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) :|: 10 < X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 10
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(29, X₁) :|: X₀ ≤ 25 ∧ 25 ≤ X₀
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 25 ∧ X₀ ≤ 30
t₆: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 25 < X₀ ∧ X₀ ≤ 30
t₇: l3(X₀, X₁) → l1(20, X₁) :|: X₀ < 25 ∧ 30 < X₀
t₈: l3(X₀, X₁) → l1(20, X₁) :|: 25 < X₀ ∧ 30 < X₀
t₉: l4(X₀, X₁) → l5(X₀, X₁)
Preprocessing
Cut unsatisfiable transition t₇: l3→l1
Found invariant X₀ ≤ 10 for location l5
Found invariant X₀ ≤ 10 for location l4
Found invariant 11 ≤ 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) :|: 10 < X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 10
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(29, X₁) :|: X₀ ≤ 25 ∧ 25 ≤ X₀ ∧ 11 ≤ X₀
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 25 ∧ X₀ ≤ 30 ∧ 11 ≤ X₀
t₆: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 25 < X₀ ∧ X₀ ≤ 30 ∧ 11 ≤ X₀
t₈: l3(X₀, X₁) → l1(20, X₁) :|: 25 < X₀ ∧ 30 < X₀ ∧ 11 ≤ X₀
t₉: l4(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 10
Chain transitions t₈: l3→l1 and t₃: l1→l4 to t₁₀₂: l3→l4
Chain transitions t₆: l3→l1 and t₃: l1→l4 to t₁₀₃: l3→l4
Chain transitions t₆: l3→l1 and t₂: l1→l3 to t₁₀₄: l3→l3
Chain transitions t₈: l3→l1 and t₂: l1→l3 to t₁₀₅: l3→l3
Chain transitions t₅: l3→l1 and t₂: l1→l3 to t₁₀₆: l3→l3
Chain transitions t₅: l3→l1 and t₃: l1→l4 to t₁₀₇: l3→l4
Chain transitions t₄: l3→l1 and t₂: l1→l3 to t₁₀₈: l3→l3
Chain transitions t₄: l3→l1 and t₃: l1→l4 to t₁₀₉: l3→l4
Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₁₁₀: l2→l3
Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₁₁₁: l2→l4
Analysing control-flow refined program
Cut unsatisfiable transition t₁₀₂: l3→l4
Cut unsatisfiable transition t₁₀₃: l3→l4
Cut unsatisfiable transition t₁₀₉: l3→l4
Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 10 for location l5
Found invariant X₀ ≤ 18+X₁ for location l1
Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 10 for location l4
Found invariant 11 ≤ X₁ ∧ 22 ≤ X₀+X₁ ∧ X₀ ≤ 18+X₁ ∧ 11 ≤ X₀ for location l3
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₀₅: l3(X₀, X₁) -{2}> l3(20, X₁) :|: 25 < X₀ ∧ 30 < X₀ ∧ 0 < 10 ∧ 11 ≤ X₀ ∧ 11 ≤ X₁ ∧ 22 ≤ X₀+X₁ ∧ X₀ ≤ 18+X₁ ∧ 11 ≤ X₀
MPRF for transition t₁₀₆: l3(X₀, X₁) -{2}> l3(X₀-1, X₁) :|: X₀ < 25 ∧ X₀ ≤ 30 ∧ 11 < X₀ ∧ 11 ≤ X₀ ∧ 11 ≤ X₁ ∧ 22 ≤ X₀+X₁ ∧ X₀ ≤ 18+X₁ ∧ 11 ≤ X₀ of depth 1:
new bound:
20⋅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 t₂₉₈: n_l1___11→l4
Cut unsatisfiable transition t₂₉₉: n_l1___12→l4
Cut unsatisfiable transition t₃₀₁: n_l1___14→l4
Cut unsatisfiable transition t₃₀₃: n_l1___4→l4
Cut unsatisfiable transition t₃₀₄: n_l1___9→l4
Found invariant X₁ ≤ 30 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 59 ∧ X₀ ≤ 29 ∧ 25 ≤ X₀ for location n_l1___12
Found invariant X₁ ≤ 30 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 58 ∧ X₀ ≤ 28 ∧ 28 ≤ X₀ for location n_l1___9
Found invariant 31 ≤ X₁ ∧ 51 ≤ X₀+X₁ ∧ 11+X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 20 ≤ X₀ for location n_l1___11
