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) :|: 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(0, X₁) :|: X₀+5 < 0
t₇: l3(X₀, X₁) → l1(0, X₁) :|: 35 < X₀
t₅: l3(X₀, X₁) → l5(X₀, X₁) :|: 0 ≤ 5+X₀ ∧ X₀ ≤ 35
t₁₂: l4(X₀, X₁) → l7(X₀, X₁)
t₈: l5(X₀, X₁) → l1(-5, X₁) :|: X₀ < 0
t₉: l5(X₀, X₁) → l6(X₀, X₁) :|: 0 ≤ X₀
t₁₀: l6(X₀, X₁) → l1(35, X₁) :|: 30 < X₀
t₁₁: l6(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ ≤ 30
Preprocessing
Found invariant X₀ ≤ 35 ∧ 0 ≤ X₀ for location l6
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l7
Found invariant X₀ ≤ 35 ∧ 0 ≤ 5+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, l7
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(0, X₁) :|: X₀+5 < 0
t₇: l3(X₀, X₁) → l1(0, X₁) :|: 35 < X₀
t₅: l3(X₀, X₁) → l5(X₀, X₁) :|: 0 ≤ 5+X₀ ∧ X₀ ≤ 35
t₁₂: l4(X₀, X₁) → l7(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₈: l5(X₀, X₁) → l1(-5, X₁) :|: X₀ < 0 ∧ X₀ ≤ 35 ∧ 0 ≤ 5+X₀
t₉: l5(X₀, X₁) → l6(X₀, X₁) :|: 0 ≤ X₀ ∧ X₀ ≤ 35 ∧ 0 ≤ 5+X₀
t₁₀: l6(X₀, X₁) → l1(35, X₁) :|: 30 < X₀ ∧ X₀ ≤ 35 ∧ 0 ≤ X₀
t₁₁: l6(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ ≤ 30 ∧ X₀ ≤ 35 ∧ 0 ≤ X₀
Chain transitions t₁₁: l6→l1 and t₄: l1→l4 to t₃₆₆: l6→l4
Chain transitions t₁₀: l6→l1 and t₄: l1→l4 to t₃₆₇: l6→l4
Chain transitions t₁₀: l6→l1 and t₃: l1→l3 to t₃₆₈: l6→l3
Chain transitions t₁₁: l6→l1 and t₃: l1→l3 to t₃₆₉: l6→l3
Chain transitions t₈: l5→l1 and t₃: l1→l3 to t₃₇₀: l5→l3
Chain transitions t₈: l5→l1 and t₄: l1→l4 to t₃₇₁: l5→l4
Chain transitions t₈: l5→l1 and t₂: l1→l3 to t₃₇₂: l5→l3
Chain transitions t₁₀: l6→l1 and t₂: l1→l3 to t₃₇₃: l6→l3
Chain transitions t₁₁: l6→l1 and t₂: l1→l3 to t₃₇₄: l6→l3
Chain transitions t₇: l3→l1 and t₂: l1→l3 to t₃₇₅: l3→l3
Chain transitions t₇: l3→l1 and t₃: l1→l3 to t₃₇₆: l3→l3
Chain transitions t₇: l3→l1 and t₄: l1→l4 to t₃₇₇: l3→l4
Chain transitions t₆: l3→l1 and t₂: l1→l3 to t₃₇₈: l3→l3
Chain transitions t₆: l3→l1 and t₃: l1→l3 to t₃₇₉: l3→l3
Chain transitions t₆: l3→l1 and t₄: l1→l4 to t₃₈₀: l3→l4
Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₃₈₁: l2→l3
Chain transitions t₁: l2→l1 and t₃: l1→l3 to t₃₈₂: l2→l3
Chain transitions t₁: l2→l1 and t₄: l1→l4 to t₃₈₃: l2→l4
Chain transitions t₅: l3→l5 and t₉: l5→l6 to t₃₈₄: l3→l6
Chain transitions t₅: l3→l5 and t₃₇₁: l5→l4 to t₃₈₅: l3→l4
Chain transitions t₅: l3→l5 and t₃₇₂: l5→l3 to t₃₈₆: l3→l3
Chain transitions t₅: l3→l5 and t₃₇₀: l5→l3 to t₃₈₇: l3→l3
Chain transitions t₅: l3→l5 and t₈: l5→l1 to t₃₈₈: l3→l1
Chain transitions t₃₈₄: l3→l6 and t₃₆₇: l6→l4 to t₃₈₉: l3→l4
Chain transitions t₃₈₄: l3→l6 and t₃₆₆: l6→l4 to t₃₉₀: l3→l4
Chain transitions t₃₈₄: l3→l6 and t₃₇₄: l6→l3 to t₃₉₁: l3→l3
Chain transitions t₃₈₄: l3→l6 and t₃₇₃: l6→l3 to t₃₉₂: l3→l3
Chain transitions t₃₈₄: l3→l6 and t₃₆₉: l6→l3 to t₃₉₃: l3→l3
