Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅) :|: 0 < X₅
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 0 < X₂
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₂, X₄, X₅) :|: X₂ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 0 < X₅
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(5⋅X₀+(X₂)², 2⋅X₁, X₂, X₃, X₄, X₅) :|: X₀ < (X₁)² ∧ 0 < X₀

Preprocessing

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location l2

Found invariant 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅) :|: 0 < X₅
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 0 < X₂ ∧ 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₂, X₄, X₅) :|: X₂ ≤ 0 ∧ 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 0 < X₅ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(5⋅X₀+(X₂)², 2⋅X₁, X₂, X₃, X₄, X₅) :|: X₀ < (X₁)² ∧ 0 < X₀ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0

Analysing control-flow refined program

Found invariant 1 ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location n_l2___6

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ for location n_l1___3

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location n_l2___1

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location n_l2___2

Found invariant 1+X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ X₂ ≤ 1+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location n_l1___5

Found invariant 1 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1

Found invariant 1 ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location n_l2___4

Found invariant 1 ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location n_l2___6

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ for location n_l1___3

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location n_l2___1

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location n_l2___2

Found invariant 1+X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ X₂ ≤ 1+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 0 ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location n_l1___5

Found invariant 1 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1

Found invariant 1 ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location n_l2___4

Time-Bound by TWN-Loops:

TWN-Loops: t₁₄₀ 6⋅X₂+8⋅X₃+11 {O(n)}

TWN-Loops:

entry: t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅) :|: 0 < X₅
results in twn-loop: twn:Inv: [1 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀] , (X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀+X₂,X₁,X₂-1,X₃,X₁,X₅) :|: X₃ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 0 < X₅ ∧ 0 < X₂ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁
order: [X₂; X₀; X₁; X₃; X₄; X₅]
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
X₃: X₃
X₄: [[n == 0]] * X₄ + [[n != 0]] * X₁
X₅: X₅

Termination: true
Formula:

1 < 0 ∧ 0 < X₅
∨ 1 < 0 ∧ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₅
∨ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 1 < 0 ∧ 0 < X₅
∨ 1 < 0 ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₅
∨ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < X₅
∨ 0 < 2⋅X₂+1 ∧ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₅
∨ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 1 < 0 ∧ 0 < X₅
∨ 0 < 2⋅X₂+1 ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₅
∨ 2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 1 < 0 ∧ 0 < X₅
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₅
∨ 2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 1 < 0 ∧ 0 < X₅
∨ 2⋅X₃ < 2⋅X₀ ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₅
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 1 < 0 ∧ 0 < X₅
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₅
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 1 < 0 ∧ 0 < X₅
∨ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₅

Stabilization-Threshold for: X₃ ≤ X₀
alphas_abs: 1+2⋅X₀+2⋅X₂+2⋅X₃
M: 0
N: 2
Bound: 4⋅X₀+4⋅X₂+4⋅X₃+5 {O(n)}
Stabilization-Threshold for: 0 < X₂
alphas_abs: X₂
M: 0
N: 1
Bound: 2⋅X₂+2 {O(n)}

relevant size-bounds w.r.t. t₀:
X₀: X₃ {O(n)}
X₂: X₂ {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 6⋅X₂+8⋅X₃+11 {O(n)}

6⋅X₂+8⋅X₃+11 {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}
t₃: inf {Infinity}
t₄: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}
t₃: inf {Infinity}
t₄: inf {Infinity}

Sizebounds

t₀, X₀: X₃ {O(n)}
t₀, X₁: X₄ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₁: 5⋅X₄ {O(n)}
t₁, X₂: 4⋅X₅+X₂ {O(n)}
t₁, X₃: 4⋅X₂+8⋅X₅+X₃ {O(n)}
t₁, X₄: 2⋅X₄ {O(n)}
t₁, X₅: 2⋅X₅ {O(n)}
t₂, X₁: 6⋅X₄ {O(n)}
t₂, X₂: 2⋅X₂+4⋅X₅ {O(n)}
t₂, X₃: 2⋅X₂+4⋅X₅ {O(n)}
t₂, X₄: 2⋅X₄ {O(n)}
t₂, X₅: 2⋅X₅ {O(n)}
t₃, X₂: 2⋅X₂+4⋅X₅ {O(n)}
t₃, X₃: 2⋅X₂+4⋅X₅ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₀: 4⋅X₂+8⋅X₅ {O(n)}
t₄, X₁: 4⋅X₄ {O(n)}
t₄, X₂: 4⋅X₅ {O(n)}
t₄, X₃: 4⋅X₂+8⋅X₅ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}