Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀+1, X₁+X₀+1, X₂) :|: X₁ ≤ X₀
t₂: l1(X₀, X₁, X₂) → l1(X₀-X₂, X₁-2⋅X₂, X₂-1) :|: X₁ ≤ X₀
Preprocessing
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀+1, X₁+X₀+1, X₂) :|: X₁ ≤ X₀
t₂: l1(X₀, X₁, X₂) → l1(X₀-X₂, X₁-2⋅X₂, X₂-1) :|: X₁ ≤ X₀
Analysing control-flow refined program
Time-Bound by TWN-Loops:
TWN-Loops: t₅₂ 16⋅X₁+32⋅X₂+8⋅X₀+24 {O(n)}
TWN-Loops:
entry: t₅₆: l1(X₀, X₁, X₂) → n_l1___2(X₀-X₂, X₁-2⋅X₂, X₂-1) :|: X₁ ≤ X₀
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀-X₂,X₁-2⋅X₂,X₂-1) :|: 1+X₁+X₂ ≤ X₀ ∧ X₁ ≤ X₀
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]] * -2⋅X₂ * n^1 + [[n != 0, n != 1]] * n^2 + [[n != 0, n != 1]] * -1 * n^1
Termination: true
Formula:
1 < 0
∨ 1 < 0 ∧ 0 < 2⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 2+2⋅X₁+2⋅X₂ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+3 ∧ 2⋅X₂+3 ≤ 0
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+3 ∧ 2⋅X₂+3 ≤ 0 ∧ 2+2⋅X₁+2⋅X₂ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₁+2⋅X₂
∨ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < 2⋅X₂+1 ∧ 0 < 2⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 2⋅X₂+1 ∧ 2+2⋅X₁+2⋅X₂ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+3 ∧ 2⋅X₂+3 ≤ 0
∨ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+3 ∧ 2⋅X₂+3 ≤ 0 ∧ 2+2⋅X₁+2⋅X₂ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₁+2⋅X₂
∨ 2⋅X₁ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 1 < 0
∨ 2⋅X₁ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 0 < 2⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₁ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2+2⋅X₁+2⋅X₂ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+3 ∧ 2⋅X₂+3 ≤ 0
∨ 2⋅X₁ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+3 ∧ 2⋅X₂+3 ≤ 0 ∧ 2+2⋅X₁+2⋅X₂ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₁+2⋅X₂
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₁ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₁ ∧ 1 < 0
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₁ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₁ ∧ 0 < 2⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₁ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₁ ∧ 2+2⋅X₁+2⋅X₂ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+3 ∧ 2⋅X₂+3 ≤ 0
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₁ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+3 ∧ 2⋅X₂+3 ≤ 0 ∧ 2+2⋅X₁+2⋅X₂ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2+2⋅X₁+2⋅X₂
Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: 1+2⋅X₀+2⋅X₁+2⋅X₂
M: 0
N: 2
Bound: 4⋅X₀+4⋅X₁+4⋅X₂+5 {O(n)}
Stabilization-Threshold for: 1+X₁+X₂ ≤ X₀
alphas_abs: 3+2⋅X₀+2⋅X₁+2⋅X₂
M: 0
N: 2
Bound: 4⋅X₀+4⋅X₁+4⋅X₂+9 {O(n)}
relevant size-bounds w.r.t. t₅₆:
X₀: X₀+X₂ {O(n)}
X₁: 2⋅X₁+2⋅X₂ {O(n)}
X₂: X₂+1 {O(n)}
Runtime-bound of t₅₆: 1 {O(1)}
Results in: 16⋅X₁+32⋅X₂+8⋅X₀+24 {O(n)}
16⋅X₁+32⋅X₂+8⋅X₀+24 {O(n)}
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}