Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 3 ≤ X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ < 3
t₁: l2(X₀, X₁) → l1(3, X₁)
t₄: l3(X₀, X₁) → l5(X₀, X₁) :|: 5 < X₀
t₅: l3(X₀, X₁) → l6(X₀, X₁) :|: X₀ ≤ 5
t₉: l4(X₀, X₁) → l7(X₀, X₁)
t₆: l5(X₀, X₁) → l1(X₀+3, X₁)
t₇: l6(X₀, X₁) → l1(X₀-2, X₁) :|: 10 < X₀
t₈: l6(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 10
Preprocessing
Cut unsatisfiable transition t₇: l6→l1
Eliminate variables {X₁} that do not contribute to the problem
Found invariant X₀ ≤ 5 ∧ 3 ≤ X₀ for location l6
Found invariant 1 ≤ 0 for location l7
Found invariant 6 ≤ X₀ for location l5
Found invariant 3 ≤ X₀ for location l1
Found invariant 1 ≤ 0 for location l4
Found invariant 3 ≤ X₀ for location l3
Cut unsatisfiable transition t₂₁: l1→l4
Cut unsatisfiable transition t₂₅: l4→l7
Cut unreachable locations [l4; l7] from the program graph
Problem after Preprocessing
Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2, l3, l5, l6
Transitions:
t₁₉: l0(X₀) → l2(X₀)
t₂₀: l1(X₀) → l3(X₀) :|: 3 ≤ X₀ ∧ 3 ≤ X₀
t₂₂: l2(X₀) → l1(3)
t₂₃: l3(X₀) → l5(X₀) :|: 5 < X₀ ∧ 3 ≤ X₀
t₂₄: l3(X₀) → l6(X₀) :|: X₀ ≤ 5 ∧ 3 ≤ X₀
t₂₆: l5(X₀) → l1(X₀+3) :|: 6 ≤ X₀
t₂₇: l6(X₀) → l1(X₀+1) :|: X₀ ≤ 10 ∧ X₀ ≤ 5 ∧ 3 ≤ X₀
MPRF for transition t₂₄: l3(X₀) → l6(X₀) :|: X₀ ≤ 5 ∧ 3 ≤ X₀ of depth 1:
new bound:
9 {O(1)}
MPRF for transition t₂₇: l6(X₀) → l1(X₀+1) :|: X₀ ≤ 10 ∧ X₀ ≤ 5 ∧ 3 ≤ X₀ of depth 1:
new bound:
9 {O(1)}
Chain transitions t₂₇: l6→l1 and t₂₀: l1→l3 to t₆₄: l6→l3
Chain transitions t₂₆: l5→l1 and t₂₀: l1→l3 to t₆₅: l5→l3
Chain transitions t₂₂: l2→l1 and t₂₀: l1→l3 to t₆₆: l2→l3
Chain transitions t₆₄: l6→l3 and t₂₄: l3→l6 to t₆₇: l6→l6
Chain transitions t₆₅: l5→l3 and t₂₄: l3→l6 to t₆₈: l5→l6
Chain transitions t₆₅: l5→l3 and t₂₃: l3→l5 to t₆₉: l5→l5
Chain transitions t₆₄: l6→l3 and t₂₃: l3→l5 to t₇₀: l6→l5
Chain transitions t₆₆: l2→l3 and t₂₃: l3→l5 to t₇₁: l2→l5
Chain transitions t₆₆: l2→l3 and t₂₄: l3→l6 to t₇₂: l2→l6
Analysing control-flow refined program
Cut unsatisfiable transition t₆₈: l5→l6
Cut unsatisfiable transition t₇₁: l2→l5
Found invariant X₀ ≤ 5 ∧ 3 ≤ X₀ for location l6
Found invariant 6 ≤ X₀ for location l5
Found invariant 3 ≤ X₀ for location l1
Found invariant 3 ≤ X₀ for location l3
MPRF for transition t₆₇: l6(X₀) -{3}> l6(1+X₀) :|: X₀ ≤ 10 ∧ 2 ≤ X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 5 ∧ 3 ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₀ ≤ 5 ∧ 3 ≤ X₀ of depth 1:
new bound:
9 {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 X₀ ≤ 6 ∧ 5 ≤ X₀ for location n_l1___6
Found invariant 9 ≤ X₀ for location n_l5___1
Found invariant X₀ ≤ 4 ∧ 4 ≤ X₀ for location n_l1___9
Found invariant X₀ ≤ 3 ∧ 3 ≤ X₀ for location n_l6___10
Found invariant X₀ ≤ 6 ∧ 5 ≤ X₀ for location n_l3___5
Found invariant 9 ≤ X₀ for location n_l1___3
Found invariant X₀ ≤ 6 ∧ 6 ≤ X₀ for location n_l5___4
Found invariant X₀ ≤ 3 ∧ 3 ≤ X₀ for location n_l3___11
Found invariant X₀ ≤ 4 ∧ 4 ≤ X₀ for location n_l3___8
Found invariant 9 ≤ X₀ for location n_l3___2
Found invariant X₀ ≤ 5 ∧ 4 ≤ X₀ for location n_l6___7
Found invariant X₀ ≤ 3 ∧ 3 ≤ X₀ for location l1
MPRF for transition t₁₄₅: n_l1___6(X₀) → n_l3___5(X₀) :|: 4 ≤ X₀ ∧ X₀ ≤ 6 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀ ∧ 3 ≤ X₀ ∧ X₀ ≤ 6 ∧ 5 ≤ X₀ of depth 1:
new bound:
10 {O(1)}
MPRF for transition t₁₅₀: n_l3___5(X₀) → n_l6___7(X₀) :|: X₀ ≤ 6 ∧ 4 ≤ X₀ ∧ X₀ ≤ 5 ∧ 3 ≤ X₀ ∧ X₀ ≤ 6 ∧ 5 ≤ X₀ of depth 1:
new bound:
10 {O(1)}
MPRF for transition t₁₅₅: n_l6___7(X₀) → n_l1___6(X₀+1) :|: 4 ≤ X₀ ∧ X₀ ≤ 5 ∧ 3 ≤ X₀ ∧ X₀ ≤ 5 ∧ X₀ ≤ 5 ∧ 4 ≤ X₀ of depth 1:
new bound:
10 {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}
t₁₉: 1 {O(1)}
t₂₀: inf {Infinity}
t₂₂: 1 {O(1)}
t₂₃: inf {Infinity}
t₂₄: 9 {O(1)}
t₂₆: inf {Infinity}
t₂₇: 9 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₁₉: 1 {O(1)}
t₂₀: inf {Infinity}
t₂₂: 1 {O(1)}
t₂₃: inf {Infinity}
t₂₄: 9 {O(1)}
t₂₆: inf {Infinity}
t₂₇: 9 {O(1)}
Sizebounds
t₁₉, X₀: X₀ {O(n)}
t₂₂, X₀: 3 {O(1)}
t₂₄, X₀: 5 {O(1)}
t₂₇, X₀: 6 {O(1)}