Initial Problem

Start: start
Program_Vars: X₀
Temp_Vars:
Locations: a, start
Transitions:
t₂: a(X₀) → a(X₀-1) :|: 1 ≤ X₀
t₀: start(X₀) → a(X₀) :|: 1 ≤ X₀
t₁: start(X₀) → a(100) :|: X₀ ≤ 100 ∧ 100 ≤ X₀

Preprocessing

Found invariant 0 ≤ X₀ for location a

Problem after Preprocessing

Start: start
Program_Vars: X₀
Temp_Vars:
Locations: a, start
Transitions:
t₂: a(X₀) → a(X₀-1) :|: 1 ≤ X₀ ∧ 0 ≤ X₀
t₀: start(X₀) → a(X₀) :|: 1 ≤ X₀
t₁: start(X₀) → a(100) :|: X₀ ≤ 100 ∧ 100 ≤ X₀

MPRF for transition t₂: a(X₀) → a(X₀-1) :|: 1 ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+102 {O(n)}

• a: [1+X₀]

All Bounds

Timebounds

Overall timebound:X₀+104 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+102 {O(n)}

Costbounds

Overall costbound: X₀+104 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+102 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₁, X₀: 100 {O(1)}
t₂, X₀: X₀+100 {O(n)}