Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 0 < X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₂, X₁, X₂-1) :|: 0 < X₂
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 0
t₃: l2(X₀, X₁, X₂) → l2(5⋅X₀+(X₂)², 2⋅X₁, X₂) :|: X₀ < (X₁)²

Preprocessing

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l2

Found invariant 1 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 0 < X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₂, X₁, X₂-1) :|: 0 < X₂ ∧ 1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ 1 ≤ X₀
t₃: l2(X₀, X₁, X₂) → l2(5⋅X₀+(X₂)², 2⋅X₁, X₂) :|: X₀ < (X₁)² ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀

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

new bound:

X₂ {O(n)}

MPRF:

l1 [X₂ ]

Analysing control-flow refined program

Eliminate variables {X₁} that do not contribute to the problem

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l2

Found invariant X₂ ≤ 0 for location n_l2___1

Found invariant 1 ≤ X₀ for location l1

MPRF for transition t₅₀: l1(X₀, X₂) → l1(X₀+X₂, X₂-1) :|: 0 < X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l1 [X₂ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}
t₃: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}
t₃: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 2⋅X₂⋅X₂+2⋅X₂+X₀ {O(n^2)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: 2⋅X₂⋅X₂+2⋅X₀+2⋅X₂ {O(n^2)}
t₂, X₁: 2⋅X₁ {O(n)}
t₂, X₂: 2⋅X₂ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}