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(X₀-1, X₁, X₂-1) :|: X₁+1 ≤ X₀ ∧ X₁+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(X₀-1, X₁, X₂-1) :|: X₁+1 ≤ X₀ ∧ X₁+1 ≤ X₂

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

new bound:

X₁+X₂ {O(n)}

MPRF:

l1 [X₂-X₁ ]

All Bounds

Timebounds

Overall timebound:X₁+X₂+1 {O(n)}
t₁: 1 {O(1)}
t₀: X₁+X₂ {O(n)}

Costbounds

Overall costbound: X₁+X₂+1 {O(n)}
t₁: 1 {O(1)}
t₀: X₁+X₂ {O(n)}

Sizebounds

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