Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₁, X₂, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, 1, X₀+1, X₃, X₄, X₅)
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₂-2, X₁, X₂, X₃, X₄, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₁
t₅: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₂
t₇: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁+1, X₂, X₃, X₄, X₅)

Preprocessing

Eliminate variables {X₃,X₅} that do not contribute to the problem

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6

Found invariant 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l7

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location l8

Found invariant X₀ ≤ X₃ for location l1

Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location l4

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₁₉: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂₀: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ X₃
t₂₁: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₀ ≤ X₃
t₂₂: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃)
t₂₃: l3(X₀, X₁, X₂, X₃) → l6(X₀, 1, X₀+1, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀
t₂₄: l4(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ 1+X₀ ≤ 0
t₂₅: l5(X₀, X₁, X₂, X₃) → l1(X₂-2, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂₆: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₇: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ < X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₈: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₁+1, X₂, X₃) :|: 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₂₀: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF for transition t₂₃: l3(X₀, X₁, X₂, X₃) → l6(X₀, 1, X₀+1, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF for transition t₂₅: l5(X₀, X₁, X₂, X₃) → l1(X₂-2, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF for transition t₂₆: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃+1 {O(n)}

TWN: t₂₇: l6→l7

cycle: [t₂₇: l6→l7; t₂₈: l7→l6]
loop: (X₁ < X₂,(X₁,X₂) -> (X₁+1,X₂)
order: [X₁; X₂]
closed-form:
X₁: X₁ + [[n != 0]] * n^1
X₂: X₂

Termination: true
Formula:

1 < 0
∨ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₁ < X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}

TWN - Lifting for t₂₇: l6→l7 of 2⋅X₁+2⋅X₂+4 {O(n)}

relevant size-bounds w.r.t. t₂₃:
X₁: 1 {O(1)}
X₂: X₃+2 {O(n)}
Runtime-bound of t₂₃: X₃+1 {O(n)}
Results in: 2⋅X₃⋅X₃+12⋅X₃+10 {O(n^2)}

TWN: t₂₈: l7→l6

TWN - Lifting for t₂₈: l7→l6 of 2⋅X₁+2⋅X₂+4 {O(n)}

relevant size-bounds w.r.t. t₂₃:
X₁: 1 {O(1)}
X₂: X₃+2 {O(n)}
Runtime-bound of t₂₃: X₃+1 {O(n)}
Results in: 2⋅X₃⋅X₃+12⋅X₃+10 {O(n^2)}

Chain transitions t₂₅: l5→l1 and t₂₁: l1→l4 to t₅₈: l5→l4

Chain transitions t₂₂: l2→l1 and t₂₁: l1→l4 to t₅₉: l2→l4

Chain transitions t₂₂: l2→l1 and t₂₀: l1→l3 to t₆₀: l2→l3

Chain transitions t₂₅: l5→l1 and t₂₀: l1→l3 to t₆₁: l5→l3

Chain transitions t₆₁: l5→l3 and t₂₃: l3→l6 to t₆₂: l5→l6

Chain transitions t₆₀: l2→l3 and t₂₃: l3→l6 to t₆₃: l2→l6

Chain transitions t₂₆: l6→l5 and t₆₂: l5→l6 to t₆₄: l6→l6

Chain transitions t₂₆: l6→l5 and t₅₈: l5→l4 to t₆₅: l6→l4

Chain transitions t₂₆: l6→l5 and t₆₁: l5→l3 to t₆₆: l6→l3

Chain transitions t₂₆: l6→l5 and t₂₅: l5→l1 to t₆₇: l6→l1

Chain transitions t₂₇: l6→l7 and t₂₈: l7→l6 to t₆₈: l6→l6

Analysing control-flow refined program

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6

Found invariant 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l7

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location l8

Found invariant X₀ ≤ X₃ for location l1

Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location l4

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ for location l3

MPRF for transition t₆₄: l6(X₀, X₁, X₂, X₃) -{4}> l6(X₂-2, 1, X₂-1, X₃) :|: X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 2 ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃+1 {O(n)}

TWN: t₆₈: l6→l6

cycle: [t₆₈: l6→l6]
loop: (X₁ < X₂,(X₁,X₂) -> (X₁+1,X₂)
order: [X₁; X₂]
closed-form:
X₁: X₁ + [[n != 0]] * n^1
X₂: X₂

Termination: true
Formula:

1 < 0
∨ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₁ < X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}
loop: (X₁ < X₂,(X₁,X₂) -> (X₁+1,X₂)
order: [X₁; X₂]
closed-form:
X₁: X₁ + [[n != 0]] * n^1
X₂: X₂

Termination: true
Formula:

1 < 0
∨ X₁ < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₁ < X₂
alphas_abs: X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}

TWN - Lifting for t₆₈: l6→l6 of 2⋅X₁+2⋅X₂+4 {O(n)}

relevant size-bounds w.r.t. t₆₄:
X₁: 1 {O(1)}
X₂: X₃+1 {O(n)}
Runtime-bound of t₆₄: X₃+1 {O(n)}
Results in: 2⋅X₃⋅X₃+10⋅X₃+8 {O(n^2)}

