Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₂: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: X₁+X₂+1 ≤ X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: X₁+X₂+1 ≤ X₀

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₂: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: X₁+X₂+1 ≤ X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: X₁+X₂+1 ≤ X₀

MPRF for transition t₀: l1(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: X₁+X₂+1 ≤ X₀ of depth 1:

new bound:

X₀+X₁+X₂ {O(n)}

MPRF:

l1 [X₀-X₁-X₂ ]

MPRF for transition t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: X₁+X₂+1 ≤ X₀ of depth 1:

new bound:

X₀+X₁+X₂ {O(n)}

MPRF:

l1 [X₀-X₁-X₂ ]

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+2⋅X₂+1 {O(n)}
t₂: 1 {O(1)}
t₀: X₀+X₁+X₂ {O(n)}
t₁: X₀+X₁+X₂ {O(n)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+2⋅X₂+1 {O(n)}
t₂: 1 {O(1)}
t₀: X₀+X₁+X₂ {O(n)}
t₁: X₀+X₁+X₂ {O(n)}

Sizebounds

t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₀, X₀: 2⋅X₀ {O(n)}
t₀, X₁: 3⋅X₁+X₀+X₂ {O(n)}
t₀, X₂: 3⋅X₂+X₀+X₁ {O(n)}
t₁, X₀: 2⋅X₀ {O(n)}
t₁, X₁: 3⋅X₁+X₀+X₂ {O(n)}
t₁, X₂: 3⋅X₂+X₀+X₁ {O(n)}