Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂+1, X₃)
t₉: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, 0, X₃+1)
t₄: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₁
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₂
t₁₀: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₃: l6(X₀, X₁, X₂, X₃) → l3(X₀, X₁, 0, 0) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₁: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀

Preprocessing

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂+1, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₉: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, 0, X₃+1) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₀: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₃: l6(X₀, X₁, X₂, X₃) → l3(X₀, X₁, 0, 0) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₁: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₂: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀

MPRF for transition t₇: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₉: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, 0, X₃+1) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

TWN: t₄: l3→l4

cycle: [t₄: l3→l4; t₆: l4→l1; t₈: l1→l3]
loop: (X₃+1 ≤ X₁ ∧ X₂+1 ≤ X₀,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂+1,X₃)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
X₃: X₃

Termination: true
Formula:

1 < 0 ∧ X₃+1 < X₁
∨ 1 < 0 ∧ X₃+1 ≤ X₁ ∧ X₁ ≤ X₃+1
∨ X₂+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 < X₁
∨ X₂+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₁ ∧ X₁ ≤ X₃+1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂+1 ≤ X₀ ∧ X₀ ≤ X₂+1 ∧ X₃+1 < X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂+1 ≤ X₀ ∧ X₀ ≤ X₂+1 ∧ X₃+1 ≤ X₁ ∧ X₁ ≤ X₃+1

Stabilization-Threshold for: X₂+1 ≤ X₀
alphas_abs: X₂+1+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+4 {O(n)}
loop: (X₃+1 ≤ X₁ ∧ X₂+1 ≤ X₀,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂+1,X₃)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
X₃: X₃

Termination: true
Formula:

1 < 0 ∧ X₃+1 < X₁
∨ 1 < 0 ∧ X₃+1 ≤ X₁ ∧ X₁ ≤ X₃+1
∨ X₂+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 < X₁
∨ X₂+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₃+1 ≤ X₁ ∧ X₁ ≤ X₃+1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂+1 ≤ X₀ ∧ X₀ ≤ X₂+1 ∧ X₃+1 < X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂+1 ≤ X₀ ∧ X₀ ≤ X₂+1 ∧ X₃+1 ≤ X₁ ∧ X₁ ≤ X₃+1

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

TWN - Lifting for t₄: l3→l4 of 2⋅X₀+2⋅X₂+7 {O(n)}

relevant size-bounds w.r.t. t₃:
X₀: X₀ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₃: 1 {O(1)}
Results in: 2⋅X₀+7 {O(n)}

TWN - Lifting for t₄: l3→l4 of 2⋅X₀+2⋅X₂+7 {O(n)}

relevant size-bounds w.r.t. t₉:
X₀: X₀ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₉: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+7⋅X₁ {O(n^2)}

TWN: t₆: l4→l1

TWN - Lifting for t₆: l4→l1 of 2⋅X₀+2⋅X₂+7 {O(n)}

relevant size-bounds w.r.t. t₃:
X₀: X₀ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₃: 1 {O(1)}
Results in: 2⋅X₀+7 {O(n)}

TWN - Lifting for t₆: l4→l1 of 2⋅X₀+2⋅X₂+7 {O(n)}

relevant size-bounds w.r.t. t₉:
X₀: X₀ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₉: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+7⋅X₁ {O(n^2)}

TWN: t₈: l1→l3

TWN - Lifting for t₈: l1→l3 of 2⋅X₀+2⋅X₂+7 {O(n)}

relevant size-bounds w.r.t. t₃:
X₀: X₀ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₃: 1 {O(1)}
Results in: 2⋅X₀+7 {O(n)}

TWN - Lifting for t₈: l1→l3 of 2⋅X₀+2⋅X₂+7 {O(n)}

relevant size-bounds w.r.t. t₉:
X₀: X₀ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₉: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+7⋅X₁ {O(n^2)}

