Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l4(X₀, X₁, X₂, X₁, X₂, X₅, X₆, X₇, X₈) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₅, X₆, X₇, X₃, X₄, X₅, X₆, X₇, X₈)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₀-1, 3⋅X₁+2⋅X₂, -5⋅X₁-3⋅X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 < X₃+X₄
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃+X₄ ≤ 0
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l4(X₀, X₁, X₂, X₃-1, X₄-1, X₅, X₆, X₇, X₈)
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
Preprocessing
Eliminate variables {X₈} that do not contribute to the problem
Found invariant X₀ ≤ X₅ ∧ X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 0 for location l6
Found invariant X₀ ≤ X₅ ∧ X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 0 for location l7
Found invariant X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ 0 for location l5
Found invariant X₀ ≤ X₅ for location l1
Found invariant X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₇: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₀ ∧ X₀ ≤ X₅
t₁₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₁, X₂, X₅, X₆, X₇) :|: X₀ ≤ 0 ∧ X₀ ≤ X₅
t₂₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₅, X₆, X₇, X₃, X₄, X₅, X₆, X₇)
t₂₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀-1, 3⋅X₁+2⋅X₂, -5⋅X₁-3⋅X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₂₂: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₃+X₄ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 0
t₂₃: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃+X₄ ≤ 0 ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 0
t₂₄: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃-1, X₄-1, X₅, X₆, X₇) :|: X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ 0
t₂₅: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₅ ∧ X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 0
MPRF for transition t₁₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₀ ∧ X₀ ≤ X₅ of depth 1:
new bound:
X₅ {O(n)}
MPRF for transition t₂₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀-1, 3⋅X₁+2⋅X₂, -5⋅X₁-3⋅X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₅ {O(n)}
MPRF for transition t₂₂: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₃+X₄ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+X₆+X₇ {O(EXP)}
MPRF for transition t₂₄: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃-1, X₄-1, X₅, X₆, X₇) :|: X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ 0 of depth 1:
new bound:
10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+X₆+X₇ {O(EXP)}
Chain transitions t₂₄: l5→l4 and t₂₃: l4→l6 to t₄₆: l5→l6
Chain transitions t₁₉: l1→l4 and t₂₃: l4→l6 to t₄₇: l1→l6
Chain transitions t₁₉: l1→l4 and t₂₂: l4→l5 to t₄₈: l1→l5
Chain transitions t₂₄: l5→l4 and t₂₂: l4→l5 to t₄₉: l5→l5
Analysing control-flow refined program
Found invariant X₀ ≤ X₅ ∧ X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 0 for location l6
Found invariant X₀ ≤ X₅ ∧ X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 0 for location l7
Found invariant X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ 0 for location l5
Found invariant X₀ ≤ X₅ for location l1
Found invariant X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₄₉: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) -{2}> l5(X₀, X₁, X₂, X₃-1, X₄-1, X₅, X₆, X₇) :|: 2 < X₃+X₄ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂+1 ∧ X₃ ≤ X₁+1 ∧ X₀ ≤ 0 ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ 0 of depth 1:
new bound:
10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+X₆+X₇ {O(EXP)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Found invariant X₀ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₂ ∧ X₀ ≤ 0 for location n_l5___1
Found invariant X₀ ≤ X₅ ∧ X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 0 for location l6
Found invariant X₀ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ 1+X₃+X₄ ∧ 0 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ 0 for location n_l4___2
Found invariant X₀ ≤ X₅ ∧ X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 0 for location l7
Found invariant X₀ ≤ X₅ for location l1
