Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₆: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁+1 ≤ X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁+1 ≤ X₂ ∧ X₁+1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₁+1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁+1 ≤ X₂
t₃: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₁+1 ≤ X₂ ∧ X₀ ≤ X₁
t₄: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁
t₅: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁
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, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₆: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁+1 ≤ X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁+1 ≤ X₂ ∧ X₁+1 ≤ X₀
t₃: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₁+1 ≤ X₂ ∧ X₀ ≤ X₁
Time-Bound by TWN-Loops:
TWN-Loops: t₀ 2⋅X₀+2⋅X₁+5 {O(n)}
TWN-Loops:
entry: t₆: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀-1,X₁,X₂) :|: X₁+1 ≤ X₀ ∨ X₁+1 ≤ X₂ ∧ X₁+1 ≤ X₀
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂
Termination: true
Formula:
1 < 0
∨ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1
∨ 1 < 0 ∧ X₁+1 < X₂
∨ 1 < 0 ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1
∨ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 < X₂
∨ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ X₁+1 < X₂
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1 ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1
Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₆:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₆: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+5 {O(n)}
2⋅X₀+2⋅X₁+5 {O(n)}
Time-Bound by TWN-Loops:
TWN-Loops: t₁ 2⋅X₀+2⋅X₁+5 {O(n)}
relevant size-bounds w.r.t. t₆:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₆: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+5 {O(n)}
2⋅X₀+2⋅X₁+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+16⋅X₀⋅X₂+16⋅X₁⋅X₁+16⋅X₁⋅X₂+28⋅X₀+42⋅X₂+70⋅X₁+75 {O(n^2)}
TWN-Loops:
entry: t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁+1 ≤ X₂ ∧ X₁+1 ≤ X₀
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀,X₁,X₂-1) :|: X₁+1 ≤ X₂ ∧ X₀ ≤ X₁
entry: t₀: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁+1 ≤ X₀
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀,X₁,X₂-1) :|: X₁+1 ≤ X₂ ∧ X₀ ≤ X₁
entry: t₆: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀,X₁,X₂-1) :|: X₁+1 ≤ X₂ ∧ X₀ ≤ X₁
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < X₁ ∧ 1 < 0
∨ X₀ < X₁ ∧ X₁+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1
Stabilization-Threshold for: X₁+1 ≤ X₂
alphas_abs: X₁+1+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+4 {O(n)}
relevant size-bounds w.r.t. t₁:
X₁: 2⋅X₁ {O(n)}
X₂: 2⋅X₂ {O(n)}
Runtime-bound of t₁: 2⋅X₀+2⋅X₁+5 {O(n)}
Results in: 8⋅X₀⋅X₁+8⋅X₀⋅X₂+8⋅X₁⋅X₁+8⋅X₁⋅X₂+14⋅X₀+20⋅X₂+34⋅X₁+35 {O(n^2)}
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < X₁ ∧ 1 < 0
∨ X₀ < X₁ ∧ X₁+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1
Stabilization-Threshold for: X₁+1 ≤ X₂
alphas_abs: X₁+1+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+4 {O(n)}
relevant size-bounds w.r.t. t₀:
X₁: 2⋅X₁ {O(n)}
X₂: 2⋅X₂ {O(n)}
Runtime-bound of t₀: 2⋅X₀+2⋅X₁+5 {O(n)}
Results in: 8⋅X₀⋅X₁+8⋅X₀⋅X₂+8⋅X₁⋅X₁+8⋅X₁⋅X₂+14⋅X₀+20⋅X₂+34⋅X₁+35 {O(n^2)}
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < X₁ ∧ 1 < 0
∨ X₀ < X₁ ∧ X₁+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁+1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1
Stabilization-Threshold for: X₁+1 ≤ X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}
relevant size-bounds w.r.t. t₆:
X₁: X₁ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₆: 1 {O(1)}
Results in: 2⋅X₁+2⋅X₂+5 {O(n)}
16⋅X₀⋅X₁+16⋅X₀⋅X₂+16⋅X₁⋅X₁+16⋅X₁⋅X₂+28⋅X₀+42⋅X₂+70⋅X₁+75 {O(n^2)}
Analysing control-flow refined program
Found invariant X₁ ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location n_l1___2
Found invariant 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l1___3
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___1
Found invariant X₁ ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location n_l1___2
Found invariant 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l1___3
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___1
Time-Bound by TWN-Loops:
TWN-Loops: t₁₁₆ 4⋅X₁+4⋅X₂+11 {O(n)}
TWN-Loops:
entry: t₁₂₃: l1(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂-1) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁
results in twn-loop: twn:Inv: [X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁] , (X₀,X₁,X₂) -> (X₀,X₁,X₂-1) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < X₁ ∧ 1 < 0
∨ X₀ < X₁ ∧ 1 < 0 ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
