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) :|: X₂ ≤ X₁
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ < X₂
t₁: l2(X₀, X₁, X₂) → l1(X₀, X₁, 0)
t₄: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: X₂ ≤ X₀
t₅: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₀ < X₂
t₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
Preprocessing
Found invariant 1+X₁ ≤ X₂ for location l5
Found invariant 1+X₁ ≤ X₂ for location l4
Found invariant X₂ ≤ X₁ 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) :|: X₂ ≤ X₁
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ < X₂
t₁: l2(X₀, X₁, X₂) → l1(X₀, X₁, 0)
t₄: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: X₂ ≤ X₀ ∧ X₂ ≤ X₁
t₅: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₀ < X₂ ∧ X₂ ≤ X₁
t₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 1+X₁ ≤ X₂
Analysing control-flow refined program
Cut unsatisfiable transition t₆₇: n_l1___3→l4
Cut unsatisfiable transition t₆₈: n_l1___5→l4
Found invariant X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₁ for location n_l1___6
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₁ for location n_l3___4
Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location n_l1___3
Found invariant 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ for location l5
Found invariant 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l1___5
Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location n_l3___2
Found invariant X₂ ≤ 0 ∧ 0 ≤ X₂ for location l1
Found invariant 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ for location l4
Found invariant 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l3___1
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location n_l3___7
MPRF for transition t₅₁: n_l1___5(X₀, X₁, X₂) → n_l3___1(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:
new bound:
X₀+2 {O(n)}
MPRF:
n_l3___1 [X₂-X₀ ]
n_l1___5 [X₂+1-X₀ ]
MPRF for transition t₅₄: n_l3___1(X₀, X₁, X₂) → n_l1___5(X₀, X₁, X₂-1) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₀ < X₂ ∧ 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
n_l3___1 [X₂-X₀ ]
n_l1___5 [X₂-X₀ ]
MPRF for transition t₅₈: n_l3___4(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂+1) :|: X₂ ≤ 1+X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₁ of depth 1:
new bound:
3⋅X₀+5 {O(n)}
MPRF:
n_l3___2 [0 ]
n_l1___3 [X₀-X₂ ]
n_l3___4 [X₀+1-X₂ ]
n_l1___6 [X₀+1-X₂ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: inf {Infinity}
t₅: inf {Infinity}
t₆: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: inf {Infinity}
t₅: inf {Infinity}
t₆: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 0 {O(1)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: 2⋅X₀ {O(n)}
t₆, X₁: 2⋅X₁ {O(n)}