Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₁+1 ≤ X₀ ∧ X₁+1 ≤ X₂
t₂: l1(X₀, X₁, X₂) → l2(X₀-1, X₁, X₂) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ X₁
t₀: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₀
Preprocessing
Found invariant 1+X₁ ≤ X₀ for location l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₁+1 ≤ X₀ ∧ X₁+1 ≤ X₂ ∧ 1+X₁ ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀-1, X₁, X₂) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀
t₀: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₀
Analysing control-flow refined program
Found invariant 1+X₁ ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___3
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location n_l2___2
Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l1___1
Found invariant 1+X₁ ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___3
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location n_l2___2
Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l1___1
Time-Bound by TWN-Loops:
TWN-Loops: t₈₆ 4⋅X₁+4⋅X₂+11 {O(n)}
TWN-Loops:
entry: t₈₈: n_l1___4(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀] , (X₀,X₁,X₂) -> (X₀,X₁,X₂-1) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
1+X₁ < X₀ ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
∨ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
∨ 1+X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ < X₀ ∧ 1 < 0
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ 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 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ < X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 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. t₈₈:
X₁: X₁ {O(n)}
X₂: X₂+1 {O(n)}
Runtime-bound of t₈₈: 1 {O(1)}
Results in: 4⋅X₁+4⋅X₂+11 {O(n)}
4⋅X₁+4⋅X₂+11 {O(n)}
Found invariant 1+X₁ ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___3
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location n_l2___2
Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l1___1
Found invariant 1+X₁ ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___3
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l2___2
Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___1
Time-Bound by TWN-Loops:
TWN-Loops: t₈₅ 12⋅X₀+12⋅X₁+28 {O(n)}
TWN-Loops:
entry: t₈₉: n_l1___4(X₀, X₁, X₂) → n_l2___2(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀
results in twn-loop: twn:Inv: [X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀] , (X₀,X₁,X₂) -> (X₀-1,X₁,X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁
entry: t₈₇: n_l1___3(X₀, X₁, X₂) → n_l2___2(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀
results in twn-loop: twn:Inv: [X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀] , (X₀,X₁,X₂) -> (X₀-1,X₁,X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂
Termination: true
Formula:
X₂ < X₁ ∧ 1 < 0
∨ X₂ < X₁ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ < X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ X₂ < X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 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. t₈₉:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₈₉: 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:
X₂ < X₁ ∧ 1 < 0
∨ X₂ < X₁ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ < X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ X₂ < X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
Stabilization-Threshold for: 1+X₁ ≤ X₀
alphas_abs: 1+X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {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. t₈₇:
X₀: 2⋅X₀+2 {O(n)}
X₁: 2⋅X₁ {O(n)}
Runtime-bound of t₈₇: 1 {O(1)}
Results in: 8⋅X₀+8⋅X₁+17 {O(n)}
12⋅X₀+12⋅X₁+28 {O(n)}
Time-Bound by TWN-Loops:
TWN-Loops: t₉₀ 12⋅X₀+12⋅X₁+28 {O(n)}
relevant size-bounds w.r.t. t₈₉:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₈₉: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+11 {O(n)}
relevant size-bounds w.r.t. t₈₇:
X₀: 2⋅X₀+2 {O(n)}
X₁: 2⋅X₁ {O(n)}
Runtime-bound of t₈₇: 1 {O(1)}
Results in: 8⋅X₀+8⋅X₁+17 {O(n)}
12⋅X₀+12⋅X₁+28 {O(n)}
CFR: Improvement to new bound with the following program:
new bound:
24⋅X₀+28⋅X₁+4⋅X₂+67 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l2, n_l1___1, n_l1___3, n_l1___4, n_l2___2
Transitions:
t₃: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₉₁: l2(X₀, X₁, X₂) → n_l1___4(X₀, X₁, X₂) :|: 1+X₁ ≤ X₀
t₈₅: n_l1___1(X₀, X₁, X₂) → n_l2___2(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₈₆: n_l1___3(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₈₇: n_l1___3(X₀, X₁, X₂) → n_l2___2(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₈₈: n_l1___4(X₀, X₁, X₂) → n_l1___3(X₀, X₁, X₂-1) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₈₉: n_l1___4(X₀, X₁, X₂) → n_l2___2(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀
t₉₀: n_l2___2(X₀, X₁, X₂) → n_l1___1(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀
All Bounds
Timebounds
Overall timebound:24⋅X₀+28⋅X₁+4⋅X₂+72 {O(n)}
t₃: 1 {O(1)}
t₉₁: 1 {O(1)}
t₈₅: 12⋅X₀+12⋅X₁+28 {O(n)}
t₈₆: 4⋅X₁+4⋅X₂+11 {O(n)}
t₈₇: 1 {O(1)}
t₈₈: 1 {O(1)}
t₈₉: 1 {O(1)}
t₉₀: 12⋅X₀+12⋅X₁+28 {O(n)}
Costbounds
Overall costbound: 24⋅X₀+28⋅X₁+4⋅X₂+72 {O(n)}
t₃: 1 {O(1)}
t₉₁: 1 {O(1)}
t₈₅: 12⋅X₀+12⋅X₁+28 {O(n)}
t₈₆: 4⋅X₁+4⋅X₂+11 {O(n)}
t₈₇: 1 {O(1)}
t₈₈: 1 {O(1)}
t₈₉: 1 {O(1)}
t₉₀: 12⋅X₀+12⋅X₁+28 {O(n)}
Sizebounds
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₉₁, X₀: X₀ {O(n)}
t₉₁, X₁: X₁ {O(n)}
t₉₁, X₂: X₂ {O(n)}
t₈₅, X₀: 12⋅X₁+15⋅X₀+31 {O(n)}
t₈₅, X₁: 3⋅X₁ {O(n)}
t₈₅, X₂: 4⋅X₁+7⋅X₂+13 {O(n)}
t₈₆, X₀: X₀ {O(n)}
t₈₆, X₁: X₁ {O(n)}
t₈₆, X₂: 4⋅X₁+5⋅X₂+12 {O(n)}
t₈₇, X₀: 2⋅X₀+2 {O(n)}
t₈₇, X₁: 2⋅X₁ {O(n)}
t₈₇, X₂: 4⋅X₁+6⋅X₂+13 {O(n)}
t₈₈, X₀: X₀ {O(n)}
t₈₈, X₁: X₁ {O(n)}
t₈₈, X₂: X₂+1 {O(n)}
t₈₉, X₀: X₀+1 {O(n)}
t₈₉, X₁: X₁ {O(n)}
t₈₉, X₂: X₂ {O(n)}
t₉₀, X₀: 12⋅X₁+15⋅X₀+31 {O(n)}
t₉₀, X₁: 3⋅X₁ {O(n)}
t₉₀, X₂: 4⋅X₁+7⋅X₂+13 {O(n)}