Chain transitions t₃₈₄: l3→l6 and t₃₆₈: l6→l3 to t₃₉₄: l3→l3
Chain transitions t₃₈₄: l3→l6 and t₁₁: l6→l1 to t₃₉₅: l3→l1
Chain transitions t₃₈₄: l3→l6 and t₁₀: l6→l1 to t₃₉₆: l3→l1
Analysing control-flow refined program
Cut unsatisfiable transition t₃₇₅: l3→l3
Cut unsatisfiable transition t₃₇₆: l3→l3
Cut unsatisfiable transition t₃₇₈: l3→l3
Cut unsatisfiable transition t₃₇₉: l3→l3
Cut unsatisfiable transition t₃₈₅: l3→l4
Cut unsatisfiable transition t₃₈₇: l3→l3
Cut unsatisfiable transition t₃₈₉: l3→l4
Cut unsatisfiable transition t₃₉₁: l3→l3
Cut unsatisfiable transition t₃₉₂: l3→l3
Found invariant X₀ ≤ 35 ∧ 0 ≤ X₀ for location l6
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l7
Found invariant X₀ ≤ 35 ∧ 0 ≤ 5+X₀ for location l5
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
MPRF for transition t₃₉₃: l3(X₀, X₁) -{4}> l3(X₀-1, X₁) :|: 0 ≤ 5+X₀ ∧ X₀ ≤ 35 ∧ 0 ≤ X₀ ∧ X₀ ≤ 30 ∧ 1 < X₀ ∧ X₀ ≤ 35 ∧ 0 ≤ 5+X₀ ∧ X₀ ≤ 35 ∧ 0 ≤ 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 t₇₈₃: n_l1___9→n_l3___5
Cut unsatisfiable transition t₈₂₇: n_l1___10→l4
Cut unsatisfiable transition t₈₂₈: n_l1___15→l4
Cut unreachable locations [n_l3___5; n_l5___3] from the program graph
Found invariant X₁ ≤ 35 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 70 ∧ 31 ≤ X₁ ∧ 66 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 35 ∧ 35 ≤ X₀ for location n_l6___6
Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 10+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 0 ≤ 5+X₀ for location n_l5___16
Found invariant X₁ ≤ 30 ∧ X₁ ≤ 29+X₀ ∧ X₀+X₁ ≤ 59 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 29 ∧ 1 ≤ X₀ for location n_l6___1
Found invariant X₁ ≤ 30 ∧ X₁ ≤ 29+X₀ ∧ X₀+X₁ ≤ 59 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 29 ∧ 1 ≤ X₀ for location n_l3___4
Found invariant X₁ ≤ 30 ∧ X₁ ≤ 30+X₀ ∧ X₀+X₁ ≤ 59 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 29 ∧ 0 ≤ X₀ for location n_l1___9
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___17
Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l3___19
Found invariant X₁ ≤ 35 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 70 ∧ 31 ≤ X₁ ∧ 66 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 35 ∧ 35 ≤ X₀ for location n_l1___10
Found invariant X₁ ≤ 30 ∧ X₁ ≤ 29+X₀ ∧ X₀+X₁ ≤ 59 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 29 ∧ 1 ≤ X₀ for location n_l5___2
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l7
Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ 4+X₀ ∧ 6+X₀+X₁ ≤ 0 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 10+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 5+X₀ ≤ 0 ∧ 0 ≤ 5+X₀ for location n_l3___14
Found invariant X₁ ≤ 35 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 70 ∧ 31 ≤ X₁ ∧ 66 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 35 ∧ 35 ≤ X₀ for location n_l3___8
