Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(1+X₀, X₁, X₂) :|: 1+X₀ ≤ X₁
t₁: l1(X₀, X₁, X₂) → l1(1+X₀, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀

Preprocessing

Eliminate variables {D,X₂} that do not contribute to the problem

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₁₂: l0(X₀, X₁) → l1(X₀, X₁)
t₁₃: l1(X₀, X₁) → l1(1+X₀, X₁) :|: 1+X₀ ≤ X₁
t₁₄: l1(X₀, X₁) → l1(1+X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀
t₁₅: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀

MPRF for transition t₁₃: l1(X₀, X₁) → l1(1+X₀, X₁) :|: 1+X₀ ≤ X₁ of depth 1:

new bound:

X₀+X₁ {O(n)}

Analysing control-flow refined program

Cut unsatisfiable transition t₆₉: n_l1___1→l2

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant X₀ ≤ X₁ for location n_l1___2

Found invariant 2+X₁ ≤ X₀ for location n_l1___1

MPRF for transition t₆₀: n_l1___2(X₀, X₁) → n_l1___2(X₀+1, X₁) :|: X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₀+X₁+2 {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}
t₁₂: 1 {O(1)}
t₁₃: X₀+X₁ {O(n)}
t₁₄: inf {Infinity}
t₁₅: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₂: 1 {O(1)}
t₁₃: X₀+X₁ {O(n)}
t₁₄: inf {Infinity}
t₁₅: 1 {O(1)}

Sizebounds

t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: 2⋅X₀+X₁ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₀: 3⋅X₀+X₁ {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}