Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₀ < X₁
t₃: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ < X₀
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₅: l3(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁ < X₀
t₆: l3(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₀ ≤ X₁
t₇: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)

Preprocessing

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₀ < X₁
t₃: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ < X₀
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₅: l3(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₁ < X₀
t₆: l3(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₀ ≤ X₁
t₇: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4

Time-Bound by TWN-Loops:

TWN-Loops: t₂ 4⋅X₁+4⋅X₂+6 {O(n)}

TWN-Loops:

entry: t₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀+1,X₁,X₂) :|: X₀ < X₁ ∧ X₀ ≤ X₁
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

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

Stabilization-Threshold for: 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. t₁:
X₀: X₂ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 4⋅X₁+4⋅X₂+6 {O(n)}

4⋅X₁+4⋅X₂+6 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₆ 4⋅X₁+4⋅X₂+6 {O(n)}

relevant size-bounds w.r.t. t₁:
X₀: X₂ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 4⋅X₁+4⋅X₂+6 {O(n)}

4⋅X₁+4⋅X₂+6 {O(n)}

Found invariant 1 ≤ 0 for location l5

Found invariant 1 ≤ 0 for location l1

Found invariant 1 ≤ 0 for location l4

Found invariant 1 ≤ 0 for location l3

Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5

Found invariant X₀ ≤ X₂ for location l1

Found invariant X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4

Found invariant X₀ ≤ X₂ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₃ 40⋅X₁⋅X₁+40⋅X₂⋅X₂+80⋅X₁⋅X₂+126⋅X₁+126⋅X₂+100 {O(n^2)}

TWN-Loops:

entry: t₆: l3(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₀ ≤ X₁
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀-1,X₁,X₂) :|: X₁ < X₀ ∧ X₁ < X₀
entry: t₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
results in twn-loop: twn: (X₀,X₁,X₂) -> (X₀-1,X₁,X₂) :|: X₁ < X₀ ∧ X₁ < X₀
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁

Termination: true
Formula:

1 < 0
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₁ < 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: 4⋅X₁+5⋅X₂+6 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₆: 4⋅X₁+4⋅X₂+6 {O(n)}
Results in: 40⋅X₁⋅X₁+40⋅X₂⋅X₂+80⋅X₁⋅X₂+124⋅X₁+124⋅X₂+96 {O(n^2)}

order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂

Termination: true
Formula:

1 < 0
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1

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

relevant size-bounds w.r.t. t₁:
X₀: X₂ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₁+2⋅X₂+4 {O(n)}

40⋅X₁⋅X₁+40⋅X₂⋅X₂+80⋅X₁⋅X₂+126⋅X₁+126⋅X₂+100 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₅ 40⋅X₁⋅X₁+40⋅X₂⋅X₂+80⋅X₁⋅X₂+126⋅X₁+126⋅X₂+100 {O(n^2)}

relevant size-bounds w.r.t. t₆:
X₀: 4⋅X₁+5⋅X₂+6 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₆: 4⋅X₁+4⋅X₂+6 {O(n)}
Results in: 40⋅X₁⋅X₁+40⋅X₂⋅X₂+80⋅X₁⋅X₂+124⋅X₁+124⋅X₂+96 {O(n^2)}

relevant size-bounds w.r.t. t₁:
X₀: X₂ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₁+2⋅X₂+4 {O(n)}

40⋅X₁⋅X₁+40⋅X₂⋅X₂+80⋅X₁⋅X₂+126⋅X₁+126⋅X₂+100 {O(n^2)}

Analysing control-flow refined program

Cut unsatisfiable transition t₁₄₈: n_l1___2→n_l3___4

Cut unsatisfiable transition t₁₄₉: n_l1___5→n_l3___3

Cut unreachable locations [n_l3___3] from the program graph

Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location n_l3___4

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___6

Found invariant 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l1___2

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___5

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4

Found invariant 2+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___1

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l3___7

Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location n_l3___4

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___6

Found invariant 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l1___2

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___5

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4

Found invariant 2+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___1

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l3___7

Time-Bound by TWN-Loops:

