Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C, D
Locations: l0, l1
Transitions:
t₁: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀-C, X₁+D) :|: X₁+1 ≤ X₀ ∧ 0 ≤ C ∧ 1 ≤ D

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C, D
Locations: l0, l1
Transitions:
t₁: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀-C, X₁+D) :|: X₁+1 ≤ X₀ ∧ 0 ≤ C ∧ 1 ≤ D

MPRF for transition t₀: l1(X₀, X₁) → l1(X₀-C, X₁+D) :|: X₁+1 ≤ X₀ ∧ 0 ≤ C ∧ 1 ≤ D of depth 1:

new bound:

X₀+X₁ {O(n)}

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)}