Initial Problem

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

Preprocessing

Problem after Preprocessing

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

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

new bound:

X₀ {O(n)}

MPRF:

l1 [X₀ ]

Analysing control-flow refined program

Found invariant 1+X₀ ≤ 0 for location n_l1___2

Found invariant 0 ≤ X₀ for location n_l1___1

MPRF for transition t₃₂: n_l1___1(X₀) → n_l1___1(X₀-1) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

n_l1___1 [X₀+1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: X₀ {O(n)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: X₀ {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}