Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂
Temp_Vars: N, O, P
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l6(X₀, X₁, X₂, N, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂)
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l1(X₀, X₁, N, X₃, X₄, O, P, 0, X₈, 0, 0, X₁₁, X₁₂) :|: 1+X₁ ≤ X₄ ∧ X₁₂ ≤ 4
t₁₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l2(X₀, 1+X₁, N, X₃, X₄, O, X₆, 1, X₈, 1, 1, X₁₁, X₁₂) :|: 1+X₁ ≤ X₄ ∧ 5 ≤ X₁₂
t₉: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l1(X₀, X₁, N, X₃, X₄, O, P, 0, X₈, 0, 0, X₁₁, X₁₂) :|: 1+X₁ ≤ X₄
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l6(1+X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: X₄ ≤ X₁
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l1(X₀, X₁, N, X₃, X₄, O, P, 0, X₈, 0, 0, X₁₁, -2)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l1(X₀, X₁, N, X₃, X₄, O, P, 0, X₈, 0, 0, X₈-1, X₁₂) :|: X₈ ≤ 4
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l2(X₀, 1+X₁, N, X₃, X₄, O, X₆, 1, X₈, 1, 1, X₁₁, X₁₂) :|: 5 ≤ X₈
t₄: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l1(X₀, X₁, N, X₃, X₄, O, P, 0, -2, 0, 0, X₁₁, X₁₂)
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l1(X₀, X₁, N, X₃, X₄, O, P, 0, X₈, 0, 0, X₁₁, X₁₂) :|: 1+X₀ ≤ X₁ ∧ 1+X₁ ≤ X₄
t₃: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l6(1+X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁
t₀: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → l7(X₀, X₁, N, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: X₁ ≤ X₀

Preprocessing

Cut unreachable locations [l3; l4; l5] from the program graph

Eliminate variables {N,O,P,X₂,X₃,X₅,X₆,X₇,X₈,X₉,X₁₀,X₁₁} that do not contribute to the problem

Found invariant X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 2+X₀ ≤ X₁ for location l2

Found invariant X₁ ≤ X₀ for location l7

Found invariant 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₄, X₁₂
Temp_Vars:
Locations: l0, l1, l2, l6, l7
Transitions:
t₂₃: l0(X₀, X₁, X₄, X₁₂) → l6(X₀, X₁, X₄, X₁₂)
t₂₄: l1(X₀, X₁, X₄, X₁₂) → l1(X₀, X₁, X₄, X₁₂) :|: 1+X₁ ≤ X₄ ∧ X₁₂ ≤ 4 ∧ 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁
t₂₅: l1(X₀, X₁, X₄, X₁₂) → l2(X₀, 1+X₁, X₄, X₁₂) :|: 1+X₁ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁
t₂₇: l2(X₀, X₁, X₄, X₁₂) → l1(X₀, X₁, X₄, X₁₂) :|: 1+X₁ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 2+X₀ ≤ X₁
t₂₆: l2(X₀, X₁, X₄, X₁₂) → l6(1+X₀, X₁, X₄, X₁₂) :|: X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 2+X₀ ≤ X₁
t₃₀: l6(X₀, X₁, X₄, X₁₂) → l1(X₀, X₁, X₄, X₁₂) :|: 1+X₀ ≤ X₁ ∧ 1+X₁ ≤ X₄
t₂₉: l6(X₀, X₁, X₄, X₁₂) → l6(1+X₀, X₁, X₄, X₁₂) :|: 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁
t₂₈: l6(X₀, X₁, X₄, X₁₂) → l7(X₀, X₁, X₄, X₁₂) :|: X₁ ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₃₀: l6(X₀, X₁, X₄, X₁₂) → l1(X₀, X₁, X₄, X₁₂) :|: 1+X₀ ≤ X₁ ∧ 1+X₁ ≤ X₄

