Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(3⋅X₀+2⋅X₁+(X₂)², -5⋅X₀-3⋅X₁, X₂, X₃-1) :|: 1 ≤ X₃
t₂: l1(X₀, X₁, X₂, X₃) → l1(3⋅X₀+2⋅X₁+(X₂)², -5⋅X₀-3⋅X₁, X₂, X₃-2) :|: 1 ≤ X₃
t₃: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₀) :|: X₃ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃-1) :|: 1 ≤ X₃

Preprocessing

Found invariant X₃ ≤ X₀ for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(3⋅X₀+2⋅X₁+(X₂)², -5⋅X₀-3⋅X₁, X₂, X₃-1) :|: 1 ≤ X₃
t₂: l1(X₀, X₁, X₂, X₃) → l1(3⋅X₀+2⋅X₁+(X₂)², -5⋅X₀-3⋅X₁, X₂, X₃-2) :|: 1 ≤ X₃
t₃: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₀) :|: X₃ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃-1) :|: 1 ≤ X₃ ∧ X₃ ≤ X₀

MPRF for transition t₁: l1(X₀, X₁, X₂, X₃) → l1(Temp_Int₁₂₅+3⋅X₀+2⋅X₁, -5⋅X₀-3⋅X₁, X₂, X₃-1) :|: 1 ≤ X₃ ∧ 0 ≤ Temp_Int₁₂₅ of depth 1:

new bound:

X₃ {O(n)}

• l1: [X₃]

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃) → l1(Temp_Int₁₂₆+3⋅X₀+2⋅X₁, -5⋅X₀-3⋅X₁, X₂, X₃-2) :|: 1 ≤ X₃ ∧ 0 ≤ Temp_Int₁₂₆ of depth 1:

new bound:

X₃ {O(n)}

• l1: [X₃]

MPRF for transition t₄: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃-1) :|: 1 ≤ X₃ ∧ X₃ ≤ X₀ of depth 1:

new bound:

22164⋅X₂⋅X₂+30338⋅X₁+47863⋅X₀ {O(n^2)}

• l2: [X₃]

Found invariant 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location l2_v1

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l2

All Bounds

Timebounds

Overall timebound:22164⋅X₂⋅X₂+2⋅X₃+30338⋅X₁+47863⋅X₀+2 {O(n^2)}
t₀: 1 {O(1)}
t₁: X₃ {O(n)}
t₂: X₃ {O(n)}
t₃: 1 {O(1)}
t₄: 22164⋅X₂⋅X₂+30338⋅X₁+47863⋅X₀ {O(n^2)}

Costbounds

Overall costbound: 22164⋅X₂⋅X₂+2⋅X₃+30338⋅X₁+47863⋅X₀+2 {O(n^2)}
t₀: 1 {O(1)}
t₁: X₃ {O(n)}
t₂: X₃ {O(n)}
t₃: 1 {O(1)}
t₄: 22164⋅X₂⋅X₂+30338⋅X₁+47863⋅X₀ {O(n^2)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: 472⋅X₂⋅X₂+1016⋅X₀+644⋅X₁ {O(n^2)}
t₁, X₁: 806⋅X₂⋅X₂+1108⋅X₁+1748⋅X₀ {O(n^2)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: 21692⋅X₂⋅X₂+29694⋅X₁+46846⋅X₀ {O(n^2)}
t₂, X₁: 37308⋅X₂⋅X₂+51088⋅X₁+80598⋅X₀ {O(n^2)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: 22164⋅X₂⋅X₂+30338⋅X₁+47863⋅X₀ {O(n^2)}
t₃, X₁: 38114⋅X₂⋅X₂+52197⋅X₁+82346⋅X₀ {O(n^2)}
t₃, X₂: 3⋅X₂ {O(n)}
t₃, X₃: 22164⋅X₂⋅X₂+30338⋅X₁+47863⋅X₀ {O(n^2)}
t₄, X₀: 22164⋅X₂⋅X₂+30338⋅X₁+47863⋅X₀ {O(n^2)}
t₄, X₁: 38114⋅X₂⋅X₂+52197⋅X₁+82346⋅X₀ {O(n^2)}
t₄, X₂: 3⋅X₂ {O(n)}
t₄, X₃: 22164⋅X₂⋅X₂+30338⋅X₁+47863⋅X₀ {O(n^2)}