Initial Problem

Start: start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁, X₂) → eval(X₀, 1+X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂
t₁: eval(X₀, X₁, X₂) → eval(X₀, X₁, 1+X₂) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁
t₂: start(X₀, X₁, X₂) → eval(X₀, X₁, X₂)

Preprocessing

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁, X₂) → eval(X₀, 1+X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂
t₁: eval(X₀, X₁, X₂) → eval(X₀, X₁, 1+X₂) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁
t₂: start(X₀, X₁, X₂) → eval(X₀, X₁, X₂)

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

new bound:

X₀+X₁ {O(n)}

• eval: [X₀-X₁]

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

new bound:

X₀+X₂ {O(n)}

• eval: [X₀-X₂]

All Bounds

Timebounds

Overall timebound:2⋅X₀+X₁+X₂+1 {O(n)}
t₀: X₀+X₁ {O(n)}
t₁: X₀+X₂ {O(n)}
t₂: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+X₁+X₂+1 {O(n)}
t₀: X₀+X₁ {O(n)}
t₁: X₀+X₂ {O(n)}
t₂: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: 2⋅X₁+X₀ {O(n)}
t₀, X₂: 2⋅X₂+X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 2⋅X₁+X₀ {O(n)}
t₁, X₂: 2⋅X₂+X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}