Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₂: l0(X₀, X₁, X₂) → l1(0, 0, X₂) :|: 1 ≤ X₂
t₀: l1(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: X₁+1 ≤ X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀+1, 0, X₂) :|: X₀+2 ≤ X₂ ∧ X₀ ≤ X₁

Preprocessing

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₂: l0(X₀, X₁, X₂) → l1(0, 0, X₂) :|: 1 ≤ X₂
t₀: l1(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: X₁+1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀+1, 0, X₂) :|: X₀+2 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

MPRF for transition t₁: l1(X₀, X₁, X₂) → l1(X₀+1, 0, X₂) :|: X₀+2 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₀: l1(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: X₁+1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+X₂ {O(n^2)}

Analysing control-flow refined program

Found invariant 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___2

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___1

MPRF for transition t₃₉: n_l1___1(X₀, X₁, X₂) → n_l1___2(X₀+1, 0, X₂) :|: 1 ≤ X₁ ∧ 2+X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₄₀: n_l1___2(X₀, X₁, X₂) → n_l1___1(X₀, X₁+1, X₂) :|: 1+X₁ ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₃₈: n_l1___1(X₀, X₁, X₂) → n_l1___1(X₀, X₁+1, X₂) :|: 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+5⋅X₂+4 {O(n^2)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:X₂⋅X₂+2⋅X₂+1 {O(n^2)}
t₀: X₂⋅X₂+X₂ {O(n^2)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}

Costbounds

Overall costbound: X₂⋅X₂+2⋅X₂+1 {O(n^2)}
t₀: X₂⋅X₂+X₂ {O(n^2)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}

Sizebounds

t₀, X₀: X₂ {O(n)}
t₀, X₁: X₂⋅X₂+X₂ {O(n^2)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: 0 {O(1)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: 0 {O(1)}
t₂, X₁: 0 {O(1)}
t₂, X₂: X₂ {O(n)}