Initial Problem

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀) → l1(X₀) :|: 1 ≤ X₀
t₁: l0(X₀) → l1(100) :|: X₀ ≤ 100 ∧ 100 ≤ X₀
t₂: l1(X₀) → l1(X₀-1) :|: 1 ≤ X₀

Preprocessing

Found invariant 0 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀) → l1(X₀) :|: 1 ≤ X₀
t₁: l0(X₀) → l1(100) :|: X₀ ≤ 100 ∧ 100 ≤ X₀
t₂: l1(X₀) → l1(X₀-1) :|: 1 ≤ X₀ ∧ 0 ≤ X₀

MPRF for transition t₂: l1(X₀) → l1(X₀-1) :|: 1 ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+102 {O(n)}

MPRF:

l1 [X₀+1 ]

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)}