Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₂: 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) → l2(X₀, X₁, D) :|: X₁ ≤ X₀

Preprocessing

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

Found invariant X₁ ≤ X₀ for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₀, X₁) → l1(X₀, X₁)
t₈: l1(X₀, X₁) → l1(1+X₀, X₁) :|: 1+X₀ ≤ X₁
t₉: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ X₀

MPRF for transition t₈: l1(X₀, X₁) → l1(1+X₀, X₁) :|: 1+X₀ ≤ X₁ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

l1 [X₁-X₀ ]

All Bounds

Timebounds

Overall timebound:X₀+X₁+2 {O(n)}
t₇: 1 {O(1)}
t₈: X₀+X₁ {O(n)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₁+2 {O(n)}
t₇: 1 {O(1)}
t₈: X₀+X₁ {O(n)}
t₉: 1 {O(1)}

Sizebounds

t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₈, X₀: 2⋅X₀+X₁ {O(n)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: 3⋅X₀+X₁ {O(n)}
t₉, X₁: 2⋅X₁ {O(n)}