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:
t₆: l0(X₀, X₁) → l1(X₀, X₁)
t₇: l1(X₀, X₁) → l1(1+X₀, X₁) :|: 1+X₀ ≤ X₁
t₈: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ X₀

MPRF for transition t₇: l1(X₀, X₁) → l1(1+X₀, X₁) :|: 1+X₀ ≤ X₁ of depth 1:

new bound:

X₀+X₁ {O(n)}

All Bounds

Timebounds

Overall timebound:X₀+X₁+2 {O(n)}
t₆: 1 {O(1)}
t₇: X₀+X₁ {O(n)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₁+2 {O(n)}
t₆: 1 {O(1)}
t₇: X₀+X₁ {O(n)}
t₈: 1 {O(1)}

Sizebounds

t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: 2⋅X₀+X₁ {O(n)}
t₇, X₁: X₁ {O(n)}
t₈, X₀: 3⋅X₀+X₁ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}