Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₃: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁
t₂: l1(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ X₁ ≤ 0
Preprocessing
Cut unsatisfiable transition t₂: l1→l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₃: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁
Time-Bound by TWN-Loops:
TWN-Loops: t₀ 2⋅X₁+4⋅X₀+6 {O(n)}
TWN-Loops:
entry: t₃: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀-1,X₁) :|: 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
Termination: true
Formula:
1 < 0
∨ 1 < 0 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
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. t₃:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₃: 1 {O(1)}
Results in: 2⋅X₁+4⋅X₀+6 {O(n)}
2⋅X₁+4⋅X₀+6 {O(n)}
Found invariant 1 ≤ 0 for location l1
Time-Bound by TWN-Loops:
TWN-Loops: t₁ 20⋅X₀⋅X₁+8⋅X₀⋅X₀+8⋅X₁⋅X₁+50⋅X₁+58⋅X₀+73 {O(n^2)}
TWN-Loops:
entry: t₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
results in twn-loop: twn: (X₀,X₁) -> (X₀,X₁-1) :|: 1 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁
entry: t₃: l0(X₀, X₁) → l1(X₀, X₁)
results in twn-loop: twn: (X₀,X₁) -> (X₀,X₁-1) :|: 1 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₁
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < 0 ∧ 1 < 0
∨ 1 < 0 ∧ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0
∨ 1 < 0 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ < 0 ∧ 1 < 0
∨ 1 < X₁ ∧ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0
∨ 1 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₀ < 0 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
Stabilization-Threshold for: 1 ≤ X₁
alphas_abs: 1+X₁
M: 0
N: 1
Bound: 2⋅X₁+4 {O(n)}
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. t₀:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₀: 2⋅X₁+4⋅X₀+6 {O(n)}
Results in: 20⋅X₀⋅X₁+8⋅X₀⋅X₀+8⋅X₁⋅X₁+46⋅X₁+56⋅X₀+66 {O(n^2)}
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < 0 ∧ 1 < 0
∨ 1 < 0 ∧ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0
∨ 1 < 0 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ < 0 ∧ 1 < 0
∨ 1 < X₁ ∧ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0
∨ 1 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₀ < 0 ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1
Stabilization-Threshold for: 1 ≤ X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}
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. t₃:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₃: 1 {O(1)}
Results in: 2⋅X₀+4⋅X₁+7 {O(n)}
20⋅X₀⋅X₁+8⋅X₀⋅X₀+8⋅X₁⋅X₁+50⋅X₁+58⋅X₀+73 {O(n^2)}
Analysing control-flow refined program
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___2
Found invariant 0 ≤ 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 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___2
Found invariant 0 ≤ 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: t₅₆ 4⋅X₁+7 {O(n)}
TWN-Loops:
entry: t₅₉: l1(X₀, X₁) → n_l1___2(X₀, X₁-1) :|: 1 ≤ X₀+X₁ ∧ X₀ ≤ 0
results in twn-loop: twn:Inv: [0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0] , (X₀,X₁) -> (X₀,X₁-1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₀+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 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 0 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0
∨ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0
∨ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0
∨ X₀ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0
Stabilization-Threshold for: 1 ≤ X₀+X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 0 ≤ X₀+X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₅₉:
X₁: X₁ {O(n)}
Runtime-bound of t₅₉: 1 {O(1)}
Results in: 4⋅X₁+7 {O(n)}
4⋅X₁+7 {O(n)}
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___2
Found invariant 0 ≤ 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: t₅₈ 4⋅X₁+8⋅X₀+10 {O(n)}
TWN-Loops:
entry: t₆₀: l1(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
results in twn-loop: twn:Inv: [0 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁) -> (X₀-1,X₁) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
Termination: true
Formula:
1 < 0
∨ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 0 < X₀+X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < 0
