Initial Problem

Start: start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: end, start, sumto
Transitions:
t₂: start(X₀, X₁) → sumto(X₀, X₁)
t₀: sumto(X₀, X₁) → end(X₀, X₁) :|: 1+X₁ ≤ X₀
t₁: sumto(X₀, X₁) → sumto(1+X₀, X₁) :|: X₀ ≤ X₁

Preprocessing

Found invariant 1+X₁ ≤ X₀ for location end

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: end, start, sumto
Transitions:
t₂: start(X₀, X₁) → sumto(X₀, X₁)
t₀: sumto(X₀, X₁) → end(X₀, X₁) :|: 1+X₁ ≤ X₀
t₁: sumto(X₀, X₁) → sumto(1+X₀, X₁) :|: X₀ ≤ X₁

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

new bound:

X₀+X₁+1 {O(n)}

• sumto: [1+X₁-X₀]

All Bounds

Timebounds

Overall timebound:X₀+X₁+3 {O(n)}
t₀: 1 {O(1)}
t₁: X₀+X₁+1 {O(n)}
t₂: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₁+3 {O(n)}
t₀: 1 {O(1)}
t₁: X₀+X₁+1 {O(n)}
t₂: 1 {O(1)}

Sizebounds

t₀, X₀: 3⋅X₀+X₁+1 {O(n)}
t₀, X₁: 2⋅X₁ {O(n)}
t₁, X₀: 2⋅X₀+X₁+1 {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}