Found invariant X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l3
Found invariant X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ 0 for location n_l5___3
MPRF for transition t₉₈: n_l4___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l5___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₃+X₄ ∧ 1+X₃ ≤ X₁ ∧ 1+X₄ ≤ X₂ ∧ 0 < X₃+X₄ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₀ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₀ ≤ X₅ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ 1+X₃+X₄ ∧ 0 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ 0 of depth 1:
new bound:
10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+X₆+X₇+2 {O(EXP)}
MPRF for transition t₁₀₀: n_l5___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l4___2(X₀, X₁, X₂, X₃-1, X₄-1, X₅, X₆, X₇) :|: 1+X₄ ≤ X₂ ∧ 0 < X₃+X₄ ∧ 1+X₃ ≤ X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ X₀ ≤ X₅ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₂ ∧ X₀ ≤ 0 of depth 1:
new bound:
10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+X₆+X₇+1 {O(EXP)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:10^(X₅)⋅4⋅X₆+10^(X₅)⋅4⋅X₇+2⋅X₅+2⋅X₆+2⋅X₇+5 {O(EXP)}
t₁₇: 1 {O(1)}
t₁₈: X₅ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₅ {O(n)}
t₂₂: 10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+X₆+X₇ {O(EXP)}
t₂₃: 1 {O(1)}
t₂₄: 10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+X₆+X₇ {O(EXP)}
t₂₅: 1 {O(1)}
Costbounds
Overall costbound: 10^(X₅)⋅4⋅X₆+10^(X₅)⋅4⋅X₇+2⋅X₅+2⋅X₆+2⋅X₇+5 {O(EXP)}
t₁₇: 1 {O(1)}
t₁₈: X₅ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₅ {O(n)}
t₂₂: 10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+X₆+X₇ {O(EXP)}
t₂₃: 1 {O(1)}
t₂₄: 10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+X₆+X₇ {O(EXP)}
t₂₅: 1 {O(1)}
Sizebounds
t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₇, X₅: X₅ {O(n)}
t₁₇, X₆: X₆ {O(n)}
t₁₇, X₇: X₇ {O(n)}
t₁₈, X₀: X₅ {O(n)}
t₁₈, X₁: 10^(X₅)⋅X₆+10^(X₅)⋅X₇ {O(EXP)}
t₁₈, X₂: 10^(X₅)⋅X₆+10^(X₅)⋅X₇ {O(EXP)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₈, X₆: X₆ {O(n)}
t₁₈, X₇: X₇ {O(n)}
t₁₉, X₀: 2⋅X₅ {O(n)}
t₁₉, X₁: 10^(X₅)⋅X₆+10^(X₅)⋅X₇+X₆ {O(EXP)}
t₁₉, X₂: 10^(X₅)⋅X₆+10^(X₅)⋅X₇+X₇ {O(EXP)}
t₁₉, X₃: 10^(X₅)⋅X₆+10^(X₅)⋅X₇+X₆ {O(EXP)}
t₁₉, X₄: 10^(X₅)⋅X₆+10^(X₅)⋅X₇+X₇ {O(EXP)}
t₁₉, X₅: 2⋅X₅ {O(n)}
t₁₉, X₆: 2⋅X₆ {O(n)}
t₁₉, X₇: 2⋅X₇ {O(n)}
t₂₀, X₀: X₅ {O(n)}
t₂₀, X₁: X₆ {O(n)}
t₂₀, X₂: X₇ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₀, X₅: X₅ {O(n)}
t₂₀, X₆: X₆ {O(n)}
t₂₀, X₇: X₇ {O(n)}
t₂₁, X₀: X₅ {O(n)}
t₂₁, X₁: 10^(X₅)⋅X₆+10^(X₅)⋅X₇ {O(EXP)}
t₂₁, X₂: 10^(X₅)⋅X₆+10^(X₅)⋅X₇ {O(EXP)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₁, X₆: X₆ {O(n)}
t₂₁, X₇: X₇ {O(n)}
t₂₂, X₀: 2⋅X₅ {O(n)}
t₂₂, X₁: 10^(X₅)⋅X₆+10^(X₅)⋅X₇+X₆ {O(EXP)}
t₂₂, X₂: 10^(X₅)⋅X₆+10^(X₅)⋅X₇+X₇ {O(EXP)}
t₂₂, X₃: 10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+10^(X₅)⋅X₆+10^(X₅)⋅X₇+2⋅X₆+X₇ {O(EXP)}
t₂₂, X₄: 10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+10^(X₅)⋅X₆+10^(X₅)⋅X₇+2⋅X₇+X₆ {O(EXP)}
t₂₂, X₅: 2⋅X₅ {O(n)}
t₂₂, X₆: 2⋅X₆ {O(n)}
t₂₂, X₇: 2⋅X₇ {O(n)}
t₂₃, X₀: 4⋅X₅ {O(n)}
t₂₃, X₁: 10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+2⋅X₆ {O(EXP)}
t₂₃, X₂: 10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+2⋅X₇ {O(EXP)}
t₂₃, X₃: 10^(X₅)⋅4⋅X₆+10^(X₅)⋅4⋅X₇+3⋅X₆+X₇ {O(EXP)}
t₂₃, X₄: 10^(X₅)⋅4⋅X₆+10^(X₅)⋅4⋅X₇+3⋅X₇+X₆ {O(EXP)}
t₂₃, X₅: 4⋅X₅ {O(n)}
t₂₃, X₆: 4⋅X₆ {O(n)}
t₂₃, X₇: 4⋅X₇ {O(n)}
t₂₄, X₀: 2⋅X₅ {O(n)}
t₂₄, X₁: 10^(X₅)⋅X₆+10^(X₅)⋅X₇+X₆ {O(EXP)}
t₂₄, X₂: 10^(X₅)⋅X₆+10^(X₅)⋅X₇+X₇ {O(EXP)}
t₂₄, X₃: 10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+10^(X₅)⋅X₆+10^(X₅)⋅X₇+2⋅X₆+X₇ {O(EXP)}
t₂₄, X₄: 10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+10^(X₅)⋅X₆+10^(X₅)⋅X₇+2⋅X₇+X₆ {O(EXP)}
t₂₄, X₅: 2⋅X₅ {O(n)}
t₂₄, X₆: 2⋅X₆ {O(n)}
t₂₄, X₇: 2⋅X₇ {O(n)}
t₂₅, X₀: 4⋅X₅ {O(n)}
t₂₅, X₁: 10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+2⋅X₆ {O(EXP)}
t₂₅, X₂: 10^(X₅)⋅2⋅X₆+10^(X₅)⋅2⋅X₇+2⋅X₇ {O(EXP)}
t₂₅, X₃: 10^(X₅)⋅4⋅X₆+10^(X₅)⋅4⋅X₇+3⋅X₆+X₇ {O(EXP)}
t₂₅, X₄: 10^(X₅)⋅4⋅X₆+10^(X₅)⋅4⋅X₇+3⋅X₇+X₆ {O(EXP)}
t₂₅, X₅: 4⋅X₅ {O(n)}
t₂₅, X₆: 4⋅X₆ {O(n)}
t₂₅, X₇: 4⋅X₇ {O(n)}