Chain transitions t₆: l4→l1 and t₈: l1→l3 to t₇₁: l4→l3

Chain transitions t₇: l4→l2 and t₉: l2→l3 to t₇₂: l4→l3

Chain transitions t₃: l6→l3 and t₅: l3→l5 to t₇₃: l6→l5

Chain transitions t₇₂: l4→l3 and t₅: l3→l5 to t₇₄: l4→l5

Chain transitions t₇₂: l4→l3 and t₄: l3→l4 to t₇₅: l4→l4

Chain transitions t₃: l6→l3 and t₄: l3→l4 to t₇₆: l6→l4

Chain transitions t₇₁: l4→l3 and t₄: l3→l4 to t₇₇: l4→l4

Chain transitions t₇₁: l4→l3 and t₅: l3→l5 to t₇₈: l4→l5

Analysing control-flow refined program

Cut unsatisfiable transition t₇₃: l6→l5

Cut unsatisfiable transition t₇₈: l4→l5

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4

Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3

MPRF for transition t₇₅: l4(X₀, X₁, X₂, X₃) -{3}> l4(X₀, X₁, 0, 1+X₃) :|: X₀ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ X₃+1 ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

TWN: t₇₇: l4→l4

cycle: [t₇₇: l4→l4]
loop: (X₂+1 ≤ X₀ ∧ X₃+1 ≤ X₁,(X₀,X₁,X₂,X₃) -> (X₀,X₁,1+X₂,X₃)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
X₃: X₃

Termination: true
Formula:

X₃+1 < X₁ ∧ 1 < 0
∨ X₃+1 < X₁ ∧ X₂+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₃+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂+1 ≤ X₀ ∧ X₀ ≤ X₂+1
∨ X₃+1 ≤ X₁ ∧ X₁ ≤ X₃+1 ∧ 1 < 0
∨ X₃+1 ≤ X₁ ∧ X₁ ≤ X₃+1 ∧ X₂+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₃+1 ≤ X₁ ∧ X₁ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂+1 ≤ X₀ ∧ X₀ ≤ X₂+1

Stabilization-Threshold for: X₂+1 ≤ X₀
alphas_abs: X₂+1+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+4 {O(n)}
loop: (X₂+1 ≤ X₀ ∧ X₃+1 ≤ X₁,(X₀,X₁,X₂,X₃) -> (X₀,X₁,1+X₂,X₃)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
X₃: X₃

Termination: true
Formula:

X₃+1 < X₁ ∧ 1 < 0
∨ X₃+1 < X₁ ∧ X₂+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₃+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂+1 ≤ X₀ ∧ X₀ ≤ X₂+1
∨ X₃+1 ≤ X₁ ∧ X₁ ≤ X₃+1 ∧ 1 < 0
∨ X₃+1 ≤ X₁ ∧ X₁ ≤ X₃+1 ∧ X₂+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₃+1 ≤ X₁ ∧ X₁ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂+1 ≤ X₀ ∧ X₀ ≤ X₂+1

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

TWN - Lifting for t₇₇: l4→l4 of 2⋅X₀+2⋅X₂+7 {O(n)}

relevant size-bounds w.r.t. t₇₆:
X₀: X₀ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₇₆: 1 {O(1)}
Results in: 2⋅X₀+7 {O(n)}

TWN - Lifting for t₇₇: l4→l4 of 2⋅X₀+2⋅X₂+7 {O(n)}

relevant size-bounds w.r.t. t₇₅:
X₀: X₀ {O(n)}
X₂: 0 {O(1)}
Runtime-bound of t₇₅: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+7⋅X₁ {O(n^2)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Cut unsatisfiable transition t₅: l3→l5

