Initial Problem

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

Preprocessing

Problem after Preprocessing

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

MPRF for transition t₁: l1(X₀, X₁, X₂) → l1(X₀+X₁, X₁-X₂, X₂+1) :|: 1 ≤ X₀ of depth 3:

new bound:

27⋅X₀+27⋅X₁+27⋅X₂+55 {O(n)}

All Bounds

Timebounds

Overall timebound:27⋅X₀+27⋅X₁+27⋅X₂+56 {O(n)}
t₀: 1 {O(1)}
t₁: 27⋅X₀+27⋅X₁+27⋅X₂+55 {O(n)}

Costbounds

Overall costbound: 27⋅X₀+27⋅X₁+27⋅X₂+56 {O(n)}
t₀: 1 {O(1)}
t₁: 27⋅X₀+27⋅X₁+27⋅X₂+55 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 121014⋅X₀⋅X₁⋅X₂+19683⋅X₀⋅X₀⋅X₀+19683⋅X₁⋅X₁⋅X₁+21141⋅X₂⋅X₂⋅X₂+59049⋅X₀⋅X₀⋅X₁+59049⋅X₀⋅X₁⋅X₁+60507⋅X₀⋅X₀⋅X₂+60507⋅X₁⋅X₁⋅X₂+61965⋅X₀⋅X₂⋅X₂+61965⋅X₁⋅X₂⋅X₂+121743⋅X₀⋅X₀+121797⋅X₁⋅X₁+127791⋅X₂⋅X₂+243540⋅X₀⋅X₁+249534⋅X₀⋅X₂+249588⋅X₁⋅X₂+250993⋅X₀+251104⋅X₁+257264⋅X₂+172480 {O(n^3)}
t₁, X₁: 1458⋅X₀⋅X₁+1512⋅X₀⋅X₂+1512⋅X₁⋅X₂+729⋅X₀⋅X₀+729⋅X₁⋅X₁+783⋅X₂⋅X₂+2997⋅X₀+2998⋅X₁+3109⋅X₂+3080 {O(n^2)}
t₁, X₂: 27⋅X₀+27⋅X₁+28⋅X₂+55 {O(n)}