Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₆: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀
t₁: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀
t₂: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁
t₃: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₄: l1(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₁ ≤ 0
t₅: l1(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ X₁ ≤ 0
Preprocessing
Cut unsatisfiable transition t₂: l1→l1
Cut unsatisfiable transition t₄: l1→l1
Cut unsatisfiable transition t₅: l1→l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₆: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀
t₁: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀
t₃: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
Time-Bound by TWN-Loops:
TWN-Loops: t₀ 2⋅X₀+5 {O(n)}
TWN-Loops:
entry: t₆: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀-1,X₁) :|: 1 ≤ X₀ ∨ 1 ≤ X₁ ∧ 1 ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
Termination: true
Formula:
1 < 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1
∨ 1 < 0 ∧ 1 < X₁
∨ 1 < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < X₁
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
relevant size-bounds w.r.t. t₆:
X₀: X₀ {O(n)}
Runtime-bound of t₆: 1 {O(1)}
Results in: 2⋅X₀+5 {O(n)}
2⋅X₀+5 {O(n)}
Time-Bound by TWN-Loops:
TWN-Loops: t₁ 2⋅X₀+5 {O(n)}
relevant size-bounds w.r.t. t₆:
X₀: X₀ {O(n)}
Runtime-bound of t₆: 1 {O(1)}
Results in: 2⋅X₀+5 {O(n)}
2⋅X₀+5 {O(n)}
Found invariant 1 ≤ 0 for location l1
Found invariant 1 ≤ 0 for location l1
Time-Bound by TWN-Loops:
TWN-Loops: t₃ 16⋅X₀⋅X₁+28⋅X₀+42⋅X₁+75 {O(n^2)}
TWN-Loops:
entry: t₁: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀
results in twn-loop: twn: (X₀,X₁) -> (X₀,X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
entry: t₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀
results in twn-loop: twn: (X₀,X₁) -> (X₀,X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
entry: t₆: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀,X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < 0 ∧ 1 < 0
∨ X₀ < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
Stabilization-Threshold for: 1 ≤ X₁
alphas_abs: 1+X₁
M: 0
N: 1
Bound: 2⋅X₁+4 {O(n)}
relevant size-bounds w.r.t. t₁:
X₁: 2⋅X₁ {O(n)}
Runtime-bound of t₁: 2⋅X₀+5 {O(n)}
Results in: 8⋅X₀⋅X₁+14⋅X₀+20⋅X₁+35 {O(n^2)}
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < 0 ∧ 1 < 0
∨ X₀ < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
Stabilization-Threshold for: 1 ≤ X₁
alphas_abs: 1+X₁
M: 0
N: 1
Bound: 2⋅X₁+4 {O(n)}
relevant size-bounds w.r.t. t₀:
X₁: 2⋅X₁ {O(n)}
Runtime-bound of t₀: 2⋅X₀+5 {O(n)}
Results in: 8⋅X₀⋅X₁+14⋅X₀+20⋅X₁+35 {O(n^2)}
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < 0 ∧ 1 < 0
∨ X₀ < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
Stabilization-Threshold for: 1 ≤ X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₆:
X₁: X₁ {O(n)}
Runtime-bound of t₆: 1 {O(1)}
Results in: 2⋅X₁+5 {O(n)}
16⋅X₀⋅X₁+28⋅X₀+42⋅X₁+75 {O(n^2)}
Analysing control-flow refined program
Found invariant 0 ≤ X₀ for location n_l1___4
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___2
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1
Found invariant 0 ≤ X₀ for location n_l1___4
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___2
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1
Time-Bound by TWN-Loops:
TWN-Loops: t₁₁₆ 4⋅X₁+7 {O(n)}
TWN-Loops:
entry: t₁₂₃: l1(X₀, X₁) → n_l1___2(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
results in twn-loop: twn:Inv: [0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0] , (X₀,X₁) -> (X₀,X₁-1) :|: X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ X₀ ≤ 0
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < 0 ∧ 1 < 0
∨ X₀ < 0 ∧ 1 < 0 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 0 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ X₀ < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ < 0 ∧ 1 < X₁ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ X₀ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₁ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
Stabilization-Threshold for: 1 ≤ X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 0 ≤ X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₃:
X₁: X₁ {O(n)}
Runtime-bound of t₁₂₃: 1 {O(1)}
Results in: 4⋅X₁+7 {O(n)}
4⋅X₁+7 {O(n)}
Found invariant 0 ≤ X₀ for location n_l1___4
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___2
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1
Time-Bound by TWN-Loops:
TWN-Loops: t₁₂₂ 4⋅X₀+6 {O(n)}
TWN-Loops:
entry: t₁₂₅: l1(X₀, X₁) → n_l1___4(X₀-1, X₁) :|: 1 ≤ X₀
results in twn-loop: twn:Inv: [0 ≤ X₀] , (X₀,X₁) -> (X₀-1,X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₀