Cut unsatisfiable transition t₁₈₇: n_l3___7→l5

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___6

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___9

Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___2

Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___3

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___8

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l1___5

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3

Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___1

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l2___4

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___7

MPRF for transition t₁₆₇: n_l1___1(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂+1, X₃) :|: 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF for transition t₁₇₀: n_l2___4(X₀, X₁, X₂, X₃) → n_l3___3(X₀, X₁, 0, X₃+1) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₁₇₂: n_l3___3(X₀, X₁, X₂, X₃) → n_l4___2(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ 0 ∧ 1 ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF for transition t₁₇₄: n_l4___2(X₀, X₁, X₂, X₃) → n_l1___1(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF for transition t₁₇₆: n_l4___6(X₀, X₁, X₂, X₃) → n_l2___4(X₀, X₁, X₀, X₃) :|: 1 ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

TWN: t₁₆₈: n_l1___5→n_l3___7

cycle: [t₁₇₅: n_l4___6→n_l1___5; t₁₇₃: n_l3___7→n_l4___6; t₁₆₈: n_l1___5→n_l3___7]
loop: (1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₂ ∧ 2+X₂ ≤ X₀,(X₀,X₁,X₂,X₃) -> (X₀,X₁,1+X₂,X₃)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
X₃: X₃

Termination: true
Formula:

1 < 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 < 1 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 < 1 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 < X₂ ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 < X₂ ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 < 1 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 < 1 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 < X₂ ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 < X₂ ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < 1 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < 1 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < X₂ ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < X₂ ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃

Stabilization-Threshold for: 2+X₂ ≤ X₀
alphas_abs: 2+X₀+X₂
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+6 {O(n)}
Stabilization-Threshold for: 0 ≤ X₂
alphas_abs: X₂
M: 0
N: 1
Bound: 2⋅X₂+2 {O(n)}
Stabilization-Threshold for: 1 ≤ X₂
alphas_abs: 1+X₂
M: 0
N: 1
Bound: 2⋅X₂+4 {O(n)}
loop: (1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 0 ≤ X₂ ∧ 2+X₂ ≤ X₀,(X₀,X₁,X₂,X₃) -> (X₀,X₁,1+X₂,X₃)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
X₃: X₃

Termination: true
Formula:

1 < 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 < 1 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 < 1 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 < X₂ ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 < X₂ ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 < 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 1 < 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 < 1 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 < 1 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 < X₂ ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 < X₂ ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ < X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 2+X₂ < X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < 1 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < 1 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < X₂ ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < X₂ ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < 1 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ < X₁
∨ 2+X₂ ≤ X₀ ∧ X₀ ≤ 2+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃

Stabilization-Threshold for: 2+X₂ ≤ X₀
alphas_abs: 2+X₀+X₂
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+6 {O(n)}
Stabilization-Threshold for: 0 ≤ X₂
alphas_abs: X₂
M: 0
N: 1
Bound: 2⋅X₂+2 {O(n)}
Stabilization-Threshold for: 1 ≤ X₂
alphas_abs: 1+X₂
M: 0
N: 1
Bound: 2⋅X₂+4 {O(n)}

TWN - Lifting for t₁₆₈: n_l1___5→n_l3___7 of 2⋅X₀+6⋅X₂+15 {O(n)}

relevant size-bounds w.r.t. t₁₆₉:
X₀: X₀ {O(n)}
X₂: 1 {O(1)}
Runtime-bound of t₁₆₉: 1 {O(1)}
Results in: 2⋅X₀+21 {O(n)}

TWN - Lifting for t₁₆₈: n_l1___5→n_l3___7 of 2⋅X₀+6⋅X₂+15 {O(n)}

relevant size-bounds w.r.t. t₁₆₇:
X₀: X₀ {O(n)}
X₂: 1 {O(1)}
Runtime-bound of t₁₆₇: X₁+1 {O(n)}
Results in: 2⋅X₀⋅X₁+2⋅X₀+21⋅X₁+21 {O(n^2)}

TWN: t₁₇₃: n_l3___7→n_l4___6

TWN - Lifting for t₁₇₃: n_l3___7→n_l4___6 of 2⋅X₀+6⋅X₂+15 {O(n)}

relevant size-bounds w.r.t. t₁₆₉:
X₀: X₀ {O(n)}
X₂: 1 {O(1)}
Runtime-bound of t₁₆₉: 1 {O(1)}
Results in: 2⋅X₀+21 {O(n)}

