Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ < 0
t₃: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₆: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀+5 ≤ 0
t₇: l3(X₀, X₁) → l1(X₀, X₁) :|: 5 ≤ X₀
t₅: l3(X₀, X₁) → l5(X₀, X₁) :|: 0 < 5+X₀ ∧ X₀ < 5
t₁₂: l4(X₀, X₁) → l6(X₀, X₁)
t₈: l5(X₀, X₁) → l1(X₀, X₁) :|: X₀ < 0 ∧ 0 < 1+X₀
t₉: l5(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ < 0 ∧ X₀+1 ≤ 0
t₁₀: l5(X₀, X₁) → l1(X₀-1, X₁) :|: 0 ≤ X₀ ∧ 0 < X₀
t₁₁: l5(X₀, X₁) → l1(X₀, X₁) :|: 0 ≤ X₀ ∧ X₀ ≤ 0

Preprocessing

Cut unsatisfiable transition t₈: l5→l1

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l6

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

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ < 0
t₃: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₆: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀+5 ≤ 0
t₇: l3(X₀, X₁) → l1(X₀, X₁) :|: 5 ≤ X₀
t₅: l3(X₀, X₁) → l5(X₀, X₁) :|: 0 < 5+X₀ ∧ X₀ < 5
t₁₂: l4(X₀, X₁) → l6(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₉: l5(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ < 0 ∧ X₀+1 ≤ 0 ∧ X₀ ≤ 4 ∧ 0 ≤ 4+X₀
t₁₀: l5(X₀, X₁) → l1(X₀-1, X₁) :|: 0 ≤ X₀ ∧ 0 < X₀ ∧ X₀ ≤ 4 ∧ 0 ≤ 4+X₀
t₁₁: l5(X₀, X₁) → l1(X₀, X₁) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ 4 ∧ 0 ≤ 4+X₀

