Initial Problem

Start: start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁, X₂) → eval(X₂, X₁-1, 1+X₀) :|: X₀ ≤ 100 ∧ X₂ ≤ X₁
t₁: 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(X₂, X₁-1, 1+X₀) :|: X₀ ≤ 100 ∧ X₂ ≤ X₁
t₁: start(X₀, X₁, X₂) → eval(X₀, X₁, X₂)

MPRF for transition t₀: eval(X₀, X₁, X₂) → eval(X₂, X₁-1, 1+X₀) :|: X₀ ≤ 100 ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₀+X₁+X₂+101 {O(n)}

• eval: [101+X₁-X₀-X₂]

All Bounds

Timebounds

Overall timebound:X₀+X₁+X₂+102 {O(n)}
t₀: X₀+X₁+X₂+101 {O(n)}
t₁: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₁+X₂+102 {O(n)}
t₀: X₀+X₁+X₂+101 {O(n)}
t₁: 1 {O(1)}

Sizebounds

t₀, X₀: 2⋅X₀+2⋅X₂+X₁+101 {O(n)}
t₀, X₁: 2⋅X₁+X₀+X₂+101 {O(n)}
t₀, X₂: 2⋅X₀+2⋅X₂+X₁+101 {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}