Found invariant X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 2+X₀ ≤ X₁ for location l2

Found invariant X₁ ≤ X₀ for location l7

Found invariant 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁ for location l1

Found invariant X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 2+X₀ ≤ X₁ for location l2

Found invariant X₁ ≤ X₀ for location l7

Found invariant 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₂₅ 4⋅X₁+4⋅X₄+7 {O(n)}

TWN-Loops:

entry: t₃₀: l6(X₀, X₁, X₄, X₁₂) → l1(X₀, X₁, X₄, X₁₂) :|: 1+X₀ ≤ X₁ ∧ 1+X₁ ≤ X₄
results in twn-loop: twn:Inv: [1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 1+X₀ ≤ X₁] , (X₀,X₁,X₄,X₁₂) -> (X₀,1+X₁,X₄,X₁₂) :|: 1+X₁ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 2+X₁ ≤ X₄
order: [X₀; X₁; X₄; X₁₂]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₄: X₄
X₁₂: X₁₂

Termination: true
Formula:

5 < X₁₂ ∧ 1 < 0
∨ 1 < 0 ∧ 5 < X₁₂ ∧ 1+X₁ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 5 < X₁₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₄ ∧ X₄ ≤ 1+X₁
∨ 5 ≤ X₁₂ ∧ X₁₂ ≤ 5 ∧ 1 < 0
∨ 1 < 0 ∧ 5 ≤ X₁₂ ∧ X₁₂ ≤ 5 ∧ 1+X₁ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 5 ≤ X₁₂ ∧ X₁₂ ≤ 5 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₄ ∧ X₄ ≤ 1+X₁
∨ 2+X₁ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 5 < X₁₂ ∧ 1 < 0
∨ 2+X₁ < X₄ ∧ 5 < X₁₂ ∧ 1+X₁ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₁ < X₄ ∧ 5 < X₁₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₄ ∧ X₄ ≤ 1+X₁
∨ 2+X₁ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 5 ≤ X₁₂ ∧ X₁₂ ≤ 5 ∧ 1 < 0
∨ 2+X₁ < X₄ ∧ 5 ≤ X₁₂ ∧ X₁₂ ≤ 5 ∧ 1+X₁ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₁ < X₄ ∧ 5 ≤ X₁₂ ∧ X₁₂ ≤ 5 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₄ ∧ X₄ ≤ 1+X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₁ ≤ X₄ ∧ X₄ ≤ 2+X₁ ∧ 5 < X₁₂ ∧ 1 < 0
∨ 2+X₁ ≤ X₄ ∧ X₄ ≤ 2+X₁ ∧ 5 < X₁₂ ∧ 1+X₁ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₁ ≤ X₄ ∧ X₄ ≤ 2+X₁ ∧ 5 < X₁₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₄ ∧ X₄ ≤ 1+X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₁ ≤ X₄ ∧ X₄ ≤ 2+X₁ ∧ 5 ≤ X₁₂ ∧ X₁₂ ≤ 5 ∧ 1 < 0
∨ 2+X₁ ≤ X₄ ∧ X₄ ≤ 2+X₁ ∧ 5 ≤ X₁₂ ∧ X₁₂ ≤ 5 ∧ 1+X₁ < X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₁ ≤ X₄ ∧ X₄ ≤ 2+X₁ ∧ 5 ≤ X₁₂ ∧ X₁₂ ≤ 5 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₄ ∧ X₄ ≤ 1+X₁

Stabilization-Threshold for: 2+X₁ ≤ X₄
alphas_abs: X₁+X₄
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₄+2 {O(n)}
Stabilization-Threshold for: 1+X₁ ≤ X₄
alphas_abs: X₁+X₄
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₄+2 {O(n)}

relevant size-bounds w.r.t. t₃₀:
X₁: X₁ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₃₀: 1 {O(1)}
Results in: 4⋅X₁+4⋅X₄+7 {O(n)}