Chain transitions t₁₁: l5→l1 and t₄: l1→l4 to t₃₂₉: l5→l4

Chain transitions t₁₀: l5→l1 and t₄: l1→l4 to t₃₃₀: l5→l4

Chain transitions t₁₀: l5→l1 and t₃: l1→l3 to t₃₃₁: l5→l3

Chain transitions t₁₁: l5→l1 and t₃: l1→l3 to t₃₃₂: l5→l3

Chain transitions t₉: l5→l1 and t₃: l1→l3 to t₃₃₃: l5→l3

Chain transitions t₉: l5→l1 and t₄: l1→l4 to t₃₃₄: l5→l4

Chain transitions t₉: l5→l1 and t₂: l1→l3 to t₃₃₅: l5→l3

Chain transitions t₁₀: l5→l1 and t₂: l1→l3 to t₃₃₆: l5→l3

Chain transitions t₁₁: l5→l1 and t₂: l1→l3 to t₃₃₇: l5→l3

Chain transitions t₇: l3→l1 and t₂: l1→l3 to t₃₃₈: l3→l3

Chain transitions t₇: l3→l1 and t₃: l1→l3 to t₃₃₉: l3→l3

Chain transitions t₇: l3→l1 and t₄: l1→l4 to t₃₄₀: l3→l4

Chain transitions t₆: l3→l1 and t₂: l1→l3 to t₃₄₁: l3→l3

Chain transitions t₆: l3→l1 and t₃: l1→l3 to t₃₄₂: l3→l3

Chain transitions t₆: l3→l1 and t₄: l1→l4 to t₃₄₃: l3→l4

Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₃₄₄: l2→l3

Chain transitions t₁: l2→l1 and t₃: l1→l3 to t₃₄₅: l2→l3

Chain transitions t₁: l2→l1 and t₄: l1→l4 to t₃₄₆: l2→l4

Chain transitions t₅: l3→l5 and t₃₃₄: l5→l4 to t₃₄₇: l3→l4

Chain transitions t₅: l3→l5 and t₃₃₀: l5→l4 to t₃₄₈: l3→l4

Chain transitions t₅: l3→l5 and t₃₂₉: l5→l4 to t₃₄₉: l3→l4

Chain transitions t₅: l3→l5 and t₃₃₇: l5→l3 to t₃₅₀: l3→l3

Chain transitions t₅: l3→l5 and t₃₃₆: l5→l3 to t₃₅₁: l3→l3

Chain transitions t₅: l3→l5 and t₃₃₅: l5→l3 to t₃₅₂: l3→l3

Chain transitions t₅: l3→l5 and t₃₃₃: l5→l3 to t₃₅₃: l3→l3

Chain transitions t₅: l3→l5 and t₃₃₂: l5→l3 to t₃₅₄: l3→l3

Chain transitions t₅: l3→l5 and t₃₃₁: l5→l3 to t₃₅₅: l3→l3

Chain transitions t₅: l3→l5 and t₁₁: l5→l1 to t₃₅₆: l3→l1

Chain transitions t₅: l3→l5 and t₁₀: l5→l1 to t₃₅₇: l3→l1

Chain transitions t₅: l3→l5 and t₉: l5→l1 to t₃₅₈: l3→l1

Analysing control-flow refined program

Cut unsatisfiable transition t₃₃₈: l3→l3

Cut unsatisfiable transition t₃₄₀: l3→l4

Cut unsatisfiable transition t₃₄₂: l3→l3

Cut unsatisfiable transition t₃₄₃: l3→l4

Cut unsatisfiable transition t₃₄₉: l3→l4

Cut unsatisfiable transition t₃₅₀: l3→l3

Cut unsatisfiable transition t₃₅₁: l3→l3

Cut unsatisfiable transition t₃₅₃: l3→l3

Cut unsatisfiable transition t₃₅₄: l3→l3

Cut unsatisfiable transition t₃₅₆: l3→l1

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l6

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

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

MPRF for transition t₃₅₂: l3(X₀, X₁) -{3}> l3(1+X₀, X₁) :|: 0 < 5+X₀ ∧ X₀ < 5 ∧ X₀ < 0 ∧ X₀+1 ≤ 0 ∧ 1+X₀ < 0 ∧ X₀ ≤ 4 ∧ 0 ≤ 4+X₀ of depth 1:

new bound:

2⋅X₁ {O(n)}

MPRF for transition t₃₅₅: l3(X₀, X₁) -{3}> l3(X₀-1, X₁) :|: 0 < 5+X₀ ∧ X₀ < 5 ∧ 0 ≤ X₀ ∧ 0 < X₀ ∧ 1 < X₀ ∧ X₀ ≤ 4 ∧ 0 ≤ 4+X₀ of depth 1:

new bound:

2⋅X₁+2 {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 t₇₄₀: n_l1___5→n_l3___4

Cut unsatisfiable transition t₇₈₁: n_l1___14→l4

Cut unsatisfiable transition t₇₈₃: n_l1___8→l4

Cut unreachable locations [n_l3___4; n_l5___2] from the program graph

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_l5___1

Found invariant X₁ ≤ 4 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l6

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_l5___9

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___11

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___15

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___3

Found invariant X₁ ≤ X₀ ∧ 5 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 5 ≤ X₀ for location n_l3___6

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

Found invariant 5+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 10+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 5+X₀ ≤ 0 for location n_l3___12

Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 0 ≤ 4+X₁ ∧ 0 ≤ 8+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 4+X₀ for location n_l5___13

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___5

Found invariant X₁ ≤ 4 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 8 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 4 ∧ 1 ≤ X₀ for location n_l5___7

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

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

Found invariant 5+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 10+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 5+X₀ ≤ 0 for location n_l1___14

Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l3___16

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___10

MPRF for transition t₇₃₉: n_l1___5(X₀, X₁) → n_l3___3(X₀, X₁) :|: 0 < 5+X₀ ∧ 0 ≤ 4+X₀ ∧ X₀ < 5 ∧ X₀ ≤ 4 ∧ 0 < X₀ ∧ 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 t₇₄₈: n_l3___3(X₀, X₁) → n_l5___1(X₀, X₁) :|: X₀ ≤ 4 ∧ 0 < X₀ ∧ 0 < 5+X₀ ∧ X₀ < 5 ∧ 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:

8 {O(1)}

MPRF for transition t₇₅₁: n_l5___1(X₀, X₁) → n_l1___5(X₀-1, X₁) :|: 0 < X₀ ∧ 0 < X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4 ∧ 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 t₇₃₅: n_l1___11(X₀, X₁) → n_l3___10(X₀, X₁) :|: 0 < 5+X₀ ∧ 0 ≤ 4+X₀ ∧ X₀ < 5 ∧ X₀ ≤ 4 ∧ 0 ≤ 3+X₀ ∧ X₀ ≤ 0 ∧ X₀ < 0 ∧ 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 t₇₄₂: n_l3___10(X₀, X₁) → n_l5___9(X₀, X₁) :|: X₀ < 0 ∧ 0 ≤ 3+X₀ ∧ 0 < 5+X₀ ∧ X₀ < 5 ∧ 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)}

MPRF for transition t₇₅₅: n_l5___9(X₀, X₁) → n_l1___11(X₀+1, X₁) :|: X₀ < 0 ∧ 0 ≤ 3+X₀ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 4+X₀ ∧ 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: inf {Infinity}
t₄: 1 {O(1)}
t₅: inf {Infinity}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₉: inf {Infinity}
t₁₀: inf {Infinity}
t₁₁: inf {Infinity}
t₁₂: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: inf {Infinity}
t₄: 1 {O(1)}
t₅: inf {Infinity}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₉: inf {Infinity}
t₁₀: inf {Infinity}
t₁₁: inf {Infinity}
t₁₂: 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+3 {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+3 {O(n)}
t₃, X₁: X₁ {O(n)}
t₄, X₀: 0 {O(1)}
t₄, X₁: 4⋅X₁ {O(n)}
t₅, X₀: 4 {O(1)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: X₁+3 {O(n)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: X₁+3 {O(n)}
t₇, X₁: X₁ {O(n)}
t₉, X₀: 3 {O(1)}
t₉, X₁: X₁ {O(n)}
t₁₀, X₀: 3 {O(1)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: 0 {O(1)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₀: 0 {O(1)}
t₁₂, X₁: 4⋅X₁ {O(n)}