Found invariant 31 ≤ X₁ ∧ 50 ≤ X₀+X₁ ∧ 12+X₀ ≤ X₁ ∧ X₀ ≤ 19 ∧ 19 ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₀ ∧ 11 ≤ X₁ ∧ 22 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 11 ≤ X₀ for location n_l3___15
Found invariant 31 ≤ X₁ ∧ 50 ≤ X₀+X₁ ∧ 12+X₀ ≤ X₁ ∧ X₀ ≤ 19 ∧ 19 ≤ X₀ for location n_l3___3
Found invariant 31 ≤ X₁ ∧ 51 ≤ X₀+X₁ ∧ 11+X₀ ≤ X₁ ∧ X₀ ≤ 20 ∧ 20 ≤ X₀ for location n_l3___5
Found invariant X₁ ≤ 30 ∧ X₁ ≤ 5+X₀ ∧ X₀+X₁ ≤ 59 ∧ X₀ ≤ 29 ∧ 25 ≤ X₀ for location n_l3___6
Found invariant X₁ ≤ 24 ∧ X₁ ≤ 14+X₀ ∧ X₀+X₁ ≤ 47 ∧ 11 ≤ X₁ ∧ 21 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 23 ∧ 10 ≤ X₀ for location n_l1___13
Found invariant 31 ≤ X₁ ∧ 41 ≤ X₀+X₁ ∧ 13+X₀ ≤ X₁ ∧ X₀ ≤ 18 ∧ 10 ≤ X₀ for location n_l1___2
Found invariant X₁ ≤ 30 ∧ X₁ ≤ 2+X₀ ∧ X₀+X₁ ≤ 58 ∧ X₀ ≤ 28 ∧ 28 ≤ X₀ for location n_l3___8
Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 10 for location l5
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1
Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 10 for location l4
Found invariant X₁ ≤ 30 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 59 ∧ X₀ ≤ 29 ∧ 29 ≤ X₀ for location n_l1___14
Found invariant 31 ≤ X₁ ∧ 42 ≤ X₀+X₁ ∧ 13+X₀ ≤ X₁ ∧ X₀ ≤ 18 ∧ 11 ≤ X₀ for location n_l3___1
Found invariant X₁ ≤ 30 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 59 ∧ X₀ ≤ 29 ∧ 29 ≤ X₀ for location n_l3___10
Found invariant X₁ ≤ 24 ∧ X₁ ≤ 13+X₀ ∧ X₀+X₁ ≤ 47 ∧ 12 ≤ X₁ ∧ 23 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 23 ∧ 11 ≤ X₀ for location n_l3___7
Cut unsatisfiable transition t₂₈₂: n_l3___6→n_l1___13
MPRF for transition t₂₇₀: n_l1___2(X₀, X₁) → n_l3___1(X₀, X₁) :|: X₀ < 25 ∧ X₀ ≤ 30 ∧ 10 ≤ X₀ ∧ X₀ ≤ 23 ∧ 10 < X₀ ∧ 31 ≤ X₁ ∧ 41 ≤ X₀+X₁ ∧ 13+X₀ ≤ X₁ ∧ X₀ ≤ 18 ∧ 10 ≤ X₀ of depth 1:
new bound:
28 {O(1)}
MPRF for transition t₂₇₃: n_l3___1(X₀, X₁) → n_l1___2(X₀-1, X₁) :|: X₀ ≤ 23 ∧ 10 < X₀ ∧ X₀ < 25 ∧ 11 ≤ X₀ ∧ 31 ≤ X₁ ∧ 42 ≤ X₀+X₁ ∧ 13+X₀ ≤ X₁ ∧ X₀ ≤ 18 ∧ 11 ≤ X₀ of depth 1:
new bound:
28 {O(1)}
MPRF for transition t₂₆₇: n_l1___13(X₀, X₁) → n_l3___7(X₀, X₁) :|: X₀ < 25 ∧ X₀ ≤ 30 ∧ 10 < X₀ ∧ X₁ ≤ 24 ∧ X₁ ≤ 14+X₀ ∧ X₀+X₁ ≤ 47 ∧ 11 ≤ X₁ ∧ 21 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 23 ∧ 10 ≤ X₀ of depth 1:
new bound:
33 {O(1)}
MPRF for transition t₂₈₄: n_l3___7(X₀, X₁) → n_l1___13(X₀-1, X₁) :|: X₀ < 25 ∧ 10 < X₀ ∧ X₀ < 25 ∧ 11 ≤ X₀ ∧ X₁ ≤ 24 ∧ X₁ ≤ 13+X₀ ∧ X₀+X₁ ≤ 47 ∧ 12 ≤ X₁ ∧ 23 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 23 ∧ 11 ≤ X₀ of depth 1:
new bound:
33 {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: inf {Infinity}
t₅: inf {Infinity}
t₆: 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: inf {Infinity}
t₅: inf {Infinity}
t₆: 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: X₁+101 {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+23 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₄, X₀: 29 {O(1)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 23 {O(1)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: 29 {O(1)}
t₆, X₁: X₁ {O(n)}
t₈, X₀: 20 {O(1)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: X₁+23 {O(n)}
t₉, X₁: 2⋅X₁ {O(n)}