TWN-Loops: t₁₄₇ 2⋅X₁+2⋅X₂+6 {O(n)}

TWN-Loops:

entry: t₁₅₆: n_l3___6(X₀, X₁, X₂) → n_l1___2(X₀-1, X₁, X₂) :|: X₁ < X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ < X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀
results in twn-loop: twn:Inv: [1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 2+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀] , (X₀,X₁,X₂) -> (X₀-1,X₁,X₂) :|: X₁ < X₀ ∧ X₁ < X₀ ∧ X₁ < X₀
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂

Termination: true
Formula:

1 < 0
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1

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. t₁₅₆:
X₀: X₂+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁₅₆: 1 {O(1)}
Results in: 2⋅X₁+2⋅X₂+6 {O(n)}

2⋅X₁+2⋅X₂+6 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₅₃ 2⋅X₁+2⋅X₂+6 {O(n)}

relevant size-bounds w.r.t. t₁₅₆:
X₀: X₂+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁₅₆: 1 {O(1)}
Results in: 2⋅X₁+2⋅X₂+6 {O(n)}

2⋅X₁+2⋅X₂+6 {O(n)}

Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location n_l3___4

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___6

Found invariant 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l1___2

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___5

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4

Found invariant 2+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___1

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l3___7

Time-Bound by TWN-Loops:

TWN-Loops: t₁₅₀ 6⋅X₁+6⋅X₂+16 {O(n)}

TWN-Loops:

entry: t₁₅₇: n_l3___7(X₀, X₁, X₂) → n_l1___5(X₀+1, X₁, X₂) :|: X₀ < X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
results in twn-loop: twn:Inv: [1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁] , (X₀,X₁,X₂) -> (X₀+1,X₁,X₂) :|: X₀ ≤ 1+X₁ ∧ X₀ < X₁ ∧ X₀ < X₁ ∧ X₀ ≤ X₁
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁
X₂: X₂

Termination: true
Formula:

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

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

relevant size-bounds w.r.t. t₁₅₇:
X₀: X₂+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁₅₇: 1 {O(1)}
Results in: 6⋅X₁+6⋅X₂+16 {O(n)}

6⋅X₁+6⋅X₂+16 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₅₅ 6⋅X₁+6⋅X₂+16 {O(n)}

relevant size-bounds w.r.t. t₁₅₇:
X₀: X₂+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁₅₇: 1 {O(1)}
Results in: 6⋅X₁+6⋅X₂+16 {O(n)}

6⋅X₁+6⋅X₂+16 {O(n)}

CFR: Improvement to new bound with the following program:

new bound:

16⋅X₁+16⋅X₂+44 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l4, l5, n_l1___2, n_l1___5, n_l3___1, n_l3___4, n_l3___6, n_l3___7
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁₅₁: l1(X₀, X₁, X₂) → n_l3___6(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ < X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁₅₂: l1(X₀, X₁, X₂) → n_l3___7(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ < X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₇: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁₆₈: n_l1___2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀
t₁₄₇: n_l1___2(X₀, X₁, X₂) → n_l3___1(X₀, X₁, X₂) :|: X₁ < X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀
t₁₆₉: n_l1___5(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁
t₁₅₀: n_l1___5(X₀, X₁, X₂) → n_l3___4(X₀, X₁, X₂) :|: X₀ ≤ 1+X₁ ∧ X₀ < X₁ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁
t₁₅₃: n_l3___1(X₀, X₁, X₂) → n_l1___2(X₀-1, X₁, X₂) :|: X₁ < X₀ ∧ X₁ < X₀ ∧ 2+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₁₅₅: n_l3___4(X₀, X₁, X₂) → n_l1___5(X₀+1, X₁, X₂) :|: X₀ < X₁ ∧ X₀ ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁
t₁₅₆: n_l3___6(X₀, X₁, X₂) → n_l1___2(X₀-1, X₁, X₂) :|: X₁ < X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ < X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₁₅₇: n_l3___7(X₀, X₁, X₂) → n_l1___5(X₀+1, X₁, X₂) :|: X₀ < X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁

