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 X₁ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₁₀: l0(X₁) → l1(X₁)
t₁₁: l1(X₁) → l1(X₁-1) :|: 1 ≤ X₁
t₁₂: l1(X₁) → l2(X₁) :|: X₁ ≤ 0
t₁₃: l2(X₁) → l2(X₁) :|: X₁ ≤ 0

MPRF for transition t₁₁: l1(X₁) → l1(X₁-1) :|: 1 ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l1 [X₁ ]

Found invariant X₁ ≤ 0 for location l2

Analysing control-flow refined program

Found invariant X₁ ≤ 0 for location l2

Found invariant X₁ ≤ 0 for location l2

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₀: 1 {O(1)}
t₁₁: X₁ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₀: 1 {O(1)}
t₁₁: X₁ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: inf {Infinity}

Sizebounds

t₁₀, X₁: X₁ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₁: 2⋅X₁ {O(n)}
t₁₃, X₁: 2⋅X₁ {O(n)}