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+X₂, -X₂-1, X₂) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁

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+X₂, -X₂-1, X₂) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁

MPRF for transition t₁: l1(X₀, X₁, X₂) → l1(X₀+X₁+X₂, -X₂-1, X₂) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

l1 [X₀+X₁+1 ]

All Bounds

Timebounds

Overall timebound:X₀+X₁+2 {O(n)}
t₀: 1 {O(1)}
t₁: X₀+X₁+1 {O(n)}

Costbounds

Overall costbound: X₀+X₁+2 {O(n)}
t₀: 1 {O(1)}
t₁: X₀+X₁+1 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 4⋅X₀⋅X₂+4⋅X₁⋅X₂+X₀⋅X₁+X₁⋅X₁+3⋅X₀+4⋅X₁+8⋅X₂+4 {O(n^2)}
t₁, X₁: 2⋅X₂+2 {O(n)}
t₁, X₂: X₂ {O(n)}