Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₁₀: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₆: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₈: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁₁: l4(X₀, X₁, X₂) → l5(X₀, X₁+1, X₂)
t₄: l5(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁+1 ≤ X₀
t₅: l5(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ < 1+X₁
t₂: l6(X₀, X₁, X₂) → l5(X₀, 0, X₂) :|: 0 ≤ X₀
t₃: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₀ < 0
t₁: l7(X₀, X₁, X₂) → l6(X₂, X₁, X₂)
t₁₃: l8(X₀, X₁, X₂) → l10(X₀, X₁, X₂)
t₁₂: l9(X₀, X₁, X₂) → l6(X₀-1, X₁, X₂)

Preprocessing

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2

Found invariant X₀ ≤ X₂ for location l6

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l8

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l10

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l9

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₁₀: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₁: l4(X₀, X₁, X₂) → l5(X₀, X₁+1, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l5(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₅: l5(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ < 1+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂: l6(X₀, X₁, X₂) → l5(X₀, 0, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ X₂
t₃: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₀ < 0 ∧ X₀ ≤ X₂
t₁: l7(X₀, X₁, X₂) → l6(X₂, X₁, X₂)
t₁₃: l8(X₀, X₁, X₂) → l10(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1+X₀ ≤ 0
t₁₂: l9(X₀, X₁, X₂) → l6(X₀-1, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀

MPRF for transition t₅: l5(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ < 1+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l3 [X₀+1 ]
l1 [X₀+1 ]
l4 [X₀+1 ]
l2 [X₀+1 ]
l5 [X₀+1 ]
l9 [X₁ ]
l6 [X₀+1 ]

MPRF for transition t₂: l6(X₀, X₁, X₂) → l5(X₀, 0, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l3 [X₀ ]
l1 [X₀ ]
l4 [X₀ ]
l2 [X₀ ]
l5 [X₀ ]
l9 [X₁ ]
l6 [X₀+1 ]

MPRF for transition t₁₂: l9(X₀, X₁, X₂) → l6(X₀-1, X₁, X₂) :|: 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l3 [X₀+1 ]
l1 [X₀+1 ]
l4 [X₀+1 ]
l2 [X₀+1 ]
l5 [X₀+1 ]
l9 [X₁+1 ]
l6 [X₀+1 ]

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2

Found invariant X₀ ≤ X₂ for location l6

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l8

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l10

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l9

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₀ 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

TWN-Loops:

entry: t₂: l6(X₀, X₁, X₂) → l5(X₀, 0, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ X₂
results in twn-loop: twn:Inv: [0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀] , (X₀,X₁,X₂) -> (X₀,X₁+1,X₂) :|: X₁+1 ≤ X₀
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₂: X₂

Termination: true
Formula:

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

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

relevant size-bounds w.r.t. t₂:
X₀: X₂+1 {O(n)}
Runtime-bound of t₂: X₂+1 {O(n)}
Results in: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₆ 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

relevant size-bounds w.r.t. t₂:
X₀: X₂+1 {O(n)}
Runtime-bound of t₂: X₂+1 {O(n)}
Results in: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₈ 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

relevant size-bounds w.r.t. t₂:
X₀: X₂+1 {O(n)}
Runtime-bound of t₂: X₂+1 {O(n)}
Results in: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₁ 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

relevant size-bounds w.r.t. t₂:
X₀: X₂+1 {O(n)}
Runtime-bound of t₂: X₂+1 {O(n)}
Results in: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₄ 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

relevant size-bounds w.r.t. t₂:
X₀: X₂+1 {O(n)}
Runtime-bound of t₂: X₂+1 {O(n)}
Results in: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

Analysing control-flow refined program

Found invariant X₀ ≤ X₂ for location l6

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___6

Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___5

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___7

Found invariant 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_l3___3

Found invariant 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_l1___2

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___9

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___8

Found invariant 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___1

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l8

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l10

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l9

Found invariant 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_l2___4

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₁₈: l5(X₀, X₁, X₂) → n_l2___9(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₁₃: n_l2___9(X₀, X₁, X₂) → n_l3___8(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₁₅: n_l3___8(X₀, X₁, X₂) → n_l1___7(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₁₁: n_l1___7(X₀, X₁, X₂) → n_l4___6(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₁₇: n_l4___6(X₀, X₁, X₂) → n_l5___5(X₀, X₁+1, X₂) :|: X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₁₁₀: n_l1___2(X₀, X₁, X₂) → n_l4___1(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+2⋅X₂+1 {O(n^2)}

MPRF:

l5 [0 ]
l6 [0 ]
n_l4___6 [0 ]
n_l2___9 [0 ]
n_l3___3 [X₂-X₁ ]
n_l1___2 [X₂-X₁ ]
n_l3___8 [0 ]
n_l1___7 [0 ]
n_l4___1 [X₂-X₁-1 ]
n_l2___4 [X₂-X₁ ]
n_l5___5 [X₂-X₁ ]
l9 [0 ]

MPRF for transition t₁₁₂: n_l2___4(X₀, X₁, X₂) → n_l3___3(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+2⋅X₂+1 {O(n^2)}

