Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₅: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ < X₁
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ < X₀
t₈: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₂, X₁, X₂) :|: 0 < X₁
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ 0
t₆: l4(X₀, X₁, X₂) → l1(0, X₁, X₂) :|: X₁ < X₀
t₇: l4(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₀ ≤ X₁

Preprocessing

Found invariant 1 ≤ X₁ for location l1

Found invariant 1 ≤ 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) → l3(X₀, X₁, X₂)
t₅: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ < X₁ ∧ 1 ≤ X₁
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ < X₀ ∧ 1 ≤ X₁
t₈: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₂, X₁, X₂) :|: 0 < X₁
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ 0
t₆: l4(X₀, X₁, X₂) → l1(0, X₁, X₂) :|: X₁ < X₀ ∧ 1 ≤ X₁
t₇: l4(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1 ≤ X₁

Analysing control-flow refined program

Cut unsatisfiable transition t₂₂₉: n_l1___2→l2

Cut unsatisfiable transition t₂₁₁: n_l1___4→n_l4___3

Cut unreachable locations [n_l4___3] from the program graph

Found invariant 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location n_l4___6

Found invariant 1 ≤ X₁ ∧ X₀ ≤ X₁ for location n_l1___4

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___2

Found invariant X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___5

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___1

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ for location l1

Found invariant 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___6

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___4

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___2

Found invariant X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___5

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___1

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ for location l1

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location n_l4___6

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ for location n_l1___4

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___2

Found invariant X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___5

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___1

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₂₁₂ 12⋅X₁+6⋅X₂+20 {O(n)}

TWN-Loops:

entry: t₂₁₅: n_l4___1(X₀, X₁, X₂) → n_l1___4(X₀+1, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁] , (X₀,X₁,X₂) -> (X₀+1,X₁,X₂) :|: 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ X₀ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
entry: t₂₁₄: l1(X₀, X₁, X₂) → n_l4___6(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ < X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁
results in twn-loop: twn:Inv: [1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁] , (X₀,X₁,X₂) -> (1+X₀,X₁,X₂) :|: X₀ < X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₀ < X₁
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁
X₂: X₂

Termination: true
Formula:

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

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

relevant size-bounds w.r.t. t₂₁₅:
X₁: X₁ {O(n)}
Runtime-bound of t₂₁₅: 1 {O(1)}
Results in: 6⋅X₁+11 {O(n)}

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

Termination: true
Formula:

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

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: 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. t₂₁₄:
X₀: X₂ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₁₄: 1 {O(1)}
Results in: 6⋅X₁+6⋅X₂+9 {O(n)}

12⋅X₁+6⋅X₂+20 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₁₈ 12⋅X₁+6⋅X₂+20 {O(n)}

relevant size-bounds w.r.t. t₂₁₅:
X₁: X₁ {O(n)}
Runtime-bound of t₂₁₅: 1 {O(1)}
Results in: 6⋅X₁+11 {O(n)}

relevant size-bounds w.r.t. t₂₁₄:
X₀: X₂ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₁₄: 1 {O(1)}
Results in: 6⋅X₁+6⋅X₂+9 {O(n)}

12⋅X₁+6⋅X₂+20 {O(n)}

CFR: Improvement to new bound with the following program:

new bound:

12⋅X₂+24⋅X₁+40 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l5, n_l1___2, n_l1___4, n_l4___1, n_l4___5, n_l4___6
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₅: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁
t₂₁₃: l1(X₀, X₁, X₂) → n_l4___5(X₀, X₁, X₂) :|: X₁ < X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁
t₂₁₄: l1(X₀, X₁, X₂) → n_l4___6(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ < X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁
t₈: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₂, X₁, X₂) :|: 0 < X₁
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ 0
t₂₁₀: n_l1___2(X₀, X₁, X₂) → n_l4___1(X₀, X₁, X₂) :|: X₀ < X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ X₀ < X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₃₀: n_l1___4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
t₂₁₂: n_l1___4(X₀, X₁, X₂) → n_l4___6(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ X₀ < X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
t₂₁₅: n_l4___1(X₀, X₁, X₂) → n_l1___4(X₀+1, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₁₇: n_l4___5(X₀, X₁, X₂) → n_l1___2(0, X₁, X₂) :|: X₁ < X₀ ∧ 1 ≤ X₁ ∧ X₁ < X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₁₈: n_l4___6(X₀, X₁, X₂) → n_l1___4(X₀+1, X₁, X₂) :|: X₀ < X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁

All Bounds

Timebounds

Overall timebound:12⋅X₂+24⋅X₁+51 {O(n)}
t₀: 1 {O(1)}
t₅: 1 {O(1)}
t₂₁₃: 1 {O(1)}
t₂₁₄: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₂₁₀: 1 {O(1)}
t₂₁₂: 12⋅X₁+6⋅X₂+20 {O(n)}
t₂₃₀: 1 {O(1)}
t₂₁₅: 1 {O(1)}
t₂₁₇: 1 {O(1)}
t₂₁₈: 12⋅X₁+6⋅X₂+20 {O(n)}

Costbounds

Overall costbound: 12⋅X₂+24⋅X₁+51 {O(n)}
t₀: 1 {O(1)}
t₅: 1 {O(1)}
t₂₁₃: 1 {O(1)}
t₂₁₄: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₂₁₀: 1 {O(1)}
t₂₁₂: 12⋅X₁+6⋅X₂+20 {O(n)}
t₂₃₀: 1 {O(1)}
t₂₁₅: 1 {O(1)}
t₂₁₇: 1 {O(1)}
t₂₁₈: 12⋅X₁+6⋅X₂+20 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₅, X₀: X₂ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₂₁₃, X₀: X₂ {O(n)}
t₂₁₃, X₁: X₁ {O(n)}
t₂₁₃, X₂: X₂ {O(n)}
t₂₁₄, X₀: X₂ {O(n)}
t₂₁₄, X₁: X₁ {O(n)}
t₂₁₄, X₂: X₂ {O(n)}
t₈, X₀: 12⋅X₁+8⋅X₂+X₀+22 {O(n)}
t₈, X₁: 5⋅X₁ {O(n)}
t₈, X₂: 5⋅X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂₁₀, X₀: 0 {O(1)}
t₂₁₀, X₁: X₁ {O(n)}
t₂₁₀, X₂: X₂ {O(n)}
t₂₁₂, X₀: 12⋅X₁+7⋅X₂+21 {O(n)}
t₂₁₂, X₁: 2⋅X₁ {O(n)}
t₂₁₂, X₂: 2⋅X₂ {O(n)}
t₂₃₀, X₀: 12⋅X₁+7⋅X₂+22 {O(n)}
t₂₃₀, X₁: 3⋅X₁ {O(n)}
t₂₃₀, X₂: 3⋅X₂ {O(n)}
t₂₁₅, X₀: 1 {O(1)}
t₂₁₅, X₁: X₁ {O(n)}
t₂₁₅, X₂: X₂ {O(n)}
t₂₁₇, X₀: 0 {O(1)}
t₂₁₇, X₁: X₁ {O(n)}
t₂₁₇, X₂: X₂ {O(n)}
t₂₁₈, X₀: 12⋅X₁+7⋅X₂+21 {O(n)}
t₂₁₈, X₁: 2⋅X₁ {O(n)}
t₂₁₈, X₂: 2⋅X₂ {O(n)}