∨ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0
∨ X₀ < X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0 ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ < X₂ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
Stabilization-Threshold for: 1+X₁ ≤ X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₃:
X₁: X₁ {O(n)}
X₂: X₂+1 {O(n)}
Runtime-bound of t₁₂₃: 1 {O(1)}
Results in: 4⋅X₁+4⋅X₂+11 {O(n)}
4⋅X₁+4⋅X₂+11 {O(n)}
Found invariant X₁ ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location n_l1___2
Found invariant 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l1___3
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___1
Time-Bound by TWN-Loops:
TWN-Loops: t₁₂₂ 4⋅X₀+4⋅X₁+10 {O(n)}
TWN-Loops:
entry: t₁₂₅: l1(X₀, X₁, X₂) → n_l1___4(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ X₀] , (X₀,X₁,X₂) -> (X₀-1,X₁,X₂) :|: X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
Termination: true
Formula:
1 < 0
∨ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
Stabilization-Threshold for: 1+X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₅:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁₂₅: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+10 {O(n)}
4⋅X₀+4⋅X₁+10 {O(n)}
Found invariant X₁ ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location n_l1___2
Found invariant 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l1___3
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___1
Found invariant X₁ ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location n_l1___2
Found invariant 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l1___3
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___1
Found invariant X₁ ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location n_l1___2
Found invariant 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l1___3
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___1
Found invariant X₁ ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location n_l1___2
Found invariant 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l1___3
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___1
Time-Bound by TWN-Loops:
TWN-Loops: t₁₁₈ 56⋅X₀+56⋅X₁+148 {O(n)}
TWN-Loops:
entry: t₁₂₁: n_l1___4(X₀, X₁, X₂) → n_l1___3(X₀-1, X₁, X₂) :|: X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀
results in twn-loop: twn:Inv: [1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀] , (X₀,X₁,X₂) -> (X₀-1,X₁,X₂) :|: 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∨ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂
entry: t₁₂₄: l1(X₀, X₁, X₂) → n_l1___3(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂
results in twn-loop: twn:Inv: [1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀] , (X₀,X₁,X₂) -> (X₀-1,X₁,X₂) :|: 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∨ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂
entry: t₁₂₁: n_l1___4(X₀, X₁, X₂) → n_l1___3(X₀-1, X₁, X₂) :|: X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀
results in twn-loop: twn:Inv: [1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀] , (X₀,X₁,X₂) -> (X₀-1,X₁,X₂) :|: 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∨ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂
entry: t₁₂₄: l1(X₀, X₁, X₂) → n_l1___3(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂
results in twn-loop: twn:Inv: [1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀] , (X₀,X₁,X₂) -> (X₀-1,X₁,X₂) :|: 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∨ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂
Termination: true
Formula:
1 < 0 ∧ 1+X₁ < X₂
∨ 1 < 0 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₂
∨ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₂
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 1+X₁ < X₂
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₂
∨ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₂
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₁ < X₂
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₂
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₂
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₂ ∧ 1 < 0
∨ 1+X₁ < X₂ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
Stabilization-Threshold for: 1+X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₁:
X₀: 4⋅X₁+6⋅X₀+14 {O(n)}
X₁: 2⋅X₁ {O(n)}
Runtime-bound of t₁₂₁: 1 {O(1)}
Results in: 24⋅X₀+24⋅X₁+63 {O(n)}
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂
Termination: true
Formula:
1 < 0 ∧ 1+X₁ < X₂
∨ 1 < 0 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₂
∨ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₂
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 1+X₁ < X₂
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₂
