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+X₀, X₂) :|: X₁ ≤ X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀-X₂, X₁+(X₂)², X₂-1) :|: X₁ ≤ X₀
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+X₀, X₂) :|: X₁ ≤ X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀-X₂, X₁+(X₂)², X₂-1) :|: X₁ ≤ X₀
TWN. Size Bound: t₁: l1→l1 for X₁
cycle: [t₁: l1→l1]
loop: (X₁ ≤ X₀,(X₀,X₁,X₂) -> (X₀-X₂,X₁+(X₂)²,X₂-1)
order: [X₂; X₀; X₁]
closed-form:
X₂: X₂ + [[n != 0]] * -1 * n^1
X₀: X₀ + [[n != 0]] * -X₂ * n^1 + [[n != 0, n != 1]] * 1/2 * n^2 + [[n != 0, n != 1]] * -1/2 * n^1
X₁: X₁ + [[n != 0]] * (X₂)² * n^1 + [[n != 0, n != 1]] * 1/3 * n^3 + [[n != 0, n != 1]] * -1/2-X₂ * n^2 + [[n != 0, n != 1]] * 1/6+X₂ * n^1
Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: 3+3⋅X₀+3⋅X₁+6⋅X₂+3⋅(X₂)²
M: 0
N: 3
Bound: 6⋅X₂⋅X₂+12⋅X₂+6⋅X₀+6⋅X₁+10 {O(n^2)}
loop: (X₁ ≤ X₀,(X₁,X₂) -> (X₁+(X₂)²,X₂-1)
closed-form: X₁ + [[n != 0]] * (X₂)² * n^1 + [[n != 0, n != 1]] * 1/3 * n^3 + [[n != 0, n != 1]] * -1/2-X₂ * n^2 + [[n != 0, n != 1]] * 1/6+X₂ * n^1
runtime bound: 6⋅X₂⋅X₂+12⋅X₂+6⋅X₀+6⋅X₁+12 {O(n^2)}
TWN Size Bound - Lifting for t₁: l1→l1 and X₁: inf {Infinity}
TWN Size Bound - Lifting for t₁: l1→l1 and X₁: inf {Infinity}
Analysing control-flow refined program
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: inf {Infinity}
t₁: inf {Infinity}
t₂: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₀: inf {Infinity}
t₁: inf {Infinity}
t₂: 1 {O(1)}
Sizebounds
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}