Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(0, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁-1, D) :|: 1 ≤ X₁
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: X₁ ≤ 0
t₃: l2(X₀, X₁, X₂) → l2(1, X₁, D)

Preprocessing

Eliminate variables {D,X₀,X₂} that do not contribute to the problem

Found invariant X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₉: l0(X₀) → l1(X₀)
t₁₀: l1(X₀) → l1(X₀-1) :|: 1 ≤ X₀
t₁₁: l1(X₀) → l2(X₀) :|: X₀ ≤ 0
t₁₂: l2(X₀) → l2(X₀) :|: X₀ ≤ 0

MPRF for transition t₁₀: l1(X₀) → l1(X₀-1) :|: 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

Analysing control-flow refined program

Found invariant X₀ ≤ 0 for location l2

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₉: 1 {O(1)}
t₁₀: X₀ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: X₀ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: inf {Infinity}

Sizebounds

t₉, X₀: X₀ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₁, X₀: 2⋅X₀ {O(n)}
t₁₂, X₀: 2⋅X₀ {O(n)}