Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l1(0, 1+X₁, 1+X₂, X₃) :|: 2+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, E) :|: X₂ ≤ X₁
t₂: l1(X₀, X₁, X₂, X₃) → l2(1, 1+X₁, X₂, E) :|: X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀

Preprocessing

Eliminate variables {E,X₃} that do not contribute to the problem

Found invariant X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ for location l2

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₁₁: l0(X₀, X₁, X₂) → l1(0, X₁, X₂)
t₁₄: l1(X₀, X₁, X₂) → l1(0, 1+X₁, 1+X₂) :|: 2+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₃: l1(X₀, X₁, X₂) → l2(1, 1+X₁, X₂) :|: X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀

Found invariant X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ for location l2

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Analysing control-flow refined program

Found invariant X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ for location l2

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant 2+X₁ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1

Found invariant X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ for location l2

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant 2+X₁ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: inf {Infinity}

Sizebounds

t₁₁, X₀: 0 {O(1)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₂, X₀: 0 {O(1)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₃, X₀: 1 {O(1)}
t₁₃, X₁: X₁+1 {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₄, X₀: 0 {O(1)}