All Bounds

Timebounds

Overall timebound:16⋅X₁+16⋅X₂+54 {O(n)}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₁₅₁: 1 {O(1)}
t₁₅₂: 1 {O(1)}
t₁: 1 {O(1)}
t₇: 1 {O(1)}
t₁₄₇: 2⋅X₁+2⋅X₂+6 {O(n)}
t₁₆₈: 1 {O(1)}
t₁₅₀: 6⋅X₁+6⋅X₂+16 {O(n)}
t₁₆₉: 1 {O(1)}
t₁₅₃: 2⋅X₁+2⋅X₂+6 {O(n)}
t₁₅₅: 6⋅X₁+6⋅X₂+16 {O(n)}
t₁₅₆: 1 {O(1)}
t₁₅₇: 1 {O(1)}

Costbounds

Overall costbound: 16⋅X₁+16⋅X₂+54 {O(n)}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₁₅₁: 1 {O(1)}
t₁₅₂: 1 {O(1)}
t₁: 1 {O(1)}
t₇: 1 {O(1)}
t₁₄₇: 2⋅X₁+2⋅X₂+6 {O(n)}
t₁₆₈: 1 {O(1)}
t₁₅₀: 6⋅X₁+6⋅X₂+16 {O(n)}
t₁₆₉: 1 {O(1)}
t₁₅₃: 2⋅X₁+2⋅X₂+6 {O(n)}
t₁₅₅: 6⋅X₁+6⋅X₂+16 {O(n)}
t₁₅₆: 1 {O(1)}
t₁₅₇: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₁₅₁, X₀: X₂ {O(n)}
t₁₅₁, X₁: X₁ {O(n)}
t₁₅₁, X₂: X₂ {O(n)}
t₁₅₂, X₀: X₂ {O(n)}
t₁₅₂, X₁: X₁ {O(n)}
t₁₅₂, X₂: X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₇, X₀: 13⋅X₂+8⋅X₁+26 {O(n)}
t₇, X₁: 5⋅X₁ {O(n)}
t₇, X₂: 5⋅X₂ {O(n)}
t₁₄₇, X₀: 2⋅X₁+3⋅X₂+7 {O(n)}
t₁₄₇, X₁: X₁ {O(n)}
t₁₄₇, X₂: X₂ {O(n)}
t₁₆₈, X₀: 2⋅X₁+4⋅X₂+8 {O(n)}
t₁₆₈, X₁: 2⋅X₁ {O(n)}
t₁₆₈, X₂: 2⋅X₂ {O(n)}
t₁₅₀, X₀: 6⋅X₁+7⋅X₂+17 {O(n)}
t₁₅₀, X₁: X₁ {O(n)}
t₁₅₀, X₂: X₂ {O(n)}
t₁₆₉, X₀: 6⋅X₁+8⋅X₂+18 {O(n)}
t₁₆₉, X₁: 2⋅X₁ {O(n)}
t₁₆₉, X₂: 2⋅X₂ {O(n)}
t₁₅₃, X₀: 2⋅X₁+3⋅X₂+7 {O(n)}
t₁₅₃, X₁: X₁ {O(n)}
t₁₅₃, X₂: X₂ {O(n)}
t₁₅₅, X₀: 6⋅X₁+7⋅X₂+17 {O(n)}
t₁₅₅, X₁: X₁ {O(n)}
t₁₅₅, X₂: X₂ {O(n)}
t₁₅₆, X₀: X₂+1 {O(n)}
t₁₅₆, X₁: X₁ {O(n)}
t₁₅₆, X₂: X₂ {O(n)}
t₁₅₇, X₀: X₂+1 {O(n)}
t₁₅₇, X₁: X₁ {O(n)}
t₁₅₇, X₂: X₂ {O(n)}