4⋅X₁+4⋅X₄+7 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₇ 4⋅X₁+4⋅X₄+7 {O(n)}

relevant size-bounds w.r.t. t₃₀:
X₁: X₁ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₃₀: 1 {O(1)}
Results in: 4⋅X₁+4⋅X₄+7 {O(n)}

4⋅X₁+4⋅X₄+7 {O(n)}

knowledge_propagation leads to new time bound 4⋅X₁+4⋅X₄+7 {O(n)} for transition t₂₆: l2(X₀, X₁, X₄, X₁₂) → l6(1+X₀, X₁, X₄, X₁₂) :|: X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 2+X₀ ≤ X₁

Found invariant 1 ≤ 0 for location l2

Found invariant 1 ≤ 0 for location l6

Found invariant 1 ≤ 0 for location l7

Found invariant 1 ≤ 0 for location l1

Found invariant X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 2+X₀ ≤ X₁ for location l2

Found invariant X₁ ≤ X₀ for location l7

Found invariant 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₂₉ 32⋅X₄⋅X₄+40⋅X₁⋅X₁+72⋅X₁⋅X₄+8⋅X₀⋅X₁+8⋅X₀⋅X₄+148⋅X₄+16⋅X₀+164⋅X₁+166 {O(n^2)}

TWN-Loops:

entry: t₂₆: l2(X₀, X₁, X₄, X₁₂) → l6(1+X₀, X₁, X₄, X₁₂) :|: X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 2+X₀ ≤ X₁
results in twn-loop: twn: (X₀,X₁,X₄,X₁₂) -> (1+X₀,X₁,X₄,X₁₂) :|: 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁
entry: t₂₃: l0(X₀, X₁, X₄, X₁₂) → l6(X₀, X₁, X₄, X₁₂)
results in twn-loop: twn: (X₀,X₁,X₄,X₁₂) -> (1+X₀,X₁,X₄,X₁₂) :|: 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁
order: [X₀; X₁; X₄]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁
X₄: X₄

Termination: true
Formula:

X₄ < X₁ ∧ 1 < 0
∨ X₄ < X₁ ∧ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀
∨ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 < 0
∨ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀

Stabilization-Threshold for: 1+X₀ ≤ X₁
alphas_abs: 1+X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₂₆:
X₀: X₀+1 {O(n)}
X₁: 4⋅X₄+5⋅X₁+7 {O(n)}
Runtime-bound of t₂₆: 4⋅X₁+4⋅X₄+7 {O(n)}
Results in: 32⋅X₄⋅X₄+40⋅X₁⋅X₁+72⋅X₁⋅X₄+8⋅X₀⋅X₁+8⋅X₀⋅X₄+14⋅X₀+148⋅X₄+162⋅X₁+161 {O(n^2)}

order: [X₀; X₁; X₄]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁
X₄: X₄

Termination: true
Formula:

X₄ < X₁ ∧ 1 < 0
∨ X₄ < X₁ ∧ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀
∨ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 < 0
∨ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀

Stabilization-Threshold for: 1+X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₃:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₃: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+5 {O(n)}

32⋅X₄⋅X₄+40⋅X₁⋅X₁+72⋅X₁⋅X₄+8⋅X₀⋅X₁+8⋅X₀⋅X₄+148⋅X₄+16⋅X₀+164⋅X₁+166 {O(n^2)}

Analysing control-flow refined program

Found invariant X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 2+X₀ ≤ X₁ for location l2

Found invariant X₄ ≤ X₁ ∧ X₀ ≤ X₁ for location n_l6___1

Found invariant X₁ ≤ X₀ for location l7

Found invariant 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁ for location l1

Found invariant 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ X₁₂ ≤ 4 ∧ 1+X₀ ≤ X₁ for location n_l1___1

Found invariant X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 2+X₀ ≤ X₁ for location l2

