Initial Problem

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

Preprocessing

Problem after Preprocessing

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

MPRF for transition t₁: l1(X₀, X₁) → l1(X₀-X₁, X₁+1) :|: 1 ≤ X₀ of depth 2:

new bound:

8⋅X₀+8⋅X₁+9 {O(n)}

MPRF:

l1 [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)}