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
1 < 0
∨ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₀ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₅:
X₀: X₀ {O(n)}
Runtime-bound of t₁₂₅: 1 {O(1)}
Results in: 4⋅X₀+6 {O(n)}
4⋅X₀+6 {O(n)}
Found invariant 0 ≤ X₀ for location n_l1___4
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___2
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1
Found invariant 0 ≤ X₀ for location n_l1___4
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___2
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1
Found invariant 0 ≤ X₀ for location n_l1___4
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___2
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1
Found invariant 0 ≤ X₀ for location n_l1___4
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___2
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1
Time-Bound by TWN-Loops:
TWN-Loops: t₁₁₈ 24⋅X₀+28 {O(n)}
TWN-Loops:
entry: t₁₂₁: n_l1___4(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁) -> (X₀-1,X₁) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∨ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁
entry: t₁₂₄: l1(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
results in twn-loop: twn:Inv: [1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁) -> (X₀-1,X₁) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∨ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁
entry: t₁₂₁: n_l1___4(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁) -> (X₀-1,X₁) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∨ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁
entry: t₁₂₄: l1(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
results in twn-loop: twn:Inv: [1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁) -> (X₀-1,X₁) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∨ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
Termination: true
Formula:
1 < X₁ ∧ 1 < 0
∨ 1 < 0 ∧ 1 < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < X₁ ∧ 1 < 0
∨ 1 < X₀ ∧ 1 < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₁ ∧ 1 < 0
∨ 1 < X₁ ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₁ ∧ 1 < X₀ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0
∨ 1 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₁:
X₀: 2⋅X₀ {O(n)}
Runtime-bound of t₁₂₁: 1 {O(1)}
Results in: 8⋅X₀+7 {O(n)}
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
Termination: true
Formula:
1 < X₁ ∧ 1 < 0
∨ 1 < 0 ∧ 1 < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < X₁ ∧ 1 < 0
∨ 1 < X₀ ∧ 1 < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₁ ∧ 1 < 0
∨ 1 < X₁ ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₁ ∧ 1 < X₀ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0
∨ 1 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₄:
X₀: X₀ {O(n)}
Runtime-bound of t₁₂₄: 1 {O(1)}
Results in: 4⋅X₀+7 {O(n)}
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
Termination: true
Formula:
1 < X₁ ∧ 1 < 0
∨ 1 < 0 ∧ 1 < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < X₁ ∧ 1 < 0
∨ 1 < X₀ ∧ 1 < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₁ ∧ 1 < 0
∨ 1 < X₁ ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₁ ∧ 1 < X₀ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0
∨ 1 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₁:
X₀: 2⋅X₀ {O(n)}
Runtime-bound of t₁₂₁: 1 {O(1)}
Results in: 8⋅X₀+7 {O(n)}
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
Termination: true
Formula:
1 < X₁ ∧ 1 < 0
∨ 1 < 0 ∧ 1 < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < X₁ ∧ 1 < 0
∨ 1 < X₀ ∧ 1 < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₁ ∧ 1 < 0
∨ 1 < X₁ ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₁ ∧ 1 < X₀ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0
∨ 1 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₄:
X₀: X₀ {O(n)}
Runtime-bound of t₁₂₄: 1 {O(1)}
Results in: 4⋅X₀+7 {O(n)}
24⋅X₀+28 {O(n)}
Time-Bound by TWN-Loops:
TWN-Loops: t₁₁₉ 24⋅X₀+28 {O(n)}
relevant size-bounds w.r.t. t₁₂₁:
X₀: 2⋅X₀ {O(n)}
Runtime-bound of t₁₂₁: 1 {O(1)}
Results in: 8⋅X₀+7 {O(n)}
relevant size-bounds w.r.t. t₁₂₄:
X₀: X₀ {O(n)}
Runtime-bound of t₁₂₄: 1 {O(1)}
Results in: 4⋅X₀+7 {O(n)}
relevant size-bounds w.r.t. t₁₂₁:
X₀: 2⋅X₀ {O(n)}
Runtime-bound of t₁₂₁: 1 {O(1)}
Results in: 8⋅X₀+7 {O(n)}
relevant size-bounds w.r.t. t₁₂₄:
X₀: X₀ {O(n)}
Runtime-bound of t₁₂₄: 1 {O(1)}
Results in: 4⋅X₀+7 {O(n)}
24⋅X₀+28 {O(n)}
Found invariant 0 ≤ X₀ for location n_l1___4
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___2
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1
Found invariant 0 ≤ X₀ for location n_l1___4
Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___2