MPRF:

l5 [0 ]
l6 [0 ]
n_l4___6 [0 ]
n_l2___9 [0 ]
n_l3___3 [X₂-X₁-1 ]
n_l1___2 [X₂-X₁-1 ]
n_l3___8 [0 ]
n_l1___7 [0 ]
n_l4___1 [X₂-X₁-1 ]
n_l2___4 [X₂-X₁ ]
n_l5___5 [X₂-X₁ ]
l9 [0 ]

MPRF for transition t₁₁₄: n_l3___3(X₀, X₁, X₂) → n_l1___2(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+6⋅X₂+2 {O(n^2)}

MPRF:

l5 [X₀-2⋅X₂ ]
l6 [X₀-2⋅X₂ ]
n_l4___6 [X₀-2⋅X₂ ]
n_l2___9 [X₀-2⋅X₂ ]
n_l3___3 [X₀-X₁ ]
n_l1___2 [X₀-X₁-1 ]
n_l3___8 [X₀-2⋅X₂ ]
n_l1___7 [X₀-2⋅X₂ ]
n_l4___1 [X₀-X₁-1 ]
n_l2___4 [X₀-X₁ ]
n_l5___5 [X₀-X₁ ]
l9 [X₁-2⋅X₂ ]

MPRF for transition t₁₁₆: n_l4___1(X₀, X₁, X₂) → n_l5___5(X₀, X₁+1, X₂) :|: X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+2⋅X₂+1 {O(n^2)}

MPRF:

l5 [0 ]
l6 [0 ]
n_l4___6 [0 ]
n_l2___9 [0 ]
n_l3___3 [X₂-X₁ ]
n_l1___2 [X₂-X₁ ]
n_l3___8 [0 ]
n_l1___7 [0 ]
n_l4___1 [X₂-X₁ ]
n_l2___4 [X₂-X₁ ]
n_l5___5 [X₂-X₁ ]
l9 [0 ]

MPRF for transition t₁₁₉: n_l5___5(X₀, X₁, X₂) → n_l2___4(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+3⋅X₂+2 {O(n^2)}

MPRF:

l5 [0 ]
l6 [0 ]
n_l4___6 [0 ]
n_l2___9 [0 ]
n_l3___3 [X₂-X₁ ]
n_l1___2 [X₂-X₁ ]
n_l3___8 [0 ]
n_l1___7 [0 ]
n_l4___1 [X₂-X₁ ]
n_l2___4 [X₂-X₁ ]
n_l5___5 [X₂+1-X₁ ]
l9 [0 ]

MPRF for transition t₁₂₆: n_l5___5(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ < 1+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+2 {O(n)}

MPRF:

l5 [X₀+2 ]
l6 [X₀+2 ]
n_l2___9 [X₀+2 ]
n_l3___3 [X₀+2 ]
n_l1___2 [X₀+2 ]
n_l3___8 [X₀+2 ]
n_l1___7 [X₀+2 ]
n_l4___1 [X₀+2 ]
n_l4___6 [X₀+2 ]
n_l2___4 [X₀+2 ]
n_l5___5 [X₀+2 ]
l9 [X₀+1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:10⋅X₂⋅X₂+43⋅X₂+37 {O(n^2)}
t₀: 1 {O(1)}
t₁₀: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₆: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₈: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₁₁: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₄: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₅: X₂+1 {O(n)}
t₂: X₂+1 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₂: X₂+1 {O(n)}

Costbounds

Overall costbound: 10⋅X₂⋅X₂+43⋅X₂+37 {O(n^2)}
t₀: 1 {O(1)}
t₁₀: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₆: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₈: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₁₁: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₄: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₅: X₂+1 {O(n)}
t₂: X₂+1 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₂: X₂+1 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁₀, X₀: X₂+1 {O(n)}
t₁₀, X₁: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₁₀, X₂: X₂ {O(n)}
t₆, X₀: X₂+1 {O(n)}
t₆, X₁: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₆, X₂: X₂ {O(n)}
t₈, X₀: X₂+1 {O(n)}
t₈, X₁: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₈, X₂: X₂ {O(n)}
t₁₁, X₀: X₂+1 {O(n)}
t₁₁, X₁: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₁₁, X₂: X₂ {O(n)}
t₄, X₀: X₂+1 {O(n)}
t₄, X₁: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₄, X₂: X₂ {O(n)}
t₅, X₀: X₂+1 {O(n)}
t₅, X₁: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₅, X₂: X₂ {O(n)}
t₂, X₀: X₂+1 {O(n)}
t₂, X₁: 0 {O(1)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: 2⋅X₂+1 {O(n)}
t₃, X₁: 2⋅X₂⋅X₂+8⋅X₂+X₁+6 {O(n^2)}
t₃, X₂: 2⋅X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁₃, X₀: 2⋅X₂+1 {O(n)}
t₁₃, X₁: 2⋅X₂⋅X₂+8⋅X₂+X₁+6 {O(n^2)}
t₁₃, X₂: 2⋅X₂ {O(n)}
t₁₂, X₀: X₂+1 {O(n)}
t₁₂, X₁: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}
t₁₂, X₂: X₂ {O(n)}