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 ≤ 5+X₀ ∧ X₀ ≤ 5
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀+5 < 0
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: 5 < X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₅: l3(X₀, X₁) → l1(X₀, X₁) :|: 0 < X₀ ∧ X₀ < 1
t₆: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 0 < X₀ ∧ 1 ≤ X₀
t₇: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 0 ∧ X₀ < 0
t₈: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₉: l4(X₀, X₁) → l5(X₀, X₁)

Preprocessing

Cut unsatisfiable transition t₅: l3→l1

Found invariant X₀ ≤ 5 ∧ 0 ≤ 5+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 ≤ 5+X₀ ∧ X₀ ≤ 5
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀+5 < 0
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: 5 < X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₆: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 5 ∧ 0 ≤ 5+X₀
t₇: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 0 ∧ X₀ < 0 ∧ X₀ ≤ 5 ∧ 0 ≤ 5+X₀
t₈: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 5 ∧ 0 ≤ 5+X₀
t₉: l4(X₀, X₁) → l5(X₀, X₁)

Chain transitions t₈: l3→l1 and t₄: l1→l4 to t₉₃: l3→l4

Chain transitions t₇: l3→l1 and t₄: l1→l4 to t₉₄: l3→l4

Chain transitions t₇: l3→l1 and t₃: l1→l4 to t₉₅: l3→l4

Chain transitions t₈: l3→l1 and t₃: l1→l4 to t₉₆: l3→l4

Chain transitions t₆: l3→l1 and t₃: l1→l4 to t₉₇: l3→l4

Chain transitions t₆: l3→l1 and t₄: l1→l4 to t₉₈: l3→l4

Chain transitions t₆: l3→l1 and t₂: l1→l3 to t₉₉: l3→l3

Chain transitions t₇: l3→l1 and t₂: l1→l3 to t₁₀₀: l3→l3

Chain transitions t₈: l3→l1 and t₂: l1→l3 to t₁₀₁: l3→l3

Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₁₀₂: l2→l3

Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₁₀₃: l2→l4

Chain transitions t₁: l2→l1 and t₄: l1→l4 to t₁₀₄: l2→l4

Analysing control-flow refined program

Cut unsatisfiable transition t₉₃: l3→l4

Cut unsatisfiable transition t₉₄: l3→l4

Cut unsatisfiable transition t₉₅: l3→l4

Cut unsatisfiable transition t₉₆: l3→l4

Cut unsatisfiable transition t₉₇: l3→l4

Cut unsatisfiable transition t₉₈: l3→l4

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

Found invariant X₁ ≤ 5+X₀ ∧ X₀ ≤ 5+X₁ for location l1

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

Found invariant X₁ ≤ 5 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 10 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 10+X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 5 ∧ 0 ≤ 5+X₀ for location l3

MPRF for transition t₉₉: l3(X₀, X₁) -{2}> l3(X₀-1, X₁) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ 4+X₀ ∧ X₀ ≤ 6 ∧ X₀ ≤ 5 ∧ 0 ≤ 5+X₀ ∧ X₁ ≤ 5 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 10 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 10+X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 5 ∧ 0 ≤ 5+X₀ of depth 1:

new bound:

11 {O(1)}

MPRF for transition t₁₀₀: l3(X₀, X₁) -{2}> l3(1+X₀, X₁) :|: X₀ ≤ 0 ∧ X₀ < 0 ∧ 0 ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 5 ∧ 0 ≤ 5+X₀ ∧ X₁ ≤ 5 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 10 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 10+X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 5 ∧ 0 ≤ 5+X₀ of depth 1:

new bound:

6 {O(1)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___6

Found invariant 0 ≤ 5+X₁ ∧ 0 ≤ 5+X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___4

Found invariant 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 9+X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ 4+X₀ for location n_l1___7

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

Found invariant X₁ ≤ 5 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 9 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 4 ∧ 0 ≤ X₀ for location n_l3___5

Found invariant X₁ ≤ 5 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 9 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 4 ∧ 0 ≤ X₀ for location n_l1___8

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

Found invariant 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 9+X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ 4+X₀ for location n_l3___2

Found invariant X₁ ≤ 5 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 10 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 10+X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 0 ≤ 5+X₀ for location n_l3___9

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

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

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

Cut unsatisfiable transition t₂₃₆: n_l3___2→n_l1___8

MPRF for transition t₂₃₁: n_l1___7(X₀, X₁) → n_l3___2(X₀, X₁) :|: X₀ ≤ 5 ∧ 0 ≤ 5+X₀ ∧ 0 ≤ 5+X₀ ∧ X₀ ≤ 5 ∧ 0 ≤ 5+X₀ ∧ X₀ ≤ 5 ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 9+X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ 4+X₀ of depth 1:

new bound:

5 {O(1)}

MPRF for transition t₂₃₅: n_l3___2(X₀, X₁) → n_l1___7(X₀+1, X₁) :|: X₀ < 0 ∧ X₀ ≤ 5 ∧ 0 ≤ 5+X₀ ∧ 0 ≤ 5+X₀ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 9+X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ 4+X₀ of depth 1:

new bound:

5 {O(1)}

MPRF for transition t₂₃₂: n_l1___8(X₀, X₁) → n_l3___5(X₀, X₁) :|: X₀ ≤ 5 ∧ 0 ≤ 5+X₀ ∧ 0 ≤ 5+X₀ ∧ X₀ ≤ 5 ∧ 0 ≤ X₀ ∧ X₀ ≤ 4 ∧ 0 ≤ 5+X₀ ∧ X₀ ≤ 5 ∧ X₁ ≤ 5 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 9 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 4 ∧ 0 ≤ X₀ of depth 1:

new bound:

5 {O(1)}

MPRF for transition t₂₃₉: n_l3___5(X₀, X₁) → n_l1___8(X₀-1, X₁) :|: X₀ ≤ 4 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 5 ∧ X₁ ≤ 5 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 9 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 4 ∧ 0 ≤ X₀ of depth 1:

new bound:

5 {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: 1 {O(1)}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₈: inf {Infinity}
t₉: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₈: inf {Infinity}
t₉: 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: 5 {O(1)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁ {O(n)}
t₃, X₁: X₁ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₆, X₀: 4 {O(1)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: 4 {O(1)}
t₇, X₁: X₁ {O(n)}
t₈, X₀: 0 {O(1)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: 2⋅X₁ {O(n)}
t₉, X₁: 2⋅X₁ {O(n)}