∨ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₂
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₁ < X₂
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₂
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₂
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₂ ∧ 1 < 0
∨ 1+X₁ < X₂ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
Stabilization-Threshold for: 1+X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₄:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁₂₄: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+11 {O(n)}
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂
Termination: true
Formula:
1 < 0 ∧ 1+X₁ < X₂
∨ 1 < 0 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₂
∨ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₂
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 1+X₁ < X₂
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₂
∨ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₂
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₁ < X₂
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₂
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₂
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₂ ∧ 1 < 0
∨ 1+X₁ < X₂ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
Stabilization-Threshold for: 1+X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₁:
X₀: 4⋅X₁+6⋅X₀+14 {O(n)}
X₁: 2⋅X₁ {O(n)}
Runtime-bound of t₁₂₁: 1 {O(1)}
Results in: 24⋅X₀+24⋅X₁+63 {O(n)}
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂
Termination: true
Formula:
1 < 0 ∧ 1+X₁ < X₂
∨ 1 < 0 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₂
∨ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₂
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 1+X₁ < X₂
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₂
∨ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₂
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₁ < X₂
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₂
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₂
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁
∨ 1+X₁ < X₂ ∧ 1 < 0
∨ 1+X₁ < X₂ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
Stabilization-Threshold for: 1+X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₄:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁₂₄: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+11 {O(n)}
56⋅X₀+56⋅X₁+148 {O(n)}
Time-Bound by TWN-Loops:
TWN-Loops: t₁₁₉ 56⋅X₀+56⋅X₁+148 {O(n)}
relevant size-bounds w.r.t. t₁₂₁:
X₀: 4⋅X₁+6⋅X₀+14 {O(n)}
X₁: 2⋅X₁ {O(n)}
Runtime-bound of t₁₂₁: 1 {O(1)}
Results in: 24⋅X₀+24⋅X₁+63 {O(n)}
relevant size-bounds w.r.t. t₁₂₄:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁₂₄: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+11 {O(n)}
relevant size-bounds w.r.t. t₁₂₁:
X₀: 4⋅X₁+6⋅X₀+14 {O(n)}
X₁: 2⋅X₁ {O(n)}
Runtime-bound of t₁₂₁: 1 {O(1)}
Results in: 24⋅X₀+24⋅X₁+63 {O(n)}
relevant size-bounds w.r.t. t₁₂₄:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁₂₄: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+11 {O(n)}
56⋅X₀+56⋅X₁+148 {O(n)}
Found invariant X₁ ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location n_l1___2
Found invariant 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l1___3
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___1
Found invariant X₁ ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location n_l1___2
Found invariant 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l1___3
Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___1
Time-Bound by TWN-Loops:
TWN-Loops: t₁₁₅ 68⋅X₁+68⋅X₂+44 {O(n)}
TWN-Loops:
entry: t₁₂₀: n_l1___4(X₀, X₁, X₂) → n_l1___1(X₀, X₁, X₂-1) :|: X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁] , (X₀,X₁,X₂) -> (X₀,X₁,X₂-1) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁
entry: t₁₁₇: n_l1___3(X₀, X₁, X₂) → n_l1___1(X₀, X₁, X₂-1) :|: 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁] , (X₀,X₁,X₂) -> (X₀,X₁,X₂-1) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < X₁ ∧ 1 < 0 ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1 < 0 ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1 < 0 ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0 ∧ X₁ < X₀
∨ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0 ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ < X₀
∨ 1 < 0 ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ < X₀
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ X₁ < X₀
∨ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ < X₂ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ < X₀
∨ 1+X₁ < X₂ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ < X₀
∨ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ X₁ < X₀