TWN - Lifting for t₁₇₃: n_l3___7→n_l4___6 of 2⋅X₀+6⋅X₂+15 {O(n)}

relevant size-bounds w.r.t. t₁₆₇:
X₀: X₀ {O(n)}
X₂: 1 {O(1)}
Runtime-bound of t₁₆₇: X₁+1 {O(n)}
Results in: 2⋅X₀⋅X₁+2⋅X₀+21⋅X₁+21 {O(n^2)}

TWN: t₁₇₅: n_l4___6→n_l1___5

TWN - Lifting for t₁₇₅: n_l4___6→n_l1___5 of 2⋅X₀+6⋅X₂+15 {O(n)}

relevant size-bounds w.r.t. t₁₆₉:
X₀: X₀ {O(n)}
X₂: 1 {O(1)}
Runtime-bound of t₁₆₉: 1 {O(1)}
Results in: 2⋅X₀+21 {O(n)}

TWN - Lifting for t₁₇₅: n_l4___6→n_l1___5 of 2⋅X₀+6⋅X₂+15 {O(n)}

relevant size-bounds w.r.t. t₁₆₇:
X₀: X₀ {O(n)}
X₂: 1 {O(1)}
Runtime-bound of t₁₆₇: X₁+1 {O(n)}
Results in: 2⋅X₀⋅X₁+2⋅X₀+21⋅X₁+21 {O(n^2)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:6⋅X₀⋅X₁+23⋅X₁+6⋅X₀+27 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 2⋅X₀⋅X₁+2⋅X₀+7⋅X₁+7 {O(n^2)}
t₅: 1 {O(1)}
t₆: 2⋅X₀⋅X₁+2⋅X₀+7⋅X₁+7 {O(n^2)}
t₇: X₁ {O(n)}
t₈: 2⋅X₀⋅X₁+2⋅X₀+7⋅X₁+7 {O(n^2)}
t₉: X₁ {O(n)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 6⋅X₀⋅X₁+23⋅X₁+6⋅X₀+27 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 2⋅X₀⋅X₁+2⋅X₀+7⋅X₁+7 {O(n^2)}
t₅: 1 {O(1)}
t₆: 2⋅X₀⋅X₁+2⋅X₀+7⋅X₁+7 {O(n^2)}
t₇: X₁ {O(n)}
t₈: 2⋅X₀⋅X₁+2⋅X₀+7⋅X₁+7 {O(n^2)}
t₉: X₁ {O(n)}
t₁₀: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: 0 {O(1)}
t₃, X₃: 0 {O(1)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: 2⋅X₀⋅X₁+2⋅X₀+7⋅X₁+7 {O(n^2)}
t₄, X₃: X₁ {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 2⋅X₁ {O(n)}
t₅, X₂: 2⋅X₀⋅X₁+2⋅X₀+7⋅X₁+7 {O(n^2)}
t₅, X₃: 2⋅X₁ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 2⋅X₀⋅X₁+2⋅X₀+7⋅X₁+7 {O(n^2)}
t₆, X₃: X₁ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 2⋅X₀⋅X₁+2⋅X₀+7⋅X₁+7 {O(n^2)}
t₇, X₃: X₁ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 2⋅X₀⋅X₁+2⋅X₀+7⋅X₁+7 {O(n^2)}
t₈, X₃: X₁ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 0 {O(1)}
t₉, X₃: X₁ {O(n)}
t₁₀, X₀: 4⋅X₀ {O(n)}
t₁₀, X₁: 4⋅X₁ {O(n)}
t₁₀, X₂: 2⋅X₀⋅X₁+2⋅X₀+2⋅X₂+7⋅X₁+7 {O(n^2)}
t₁₀, X₃: 2⋅X₁+2⋅X₃ {O(n)}