TWN - Lifting for t₆₈: l6→l6 of 2⋅X₁+2⋅X₂+4 {O(n)}

relevant size-bounds w.r.t. t₆₃:
X₁: 1 {O(1)}
X₂: X₃+1 {O(n)}
Runtime-bound of t₆₃: 1 {O(1)}
Results in: 2⋅X₃+8 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___2

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6

Found invariant 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l7___3

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location l8

Found invariant X₀ ≤ X₃ for location l1

Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location l4

Found invariant 2 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l7___1

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ for location l3

knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₁₄₃: l6(X₀, X₁, X₂, X₃) → n_l7___3(X₀, X₁, X₀+1, X₃) :|: X₀+1 ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ < 1+X₀ ∧ X₀+1 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₁₄₅: n_l7___3(X₀, X₁, X₂, X₃) → n_l6___2(X₀, X₁+1, X₀+1, X₃) :|: 0 < X₀ ∧ X₀+1 ≤ X₂ ∧ X₁ ≤ 1 ∧ X₀+1 ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₁₄₂: n_l6___2(X₀, X₁, X₂, X₃) → n_l7___1(X₀, X₁, X₀+1, X₃) :|: X₀+1 ≤ X₂ ∧ 2 ≤ X₁ ∧ X₁ < 1+X₀ ∧ X₀+1 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ 1+X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃⋅X₃+9⋅X₃+5 {O(n^2)}

MPRF for transition t₁₄₄: n_l7___1(X₀, X₁, X₂, X₃) → n_l6___2(X₀, X₁+1, X₀+1, X₃) :|: X₁ < 1+X₀ ∧ 2 ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ X₀+1 ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₃⋅X₃+4⋅X₃+3 {O(n^2)}

MPRF for transition t₁₄₉: n_l6___2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃+1 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:4⋅X₃⋅X₃+28⋅X₃+28 {O(n^2)}
t₁₉: 1 {O(1)}
t₂₀: X₃+1 {O(n)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: X₃+1 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₃+1 {O(n)}
t₂₆: X₃+1 {O(n)}
t₂₇: 2⋅X₃⋅X₃+12⋅X₃+10 {O(n^2)}
t₂₈: 2⋅X₃⋅X₃+12⋅X₃+10 {O(n^2)}

Costbounds

Overall costbound: 4⋅X₃⋅X₃+28⋅X₃+28 {O(n^2)}
t₁₉: 1 {O(1)}
t₂₀: X₃+1 {O(n)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: X₃+1 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₃+1 {O(n)}
t₂₆: X₃+1 {O(n)}
t₂₇: 2⋅X₃⋅X₃+12⋅X₃+10 {O(n^2)}
t₂₈: 2⋅X₃⋅X₃+12⋅X₃+10 {O(n^2)}

Sizebounds

t₁₉, X₀: X₀ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₂₀, X₀: X₃+1 {O(n)}
t₂₀, X₁: 2⋅X₃⋅X₃+12⋅X₃+X₁+12 {O(n^2)}
t₂₀, X₂: 2⋅X₃+X₂+4 {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₁, X₀: 2⋅X₃+1 {O(n)}
t₂₁, X₁: 2⋅X₃⋅X₃+12⋅X₃+X₁+12 {O(n^2)}
t₂₁, X₂: 2⋅X₃+X₂+4 {O(n)}
t₂₁, X₃: 2⋅X₃ {O(n)}
t₂₂, X₀: X₃ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₃, X₀: X₃+1 {O(n)}
t₂₃, X₁: 1 {O(1)}
t₂₃, X₂: X₃+2 {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₄, X₀: 2⋅X₃+1 {O(n)}
t₂₄, X₁: 2⋅X₃⋅X₃+12⋅X₃+X₁+12 {O(n^2)}
t₂₄, X₂: 2⋅X₃+X₂+4 {O(n)}
t₂₄, X₃: 2⋅X₃ {O(n)}
t₂₅, X₀: X₃+1 {O(n)}
t₂₅, X₁: 2⋅X₃⋅X₃+12⋅X₃+12 {O(n^2)}
t₂₅, X₂: 2⋅X₃+4 {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₆, X₀: X₃+1 {O(n)}
t₂₆, X₁: 2⋅X₃⋅X₃+12⋅X₃+12 {O(n^2)}
t₂₆, X₂: 2⋅X₃+4 {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₇, X₀: X₃+1 {O(n)}
t₂₇, X₁: 2⋅X₃⋅X₃+12⋅X₃+11 {O(n^2)}
t₂₇, X₂: X₃+2 {O(n)}
t₂₇, X₃: X₃ {O(n)}
t₂₈, X₀: X₃+1 {O(n)}
t₂₈, X₁: 2⋅X₃⋅X₃+12⋅X₃+11 {O(n^2)}
t₂₈, X₂: X₃+2 {O(n)}
t₂₈, X₃: X₃ {O(n)}