Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < X₁
t₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁+1, X₂, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
Preprocessing
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5
Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ for location l1
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4
Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < X₁ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁+1, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₀ ≤ X₂
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
MPRF for transition t₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ of depth 1:
new bound:
X₂+X₃ {O(n)}
MPRF:
l3 [X₀-X₃-1 ]
l1 [X₀-X₃ ]
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5
Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ for location l1
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4
Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l3
Analysing control-flow refined program
Cut unsatisfiable transition t₈₃: n_l1___5→l4
Found invariant 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 3+X₀ ≤ X₁ for location n_l3___4
Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___6
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ for location n_l1___3
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5
Found invariant 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 3+X₀ ≤ X₁ for location n_l1___5
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ for location n_l3___2
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4
Found invariant 3+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___1
Found invariant X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l3___7
MPRF for transition t₆₇: n_l1___3(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ of depth 1:
new bound:
X₂+X₃+2 {O(n)}
MPRF:
n_l3___1 [X₀-X₃ ]
n_l1___3 [X₀+1-X₃ ]
MPRF for transition t₇₂: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___3(X₀-1, X₁+1, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ X₁ < X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ 3+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₂+X₃+1 {O(n)}
MPRF:
n_l3___1 [X₂-X₁ ]
n_l1___3 [X₂-X₁ ]
Found invariant 1+X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 3+X₀ ≤ X₁ for location n_l3___4
Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___6
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ for location n_l1___3
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5
Found invariant 1+X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 3+X₀ ≤ X₁ for location n_l1___5
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ for location n_l3___2
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4
Found invariant 3+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___1
Found invariant X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l3___7
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₂: inf {Infinity}
t₃: X₂+X₃ {O(n)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: inf {Infinity}
t₆: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₂: inf {Infinity}
t₃: X₂+X₃ {O(n)}
t₄: 1 {O(1)}
t₁: 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)}
t₀, X₃: X₃ {O(n)}
t₂, X₂: 2⋅X₂ {O(n)}
t₂, X₃: 2⋅X₃ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₄, X₂: 3⋅X₂ {O(n)}
t₄, X₃: 3⋅X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₆, X₂: 3⋅X₂ {O(n)}
t₆, X₃: 3⋅X₃ {O(n)}