Initial Problem

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f1
Transitions:
t₀: f0(X₀, X₁) → f1(X₀, X₁)
t₁: f1(X₀, X₁) → f1(X₀-X₁, 1+X₁) :|: 1 ≤ X₀

Preprocessing

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f1
Transitions:
t₀: f0(X₀, X₁) → f1(X₀, X₁)
t₁: f1(X₀, X₁) → f1(X₀-X₁, 1+X₁) :|: 1 ≤ X₀

MPRF for transition t₁: f1(X₀, X₁) → f1(X₀-X₁, 1+X₁) :|: 1 ≤ X₀ of depth 2:

new bound:

8⋅X₀+8⋅X₁+9 {O(n)}

MPRF:

• f1: [1-X₁; X₀]

All Bounds

Timebounds

Overall timebound:8⋅X₀+8⋅X₁+10 {O(n)}
t₀: 1 {O(1)}
t₁: 8⋅X₀+8⋅X₁+9 {O(n)}

Costbounds

Overall costbound: 8⋅X₀+8⋅X₁+10 {O(n)}
t₀: 1 {O(1)}
t₁: 8⋅X₀+8⋅X₁+9 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: 144⋅X₀⋅X₁+64⋅X₀⋅X₀+80⋅X₁⋅X₁+153⋅X₀+172⋅X₁+90 {O(n^2)}
t₁, X₁: 8⋅X₀+9⋅X₁+9 {O(n)}