Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l1(X₀, X₁) :|: 0 < X₀ ∧ X₀ < 1
t₃: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 0 < X₀ ∧ 1 ≤ X₀
t₄: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 0 ∧ X₀ < 0
t₅: l1(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
Preprocessing
Cut unsatisfiable transition t₂: l1→l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₃: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 0 < X₀ ∧ 1 ≤ X₀
t₄: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 0 ∧ X₀ < 0
t₅: l1(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
MPRF for transition t₃: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 0 < X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₄: l1(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 0 ∧ X₀ < 0 of depth 1:
new bound:
X₁+1 {O(n)}
Analysing control-flow refined program
Cut unsatisfiable transition t₇₁: n_l1___3→n_l1___4
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___2
Found invariant 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location n_l1___3
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1
MPRF for transition t₇₀: n_l1___3(X₀, X₁) → n_l1___3(X₀+1, X₁) :|: X₀ < 0 ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₇₃: n_l1___4(X₀, X₁) → n_l1___4(X₀-1, X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁+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)}
t₃: X₁ {O(n)}
t₄: X₁+1 {O(n)}
t₅: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₃: X₁ {O(n)}
t₄: X₁+1 {O(n)}
t₅: inf {Infinity}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₃, X₀: X₁ {O(n)}
t₃, X₁: X₁ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 0 {O(1)}
t₅, X₁: 3⋅X₁ {O(n)}