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___3
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___1
Time-Bound by TWN-Loops:
TWN-Loops: t₁₁₅ 68⋅X₁+20 {O(n)}
TWN-Loops:
entry: t₁₂₀: n_l1___4(X₀, X₁) → n_l1___1(X₀, X₁-1) :|: 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀] , (X₀,X₁) -> (X₀,X₁-1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ X₀ ≤ 0
entry: t₁₁₇: n_l1___3(X₀, X₁) → n_l1___1(X₀, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀] , (X₀,X₁) -> (X₀,X₁-1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ X₀ ≤ 0
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < 0 ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < 0 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < 0 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < X₁ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < X₁ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0 ∧ 0 < X₀
∨ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ 1 < 0 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₀
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₁ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ 1 < X₁ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₀
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₀
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
Stabilization-Threshold for: 1 ≤ X₁
alphas_abs: 1+X₁
M: 0
N: 1
Bound: 2⋅X₁+4 {O(n)}
Stabilization-Threshold for: 0 ≤ X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₀:
X₁: 2⋅X₁ {O(n)}
Runtime-bound of t₁₂₀: 1 {O(1)}
Results in: 8⋅X₁+10 {O(n)}
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < 0 ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < 0 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < 0 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < X₁ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < X₁ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0 ∧ 0 < X₀
∨ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ 1 < 0 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₀
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₁ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ 1 < X₁ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₀
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₀
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
Stabilization-Threshold for: 1 ≤ X₁
alphas_abs: 1+X₁
M: 0
N: 1
Bound: 2⋅X₁+4 {O(n)}
Stabilization-Threshold for: 0 ≤ X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₁₁₇:
X₁: 15⋅X₁ {O(n)}
Runtime-bound of t₁₁₇: 1 {O(1)}
Results in: 60⋅X₁+10 {O(n)}
68⋅X₁+20 {O(n)}
CFR: Improvement to new bound with the following program:
new bound:
52⋅X₀+72⋅X₁+89 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, n_l1___1, n_l1___2, n_l1___3, n_l1___4
Transitions:
t₆: l0(X₀, X₁) → l1(X₀, X₁)
t₁₂₃: l1(X₀, X₁) → n_l1___2(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₁₂₄: l1(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁₂₅: l1(X₀, X₁) → n_l1___4(X₀-1, X₁) :|: 1 ≤ X₀
t₁₁₅: n_l1___1(X₀, X₁) → n_l1___1(X₀, X₁-1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₁₆: n_l1___2(X₀, X₁) → n_l1___2(X₀, X₁-1) :|: X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₁₇: n_l1___3(X₀, X₁) → n_l1___1(X₀, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₁₈: n_l1___3(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₁₉: n_l1___3(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₂₀: n_l1___4(X₀, X₁) → n_l1___1(X₀, X₁-1) :|: 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₂₁: n_l1___4(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₁₂₂: n_l1___4(X₀, X₁) → n_l1___4(X₀-1, X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀
All Bounds
Timebounds
Overall timebound:52⋅X₀+72⋅X₁+96 {O(n)}
t₆: 1 {O(1)}
t₁₂₃: 1 {O(1)}
t₁₂₄: 1 {O(1)}
t₁₂₅: 1 {O(1)}
t₁₁₅: 68⋅X₁+20 {O(n)}
t₁₁₆: 4⋅X₁+7 {O(n)}
t₁₁₇: 1 {O(1)}
t₁₁₈: 24⋅X₀+28 {O(n)}
t₁₁₉: 24⋅X₀+28 {O(n)}
t₁₂₀: 1 {O(1)}
t₁₂₁: 1 {O(1)}
t₁₂₂: 4⋅X₀+6 {O(n)}
Costbounds
Overall costbound: 52⋅X₀+72⋅X₁+96 {O(n)}
t₆: 1 {O(1)}
t₁₂₃: 1 {O(1)}
t₁₂₄: 1 {O(1)}
t₁₂₅: 1 {O(1)}
t₁₁₅: 68⋅X₁+20 {O(n)}
t₁₁₆: 4⋅X₁+7 {O(n)}
t₁₁₇: 1 {O(1)}
t₁₁₈: 24⋅X₀+28 {O(n)}
t₁₁₉: 24⋅X₀+28 {O(n)}
t₁₂₀: 1 {O(1)}
t₁₂₁: 1 {O(1)}
t₁₂₂: 4⋅X₀+6 {O(n)}
Sizebounds
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₁₂₃, X₀: X₀ {O(n)}
t₁₂₃, X₁: X₁ {O(n)}
t₁₂₄, X₀: X₀ {O(n)}
t₁₂₄, X₁: X₁ {O(n)}
t₁₂₅, X₀: X₀ {O(n)}
t₁₂₅, X₁: X₁ {O(n)}
t₁₁₅, X₀: 0 {O(1)}
t₁₁₅, X₁: 17⋅X₁ {O(n)}
t₁₁₆, X₀: X₀ {O(n)}
t₁₁₆, X₁: X₁ {O(n)}
t₁₁₇, X₀: 0 {O(1)}
t₁₁₇, X₁: 15⋅X₁ {O(n)}
t₁₁₈, X₀: 6⋅X₀ {O(n)}
t₁₁₈, X₁: 6⋅X₁ {O(n)}
t₁₁₉, X₀: 6⋅X₀ {O(n)}
t₁₁₉, X₁: 6⋅X₁ {O(n)}
t₁₂₀, X₀: 0 {O(1)}
t₁₂₀, X₁: 2⋅X₁ {O(n)}
t₁₂₁, X₀: 2⋅X₀ {O(n)}
t₁₂₁, X₁: 2⋅X₁ {O(n)}
t₁₂₂, X₀: X₀ {O(n)}
t₁₂₂, X₁: X₁ {O(n)}