ≤ 4+X₁ ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ 3+X₀ of depth 1:

new bound:

4 {O(1)}

MPRF for transition t₁₇₉: n_l3___2(X₀, X₁) → n_l1___9(X₀+1, X₁) :|: X₀ < 0 ∧ 0 < 5+X₀ ∧ 0 < 5+X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1+X₀ ≤ 0 ∧ 2+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 3+X₀+X₁ ≤ 0 ∧ 0 ≤ 4+X₁ ∧ 0 ≤ 7+X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 3+X₀ of depth 1:

new bound:

3 {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+5 {O(n)}
t₅: X₁ {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+5 {O(n)}
t₅: X₁ {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: X₁+8 {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 3 {O(1)}
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)}