∨ 1 < 0 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₀+X₁ ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀+X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < 0
∨ 1 < 0 ∧ 1 < X₀+X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 < X₀+X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < 0
∨ 1 < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 < 0 ∧ 0 < X₀+X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 < 0 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 < 0 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 < 0 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 < X₀+X₁ ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 < X₀+X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 < X₀+X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 < X₀+X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 < X₀ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < 0
∨ 1 < X₀ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < X₀ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀+X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₀+X₁ ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₀+X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₀+X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₀+X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < 0
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 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: 1 ≤ X₀+X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 0 ≤ X₀+X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+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. t₆₀:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₆₀: 1 {O(1)}
Results in: 4⋅X₁+8⋅X₀+10 {O(n)}
4⋅X₁+8⋅X₀+10 {O(n)}
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l1___2
Found invariant 0 ≤ 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: t₅₅ 8⋅X₁+10 {O(n)}
TWN-Loops:
entry: t₅₇: n_l1___3(X₀, X₁) → n_l1___1(X₀, X₁-1) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ 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 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₀+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 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < 0 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+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 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ 1 < 0 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ 1 < X₀+X₁ ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀
∨ 1 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0 ∧ 0 < X₀
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₀
∨ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 0 < X₀+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 < X₀
∨ 1 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
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: 0 ≤ X₀+X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₅₇:
X₀: 0 {O(1)}
X₁: 2⋅X₁ {O(n)}
Runtime-bound of t₅₇: 1 {O(1)}
Results in: 8⋅X₁+10 {O(n)}
8⋅X₁+10 {O(n)}
CFR: Improvement to new bound with the following program:
new bound:
16⋅X₁+8⋅X₀+27 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, n_l1___1, n_l1___2, n_l1___3
Transitions:
t₃: l0(X₀, X₁) → l1(X₀, X₁)
t₅₉: l1(X₀, X₁) → n_l1___2(X₀, X₁-1) :|: 1 ≤ X₀+X₁ ∧ X₀ ≤ 0
t₆₀: l1(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅₅: n_l1___1(X₀, X₁) → n_l1___1(X₀, X₁-1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₅₆: n_l1___2(X₀, X₁) → n_l1___2(X₀, X₁-1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₅₇: n_l1___3(X₀, X₁) → n_l1___1(X₀, X₁-1) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₅₈: n_l1___3(X₀, X₁) → n_l1___3(X₀-1, X₁) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
All Bounds
Timebounds
Overall timebound:16⋅X₁+8⋅X₀+31 {O(n)}
t₃: 1 {O(1)}
t₅₉: 1 {O(1)}
t₆₀: 1 {O(1)}
t₅₅: 8⋅X₁+10 {O(n)}
t₅₆: 4⋅X₁+7 {O(n)}
t₅₇: 1 {O(1)}
t₅₈: 4⋅X₁+8⋅X₀+10 {O(n)}
Costbounds
Overall costbound: 16⋅X₁+8⋅X₀+31 {O(n)}
t₃: 1 {O(1)}
t₅₉: 1 {O(1)}
t₆₀: 1 {O(1)}
t₅₅: 8⋅X₁+10 {O(n)}
t₅₆: 4⋅X₁+7 {O(n)}
t₅₇: 1 {O(1)}
t₅₈: 4⋅X₁+8⋅X₀+10 {O(n)}
Sizebounds
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₅₉, X₀: X₀ {O(n)}
t₅₉, X₁: X₁ {O(n)}
t₆₀, X₀: X₀ {O(n)}
t₆₀, X₁: X₁ {O(n)}
t₅₅, X₀: 0 {O(1)}
t₅₅, X₁: 2⋅X₁ {O(n)}
t₅₆, X₀: X₀ {O(n)}
t₅₆, X₁: X₁ {O(n)}
t₅₇, X₀: 0 {O(1)}
t₅₇, X₁: 2⋅X₁ {O(n)}
t₅₈, X₀: X₀ {O(n)}
t₅₈, X₁: X₁ {O(n)}