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 < 0
t₃: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 0 < X₀
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁: l2(X₀, X₁, X₂) → l1(X₁, X₁, X₂)
t₅: l3(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂)
t₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
Preprocessing
Eliminate variables {X₂} that do not contribute to the problem
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5
Found invariant X₀ ≤ X₁ for location l1
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant X₀ ≤ X₁ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₄: l0(X₀, X₁) → l2(X₀, X₁)
t₁₅: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ < 0 ∧ X₀ ≤ X₁
t₁₆: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀ ∧ X₀ ≤ X₁
t₁₇: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁
t₁₈: l2(X₀, X₁) → l1(X₁, X₁)
t₁₉: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ ≤ X₁
t₂₀: l4(X₀, X₁) → l5(X₀, X₁) :|: 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
MPRF for transition t₁₆: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀ ∧ X₀ ≤ X₁ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
l3 [X₀-1 ]
l1 [X₀ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₅₃: n_l1___3→n_l3___2
Cut unsatisfiable transition t₆₈: n_l1___5→l4
Cut unreachable locations [n_l3___2] from the program graph
Found invariant 1+X₁ ≤ 0 ∧ 3+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 2+X₀ ≤ 0 for location n_l3___4
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___6
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5
Found invariant 1+X₁ ≤ 0 ∧ 3+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 2+X₀ ≤ 0 for location n_l1___5
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___1
Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l3___7
MPRF for transition t₅₂: n_l1___3(X₀, X₁) → n_l3___1(X₀, X₁) :|: X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 < X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
n_l3___1 [X₀ ]
n_l1___3 [X₀+1 ]
MPRF for transition t₅₇: n_l3___1(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: 1+X₀ ≤ X₁ ∧ 0 < X₀ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
n_l3___1 [X₀ ]
n_l1___3 [X₀ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: X₁ {O(n)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: inf {Infinity}
t₂₀: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: X₁ {O(n)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: inf {Infinity}
t₂₀: 1 {O(1)}
Sizebounds
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}
t₁₆, X₁: 2⋅X₁ {O(n)}
t₁₇, X₀: 0 {O(1)}
t₁₇, X₁: 3⋅X₁ {O(n)}
t₁₈, X₀: X₁ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₉, X₁: 2⋅X₁ {O(n)}
t₂₀, X₀: 0 {O(1)}
t₂₀, X₁: 3⋅X₁ {O(n)}