Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₁: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀, X₁+X₂, X₂) :|: X₁ ≤ X₀ ∧ 1 ≤ X₂

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₁: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀, X₁+X₂, X₂) :|: X₁ ≤ X₀ ∧ 1 ≤ X₂

Solv. Size Bound: t₀: l1→l1 for X₁

cycle: [t₀: l1→l1]
loop: (X₁ ≤ X₀ ∧ 1 ≤ X₂,(X₁,X₂) -> (X₁+X₂,X₂)
overappr. closed-form: X₂⋅n+X₁ {O(n^2)}
runtime bound: X₀+X₁+2 {O(n)}

Solv. Size Bound - Lifting for t₀: l1→l1 and X₁: X₀⋅X₂+X₁⋅X₂+2⋅X₂+X₁ {O(n^2)}

MPRF for transition t₀: l1(X₀, X₁, X₂) → l1(X₀, X₁+X₂, X₂) :|: X₁ ≤ X₀ ∧ 1 ≤ X₂ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

All Bounds

Timebounds

Overall timebound:X₀+X₁+2 {O(n)}
t₀: X₀+X₁+1 {O(n)}
t₁: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₁+2 {O(n)}
t₀: X₀+X₁+1 {O(n)}
t₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₀⋅X₂+X₁⋅X₂+2⋅X₂+X₁ {O(n^2)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}