Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₁: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₂, X₁-1, X₀+1) :|: X₀ ≤ 100 ∧ X₂ ≤ X₁

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₁: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₂, X₁-1, X₀+1) :|: X₀ ≤ 100 ∧ X₂ ≤ X₁

MPRF for transition t₀: l1(X₀, X₁, X₂) → l1(X₂, X₁-1, X₀+1) :|: X₀ ≤ 100 ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₀+X₁+X₂+101 {O(n)}

MPRF:

l1 [X₁+101-X₀-X₂ ]

All Bounds

Timebounds

Overall timebound:X₀+X₁+X₂+102 {O(n)}
t₁: 1 {O(1)}
t₀: X₀+X₁+X₂+101 {O(n)}

Costbounds

Overall costbound: X₀+X₁+X₂+102 {O(n)}
t₁: 1 {O(1)}
t₀: X₀+X₁+X₂+101 {O(n)}

Sizebounds

t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₀, X₀: 2⋅X₀+2⋅X₂+X₁+101 {O(n)}
t₀, X₁: 2⋅X₁+X₀+X₂+101 {O(n)}
t₀, X₂: 2⋅X₀+2⋅X₂+X₁+101 {O(n)}