Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₂: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂-1) :|: 0 ≤ X₀ ∧ X₂ ≤ (X₁)³
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁+X₂, X₂-1) :|: 0 ≤ X₀ ∧ X₂ ≤ (X₁)³
Preprocessing
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₂: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂-1) :|: 0 ≤ X₀ ∧ X₂ ≤ (X₁)³
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁+X₂, X₂-1) :|: 0 ≤ X₀ ∧ X₂ ≤ (X₁)³
MPRF for transition t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂-1) :|: 0 ≤ X₀ ∧ X₂ ≤ (X₁)³ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l1 [X₀+1 ]
Analysing control-flow refined program
Eliminate variables {X₁,X₂} that do not contribute to the problem
Found invariant 0 ≤ 1+X₀ for location n_l1___2
Found invariant 0 ≤ X₀ for location n_l1___1
MPRF for transition t₅₂: n_l1___1(X₀) → n_l1___2(X₀-1) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ of depth 1:
new bound:
2⋅X₀+3 {O(n)}
MPRF:
n_l1___1 [X₀+1 ]
n_l1___2 [X₀+1 ]
MPRF for transition t₅₃: n_l1___2(X₀) → n_l1___1(X₀) :|: 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
2⋅X₀+4 {O(n)}
MPRF:
n_l1___1 [X₀+1 ]
n_l1___2 [X₀+2 ]
MPRF for transition t₅₄: n_l1___2(X₀) → n_l1___2(X₀-1) :|: 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
2⋅X₀+2 {O(n)}
MPRF:
n_l1___1 [X₀ ]
n_l1___2 [X₀+1 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₂: 1 {O(1)}
t₀: X₀+1 {O(n)}
t₁: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
t₂: 1 {O(1)}
t₀: X₀+1 {O(n)}
t₁: inf {Infinity}
Sizebounds
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₀, X₀: 2⋅X₀+1 {O(n)}
t₁, X₀: 2⋅X₀+1 {O(n)}