Initial Problem

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

Preprocessing

Problem after Preprocessing

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

Solv. Size Bound: t₀: l1→l1 for X₁

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

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

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

new bound:

X₀+X₁ {O(n)}

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

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