Initial Problem
Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀) → l1(X₀)
t₁: l1(X₀) → l1(X₀-1) :|: 2 ≤ X₀
t₂: l1(X₀) → l1(X₀-1)
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) :|: 2 ≤ X₀
t₂: l1(X₀) → l1(X₀-1)
MPRF for transition t₁: l1(X₀) → l1(X₀-1) :|: 2 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l1 [X₀ ]
Analysing control-flow refined program
Found invariant 1 ≤ X₀ for location n_l1___1
MPRF for transition t₃₃: l1(X₀) → n_l1___1(X₀-1) :|: 2 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
n_l1___1 [X₀-2 ]
l1 [X₀-1 ]
MPRF for transition t₃₁: n_l1___1(X₀) → n_l1___1(X₀-1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
n_l1___1 [X₀ ]
l1 [X₀ ]
MPRF for transition t₃₂: n_l1___1(X₀) → l1(X₀-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
n_l1___1 [X₀ ]
l1 [X₀-1 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: inf {Infinity}
Sizebounds
t₀, X₀: X₀ {O(n)}