Initial Problem

Start: start
Program_Vars: X₀, X₁
Temp_Vars: C, D
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁) → eval(X₀-C, D+X₁) :|: 1 ≤ D ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ C
t₁: start(X₀, X₁) → eval(X₀, X₁)

Preprocessing

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁
Temp_Vars: C, D
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁) → eval(X₀-C, D+X₁) :|: 1 ≤ D ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ C
t₁: start(X₀, X₁) → eval(X₀, X₁)

MPRF for transition t₀: eval(X₀, X₁) → eval(X₀-C, D+X₁) :|: 1 ≤ D ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ C of depth 1:

new bound:

X₀+X₁ {O(n)}

• eval: [X₀-X₁]

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}