Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₂: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀-3, X₁, X₂) :|: 4 ≤ X₀
t₀: l2(X₀, X₁, X₂) → l2(X₀-1, X₁-1, X₂-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂

Preprocessing

Cut unreachable locations [l1] from the program graph

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l2
Transitions:
t₂: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₀: l2(X₀, X₁, X₂) → l2(X₀-1, X₁-1, X₂-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂

MPRF for transition t₀: l2(X₀, X₁, X₂) → l2(X₀-1, X₁-1, X₂-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l2 [X₀ ]

All Bounds

Timebounds

Overall timebound:X₀+1 {O(n)}
t₂: 1 {O(1)}
t₀: X₀ {O(n)}

Costbounds

Overall costbound: X₀+1 {O(n)}
t₂: 1 {O(1)}
t₀: X₀ {O(n)}

Sizebounds

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