Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₀ < X₁
t₃: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ < X₀
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₅: l3(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂)
t₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
Preprocessing
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5
Found invariant X₂ ≤ X₀ for location l1
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4
Found invariant X₂ ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₂ ≤ X₀
t₃: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₂ ≤ X₀
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₅: l3(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₂ ≤ X₀
t₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
MPRF for transition t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₂ ≤ X₀ of depth 1:
new bound:
X₁+X₂ {O(n)}
Chain transitions t₅: l3→l1 and t₄: l1→l4 to t₄₉: l3→l4
Chain transitions t₁: l2→l1 and t₄: l1→l4 to t₅₀: l2→l4
Chain transitions t₁: l2→l1 and t₃: l1→l3 to t₅₁: l2→l3
Chain transitions t₅: l3→l1 and t₃: l1→l3 to t₅₂: l3→l3
Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₅₃: l2→l3
Chain transitions t₅: l3→l1 and t₂: l1→l3 to t₅₄: l3→l3
Analysing control-flow refined program
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5
Found invariant X₂ ≤ X₀ for location l1
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4
Found invariant X₂ ≤ X₀ for location l3
MPRF for transition t₅₄: l3(X₀, X₁, X₂) -{2}> l3(1+X₀, X₁, X₂) :|: 1+X₀ < X₁ ∧ X₂ ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ X₀ of depth 1:
new bound:
2⋅X₁+2⋅X₂ {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 t₁₃₉: n_l1___5→n_l3___3
Cut unsatisfiable transition t₁₅₃: n_l1___2→l4
Cut unreachable locations [n_l3___3] from the program graph
Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location n_l3___4
Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___6
Found invariant 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ for location n_l1___2
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___5
Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4
Found invariant 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ for location n_l3___1
Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l3___7
MPRF for transition t₁₄₀: n_l1___5(X₀, X₁, X₂) → n_l3___4(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₀ < X₁ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:
new bound:
X₁+X₂+2 {O(n)}
MPRF for transition t₁₄₅: n_l3___4(X₀, X₁, X₂) → n_l1___5(X₀+1, X₁, X₂) :|: X₀ < X₁ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
X₁+X₂+1 {O(n)}
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: X₁+X₂ {O(n)}
t₃: inf {Infinity}
t₄: 1 {O(1)}
t₅: inf {Infinity}
t₆: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+X₂ {O(n)}
t₃: inf {Infinity}
t₄: 1 {O(1)}
t₅: inf {Infinity}
t₆: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₄, X₁: 2⋅X₁ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₆, X₁: 2⋅X₁ {O(n)}
t₆, X₂: 2⋅X₂ {O(n)}