Found invariant X₄ ≤ X₁ ∧ X₀ ≤ X₁ for location n_l6___1

Found invariant X₁ ≤ X₀ for location l7

Found invariant 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁ for location l1

Found invariant 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ X₁₂ ≤ 4 ∧ 1+X₀ ≤ X₁ for location n_l1___1

Found invariant X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 2+X₀ ≤ X₁ for location l2

Found invariant X₄ ≤ X₁ ∧ X₀ ≤ X₁ for location n_l6___1

Found invariant X₁ ≤ X₀ for location l7

Found invariant 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁ for location l1

Found invariant 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ X₁₂ ≤ 4 ∧ 1+X₀ ≤ X₁ for location n_l1___1

Found invariant X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ 2+X₀ ≤ X₁ for location l2

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 5 ≤ X₁₂ ∧ X₀ ≤ X₁ for location n_l6___1

Found invariant X₁ ≤ X₀ for location l7

Found invariant 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁ for location l1

Found invariant 1+X₁ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ X₁₂ ≤ 4 ∧ 1+X₀ ≤ X₁ for location n_l1___1

Time-Bound by TWN-Loops:

TWN-Loops: t₁₅₇ 16⋅X₀+32⋅X₄+48⋅X₁+96 {O(n)}

TWN-Loops:

entry: t₁₅₉: l6(X₀, X₁, X₄, X₁₂) → n_l6___1(X₀+1, X₁, X₄, X₁₂) :|: X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁
results in twn-loop: twn:Inv: [X₄ ≤ X₁ ∧ X₀ ≤ X₁] , (X₀,X₁,X₄,X₁₂) -> (X₀+1,X₁,X₄,X₁₂) :|: X₄ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁
entry: t₁₅₈: l6(X₀, X₁, X₄, X₁₂) → n_l6___1(X₀+1, X₁, X₄, X₁₂) :|: 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 5 ≤ X₁₂ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁
results in twn-loop: twn:Inv: [X₄ ≤ X₁ ∧ X₀ ≤ X₁] , (X₀,X₁,X₄,X₁₂) -> (X₀+1,X₁,X₄,X₁₂) :|: X₄ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₀ ≤ X₁
order: [X₀; X₁; X₄]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁
X₄: X₄

Termination: true
Formula:

X₄ < X₁ ∧ 1 < 0
∨ 1 < 0 ∧ X₄ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 < 0
∨ 1 < 0 ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₄ < X₁ ∧ 1 < 0
∨ 1+X₀ < X₁ ∧ X₄ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ < X₁ ∧ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 < 0
∨ 1+X₀ < X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ < X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₄ < X₁ ∧ 1 < 0
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₄ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 < 0
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀

Stabilization-Threshold for: 1+X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₁₅₉:
X₀: 2⋅X₀+3 {O(n)}
X₁: 4⋅X₄+6⋅X₁+7 {O(n)}
Runtime-bound of t₁₅₉: 1 {O(1)}
Results in: 16⋅X₄+24⋅X₁+8⋅X₀+47 {O(n)}

order: [X₀; X₁; X₄; X₁₂]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁
X₄: X₄
X₁₂: X₁₂

Termination: true
Formula:

X₄ < X₁ ∧ 1 < 0
∨ 1 < 0 ∧ X₄ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 < 0
∨ 1 < 0 ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₄ < X₁ ∧ 1 < 0
∨ 1+X₀ < X₁ ∧ X₄ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ < X₁ ∧ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 < 0
∨ 1+X₀ < X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ < X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₄ < X₁ ∧ 1 < 0
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₄ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₄ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 < 0
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀

Stabilization-Threshold for: 1+X₀ ≤ X₁
alphas_abs: 1+X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}
Stabilization-Threshold for: X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₁₅₈:
X₀: 2⋅X₀+3 {O(n)}
X₁: 4⋅X₄+6⋅X₁+7 {O(n)}
Runtime-bound of t₁₅₈: 1 {O(1)}
Results in: 16⋅X₄+24⋅X₁+8⋅X₀+49 {O(n)}