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ < X₀
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ < X₀
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
Stabilization-Threshold for: 1+X₁ ≤ X₂
alphas_abs: 1+X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+4 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}
relevant size-bounds w.r.t. t₁₂₀:
X₁: 2⋅X₁ {O(n)}
X₂: 2⋅X₂+2 {O(n)}
Runtime-bound of t₁₂₀: 1 {O(1)}
Results in: 8⋅X₁+8⋅X₂+18 {O(n)}
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₀ < X₁ ∧ 1 < 0 ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1 < 0 ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1 < 0 ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ < X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ < X₀
∨ X₀ < X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0 ∧ X₁ < X₀
∨ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0 ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ < X₀
∨ 1 < 0 ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ < X₀
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ X₁ < X₀
∨ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ < X₂ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ < X₀
∨ 1+X₁ < X₂ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ < X₀
∨ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ X₁ < X₀
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ < X₀
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ < X₀
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
Stabilization-Threshold for: 1+X₁ ≤ X₂
alphas_abs: 1+X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+4 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}
relevant size-bounds w.r.t. t₁₁₇:
X₁: 15⋅X₁ {O(n)}
X₂: 15⋅X₂+4 {O(n)}
Runtime-bound of t₁₁₇: 1 {O(1)}
Results in: 60⋅X₁+60⋅X₂+26 {O(n)}
68⋅X₁+68⋅X₂+44 {O(n)}
CFR: Improvement to new bound with the following program:
new bound:
116⋅X₀+188⋅X₁+72⋅X₂+361 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, n_l1___1, n_l1___2, n_l1___3, n_l1___4
Transitions:
t₆: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁₂₃: l1(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂-1) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁
t₁₂₄: l1(X₀, X₁, X₂) → n_l1___3(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂
t₁₂₅: l1(X₀, X₁, X₂) → n_l1___4(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀
t₁₁₅: n_l1___1(X₀, X₁, X₂) → n_l1___1(X₀, X₁, X₂-1) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁₁₆: n_l1___2(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂-1) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁
t₁₁₇: n_l1___3(X₀, X₁, X₂) → n_l1___1(X₀, X₁, X₂-1) :|: 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀
t₁₁₈: n_l1___3(X₀, X₁, X₂) → n_l1___3(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀
t₁₁₉: n_l1___3(X₀, X₁, X₂) → n_l1___3(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀
t₁₂₀: n_l1___4(X₀, X₁, X₂) → n_l1___1(X₀, X₁, X₂-1) :|: X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₂₁: n_l1___4(X₀, X₁, X₂) → n_l1___3(X₀-1, X₁, X₂) :|: X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀
t₁₂₂: n_l1___4(X₀, X₁, X₂) → n_l1___4(X₀-1, X₁, X₂) :|: X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀
All Bounds
Timebounds
Overall timebound:116⋅X₀+188⋅X₁+72⋅X₂+368 {O(n)}
t₆: 1 {O(1)}
t₁₂₃: 1 {O(1)}
t₁₂₄: 1 {O(1)}
t₁₂₅: 1 {O(1)}
t₁₁₅: 68⋅X₁+68⋅X₂+44 {O(n)}
t₁₁₆: 4⋅X₁+4⋅X₂+11 {O(n)}
t₁₁₇: 1 {O(1)}
t₁₁₈: 56⋅X₀+56⋅X₁+148 {O(n)}
t₁₁₉: 56⋅X₀+56⋅X₁+148 {O(n)}
t₁₂₀: 1 {O(1)}
t₁₂₁: 1 {O(1)}
t₁₂₂: 4⋅X₀+4⋅X₁+10 {O(n)}
Costbounds
Overall costbound: 116⋅X₀+188⋅X₁+72⋅X₂+368 {O(n)}
t₆: 1 {O(1)}
t₁₂₃: 1 {O(1)}
t₁₂₄: 1 {O(1)}
t₁₂₅: 1 {O(1)}
t₁₁₅: 68⋅X₁+68⋅X₂+44 {O(n)}
t₁₁₆: 4⋅X₁+4⋅X₂+11 {O(n)}
t₁₁₇: 1 {O(1)}
t₁₁₈: 56⋅X₀+56⋅X₁+148 {O(n)}
t₁₁₉: 56⋅X₀+56⋅X₁+148 {O(n)}
t₁₂₀: 1 {O(1)}
t₁₂₁: 1 {O(1)}
t₁₂₂: 4⋅X₀+4⋅X₁+10 {O(n)}
Sizebounds
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₁₂₃, X₀: X₀ {O(n)}
t₁₂₃, X₁: X₁ {O(n)}
t₁₂₃, X₂: X₂+1 {O(n)}
t₁₂₄, X₀: X₀+1 {O(n)}
t₁₂₄, X₁: X₁ {O(n)}
t₁₂₄, X₂: X₂ {O(n)}
t₁₂₅, X₀: X₀+1 {O(n)}
t₁₂₅, X₁: X₁ {O(n)}
t₁₂₅, X₂: X₂ {O(n)}
t₁₁₅, X₀: 248⋅X₁+265⋅X₀+679 {O(n)}
t₁₁₅, X₁: 17⋅X₁ {O(n)}
t₁₁₅, X₂: 68⋅X₁+85⋅X₂+50 {O(n)}
t₁₁₆, X₀: X₀ {O(n)}
t₁₁₆, X₁: X₁ {O(n)}
t₁₁₆, X₂: 4⋅X₁+5⋅X₂+12 {O(n)}
t₁₁₇, X₀: 244⋅X₁+259⋅X₀+667 {O(n)}
t₁₁₇, X₁: 15⋅X₁ {O(n)}
t₁₁₇, X₂: 15⋅X₂+4 {O(n)}
t₁₁₈, X₀: 120⋅X₁+126⋅X₀+326 {O(n)}
t₁₁₈, X₁: 6⋅X₁ {O(n)}
t₁₁₈, X₂: 6⋅X₂ {O(n)}
t₁₁₉, X₀: 120⋅X₁+126⋅X₀+326 {O(n)}
t₁₁₉, X₁: 6⋅X₁ {O(n)}
t₁₁₉, X₂: 6⋅X₂ {O(n)}
t₁₂₀, X₀: 4⋅X₁+6⋅X₀+12 {O(n)}
t₁₂₀, X₁: 2⋅X₁ {O(n)}
t₁₂₀, X₂: 2⋅X₂+2 {O(n)}
t₁₂₁, X₀: 4⋅X₁+6⋅X₀+14 {O(n)}
t₁₂₁, X₁: 2⋅X₁ {O(n)}
t₁₂₁, X₂: 2⋅X₂ {O(n)}
t₁₂₂, X₀: 4⋅X₁+5⋅X₀+11 {O(n)}
t₁₂₂, X₁: X₁ {O(n)}
t₁₂₂, X₂: X₂ {O(n)}