Found invariant X₁ ≤ 35 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 70 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 35 ∧ 1 ≤ X₀ for location n_l5___12
Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ 4+X₀ ∧ 6+X₀+X₁ ≤ 0 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 10+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 5+X₀ ≤ 0 ∧ 0 ≤ 5+X₀ for location n_l5___13
Found invariant X₁ ≤ 35 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 70 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 35 ∧ 1 ≤ X₀ for location n_l6___11
Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ 4+X₀ ∧ 6+X₀+X₁ ≤ 0 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 10+X₀+X₁ ∧ X₀ ≤ X₁ ∧ 5+X₀ ≤ 0 ∧ 0 ≤ 5+X₀ for location n_l1___15
Found invariant X₁ ≤ 35 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 70 ∧ 31 ≤ X₁ ∧ 66 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 35 ∧ 35 ≤ X₀ for location n_l5___7
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___18
MPRF for transition t₇₈₂: n_l1___9(X₀, X₁) → n_l3___4(X₀, X₁) :|: 0 ≤ 5+X₀ ∧ X₀ ≤ 35 ∧ X₀ ≤ 30 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 29 ∧ 0 < X₀ ∧ X₁ ≤ 30 ∧ X₁ ≤ 30+X₀ ∧ X₀+X₁ ≤ 59 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 29 ∧ 0 ≤ X₀ of depth 1:
new bound:
30 {O(1)}
MPRF for transition t₇₈₉: n_l3___4(X₀, X₁) → n_l5___2(X₀, X₁) :|: X₀ ≤ 29 ∧ 0 < X₀ ∧ 0 ≤ 5+X₀ ∧ X₀ ≤ 35 ∧ X₁ ≤ 30 ∧ X₁ ≤ 29+X₀ ∧ X₀+X₁ ≤ 59 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 29 ∧ 1 ≤ X₀ of depth 1:
new bound:
29 {O(1)}
MPRF for transition t₇₉₅: n_l5___2(X₀, X₁) → n_l6___1(X₀, X₁) :|: X₀ ≤ 29 ∧ 0 < X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 35 ∧ X₁ ≤ 30 ∧ X₁ ≤ 29+X₀ ∧ X₀+X₁ ≤ 59 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 29 ∧ 1 ≤ X₀ of depth 1:
new bound:
30 {O(1)}
MPRF for transition t₇₉₈: n_l6___1(X₀, X₁) → n_l1___9(X₀-1, X₁) :|: X₀ ≤ 29 ∧ 0 < X₀ ∧ X₀ ≤ 30 ∧ 0 ≤ X₀ ∧ X₁ ≤ 30 ∧ X₁ ≤ 29+X₀ ∧ X₀+X₁ ≤ 59 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 29 ∧ 1 ≤ X₀ of depth 1:
new bound:
30 {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}
t₈: 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}
t₈: 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+34 {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+64 {O(n)}
t₃, X₁: X₁ {O(n)}
t₄, X₀: 0 {O(1)}
t₄, X₁: 4⋅X₁ {O(n)}
t₅, X₀: 35 {O(1)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: 0 {O(1)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: 0 {O(1)}
t₇, X₁: X₁ {O(n)}
t₈, X₀: 5 {O(1)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: 35 {O(1)}
t₉, X₁: X₁ {O(n)}
t₁₀, X₀: 35 {O(1)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: 29 {O(1)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₀: 0 {O(1)}
t₁₂, X₁: 4⋅X₁ {O(n)}