Initial Problem

Start: start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: group3, start, zip3
Transitions:
t₁: group3(X₀, X₁, X₂) → group3(X₀-3, X₁, X₂) :|: 4 ≤ X₀
t₂: start(X₀, X₁, X₂) → zip3(X₀, X₁, X₂)
t₀: zip3(X₀, X₁, X₂) → zip3(X₀-1, X₁-1, X₂-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂

Preprocessing

Cut unreachable locations [group3] from the program graph

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: start, zip3
Transitions:
t₂: start(X₀, X₁, X₂) → zip3(X₀, X₁, X₂)
t₀: zip3(X₀, X₁, X₂) → zip3(X₀-1, X₁-1, X₂-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂

MPRF for transition t₀: zip3(X₀, X₁, X₂) → zip3(X₀-1, X₁-1, X₂-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ of depth 1:

new bound:

X₂ {O(n)}

• zip3: [X₂]

All Bounds

Timebounds

Overall timebound:X₂+1 {O(n)}
t₀: X₂ {O(n)}
t₂: 1 {O(1)}

Costbounds

Overall costbound: X₂+1 {O(n)}
t₀: X₂ {O(n)}
t₂: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}