16⋅X₀+32⋅X₄+48⋅X₁+96 {O(n)}

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂₃: 1 {O(1)}
t₂₄: inf {Infinity}
t₂₅: 4⋅X₁+4⋅X₄+7 {O(n)}
t₂₆: 4⋅X₁+4⋅X₄+7 {O(n)}
t₂₇: 4⋅X₁+4⋅X₄+7 {O(n)}
t₂₈: 1 {O(1)}
t₂₉: 32⋅X₄⋅X₄+40⋅X₁⋅X₁+72⋅X₁⋅X₄+8⋅X₀⋅X₁+8⋅X₀⋅X₄+148⋅X₄+16⋅X₀+164⋅X₁+166 {O(n^2)}
t₃₀: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₂₃: 1 {O(1)}
t₂₄: inf {Infinity}
t₂₅: 4⋅X₁+4⋅X₄+7 {O(n)}
t₂₆: 4⋅X₁+4⋅X₄+7 {O(n)}
t₂₇: 4⋅X₁+4⋅X₄+7 {O(n)}
t₂₈: 1 {O(1)}
t₂₉: 32⋅X₄⋅X₄+40⋅X₁⋅X₁+72⋅X₁⋅X₄+8⋅X₀⋅X₁+8⋅X₀⋅X₄+148⋅X₄+16⋅X₀+164⋅X₁+166 {O(n^2)}
t₃₀: 1 {O(1)}

Sizebounds

t₂₃, X₀: X₀ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₁₂: X₁₂ {O(n)}
t₂₄, X₀: X₀ {O(n)}
t₂₄, X₁: X₁ {O(n)}
t₂₄, X₄: X₄ {O(n)}
t₂₄, X₁₂: X₁₂ {O(n)}
t₂₅, X₀: X₀ {O(n)}
t₂₅, X₁: 4⋅X₄+5⋅X₁+7 {O(n)}
t₂₅, X₄: X₄ {O(n)}
t₂₅, X₁₂: X₁₂ {O(n)}
t₂₆, X₀: X₀+1 {O(n)}
t₂₆, X₁: 4⋅X₄+5⋅X₁+7 {O(n)}
t₂₆, X₄: X₄ {O(n)}
t₂₆, X₁₂: X₁₂ {O(n)}
t₂₇, X₀: X₀ {O(n)}
t₂₇, X₁: 4⋅X₄+5⋅X₁+7 {O(n)}
t₂₇, X₄: X₄ {O(n)}
t₂₇, X₁₂: X₁₂ {O(n)}
t₂₈, X₀: 32⋅X₄⋅X₄+40⋅X₁⋅X₁+72⋅X₁⋅X₄+8⋅X₀⋅X₁+8⋅X₀⋅X₄+148⋅X₄+164⋅X₁+19⋅X₀+167 {O(n^2)}
t₂₈, X₁: 4⋅X₄+7⋅X₁+7 {O(n)}
t₂₈, X₄: 3⋅X₄ {O(n)}
t₂₈, X₁₂: 3⋅X₁₂ {O(n)}
t₂₉, X₀: 32⋅X₄⋅X₄+40⋅X₁⋅X₁+72⋅X₁⋅X₄+8⋅X₀⋅X₁+8⋅X₀⋅X₄+148⋅X₄+164⋅X₁+18⋅X₀+167 {O(n^2)}
t₂₉, X₁: 4⋅X₄+6⋅X₁+7 {O(n)}
t₂₉, X₄: 2⋅X₄ {O(n)}
t₂₉, X₁₂: 2⋅X₁₂ {O(n)}
t₃₀, X₀: X₀ {O(n)}
t₃₀, X₁: X₁ {O(n)}
t₃₀, X₄: X₄ {O(n)}
t₃₀, X₁₂: X₁₂ {O(n)}