Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆
Temp_Vars: R, S
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₉: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l1(0, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, 0, X₁₅, X₁₆)
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l2(X₀, 0, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₀ ≤ 9
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l3(X₀, X₁, 0, X₃, 0, 0, 0, 0, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, 1000) :|: 10 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l1(X₀+1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: 10 ≤ X₁
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l2(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, S, S, X₁₆) :|: X₁ ≤ 9
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l4(X₀, X₁, X₂, 0, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₂ ≤ 9
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₄, X₅, X₆, X₇, 1500, S, X₁₄, X₁₅, X₁₆) :|: 10 ≤ X₂
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l3(X₀, X₁, X₂+1, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: 10 ≤ X₃
t₂: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l4(X₀, X₁, X₂, X₃+1, X₄+S, X₅+1, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₃ ≤ 9 ∧ R+1 ≤ 0
t₃: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → l4(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆+S, X₇+1, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₃ ≤ 9

Preprocessing

Eliminate variables {S,X₄,X₅,X₆,X₇,X₈,X₉,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₁₆} that do not contribute to the problem

Found invariant X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2

Found invariant 10 ≤ X₂ ∧ 20 ≤ X₀+X₂ ∧ 10 ≤ X₀ for location l5

Found invariant 0 ≤ X₀ for location l1

Found invariant X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ for location l4

Found invariant 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: R
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₂₂: l0(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₂₃: l1(X₀, X₁, X₂, X₃) → l2(X₀, 0, X₂, X₃) :|: X₀ ≤ 9 ∧ 0 ≤ X₀
t₂₄: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, 0, X₃) :|: 10 ≤ X₀ ∧ 0 ≤ X₀
t₂₆: l2(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: 10 ≤ X₁ ∧ X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₅: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁+1, X₂, X₃) :|: X₁ ≤ 9 ∧ X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₇: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, 0) :|: X₂ ≤ 9 ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀
t₂₈: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 10 ≤ X₂ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀
t₃₁: l4(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂+1, X₃) :|: 10 ≤ X₃ ∧ X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀
t₂₉: l4(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ 9 ∧ R+1 ≤ 0 ∧ X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀
t₃₀: l4(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ 9 ∧ X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀

MPRF for transition t₂₃: l1(X₀, X₁, X₂, X₃) → l2(X₀, 0, X₂, X₃) :|: X₀ ≤ 9 ∧ 0 ≤ X₀ of depth 1:

new bound:

10 {O(1)}

MPRF:

l2 [9-X₀ ]
l1 [10-X₀ ]

Found invariant X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2

Found invariant 10 ≤ X₂ ∧ 20 ≤ X₀+X₂ ∧ 10 ≤ X₀ for location l5

Found invariant 0 ≤ X₀ for location l1

Found invariant X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ for location l4

Found invariant 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₂₅ 220 {O(1)}

TWN-Loops:

entry: t₂₃: l1(X₀, X₁, X₂, X₃) → l2(X₀, 0, X₂, X₃) :|: X₀ ≤ 9 ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀,X₁+1,X₂,X₃) :|: X₁ ≤ 9
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁ < 9 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 9 ∧ 9 ≤ X₁

Stabilization-Threshold for: X₁ ≤ 9
alphas_abs: 9
M: 0
N: 1
Bound: 20 {O(1)}

relevant size-bounds w.r.t. t₂₃:
Runtime-bound of t₂₃: 10 {O(1)}
Results in: 220 {O(1)}

220 {O(1)}

Found invariant 1 ≤ 0 for location l2

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 ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l2

Found invariant 1 ≤ 0 for location l5

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ 0 for location l4

Found invariant 1 ≤ 0 for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₂₆ 8603 {O(1)}

TWN-Loops:

entry: t₂₅: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁+1, X₂, X₃) :|: X₁ ≤ 9 ∧ X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀] , (X₀,X₁,X₂,X₃) -> (1+X₀,0,X₂,X₃) :|: 10 ≤ X₁ ∧ X₀ ≤ 8
entry: t₂₂: l0(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
results in twn-loop: twn:Inv: [0 ≤ X₀ ∧ 0 ≤ 10 ∧ 0 ≤ 10+X₀ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀+1,0,X₂,X₃) :|: X₀ ≤ 9 ∧ 10 ≤ 0
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: [[n == 0]] * X₁

Termination: true
Formula:

1 < 0 ∧ 10 < 0 ∧ 0 < 1
∨ 1 < 0 ∧ 10 < 0 ∧ 0 < 1 ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 10 < 0 ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ 1 < 0 ∧ 10 < 0 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1
∨ 1 < 0 ∧ 10 < 0 ∧ 0 < X₀ ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 10 < 0 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ 1 < 0 ∧ 10 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < 1
∨ 1 < 0 ∧ 10 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 10 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ 1 < 0 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < 1
∨ 1 < 0 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < 1 ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ 1 < 0 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1
∨ 1 < 0 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < X₀ ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ 1 < 0 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < 1
∨ 1 < 0 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 1 < 0 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ X₀ < 8 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 10 < 0 ∧ 0 < 1
∨ X₀ < 8 ∧ 10 < 0 ∧ 0 < 1 ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 8 ∧ 10 < 0 ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ X₀ < 8 ∧ 10 < 0 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1
∨ X₀ < 8 ∧ 10 < 0 ∧ 0 < X₀ ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 8 ∧ 10 < 0 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ X₀ < 8 ∧ 10 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < 1
∨ X₀ < 8 ∧ 10 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 8 ∧ 10 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ X₀ < 8 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < 1
∨ X₀ < 8 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < 1 ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 8 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ X₀ < 8 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1
∨ X₀ < 8 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < X₀ ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 8 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ X₀ < 8 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < 1
∨ X₀ < 8 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 8 ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 < 0 ∧ 0 < 1
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 < 0 ∧ 0 < 1 ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 < 0 ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 < 0 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 < 0 ∧ 0 < X₀ ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 < 0 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < 1
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < 1
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < 1 ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < 1 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < X₀ ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < 1
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 < 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ 8 ∧ 8 ≤ X₀ ∧ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₀ ∧ 10+X₀ ≤ 0

Stabilization-Threshold for: X₀ ≤ 8
alphas_abs: 8+X₀
M: 0
N: 1
Bound: 2⋅X₀+18 {O(n)}

relevant size-bounds w.r.t. t₂₅:
X₀: 9 {O(1)}
Runtime-bound of t₂₅: 220 {O(1)}
Results in: 8580 {O(1)}

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

Termination: true
Formula:

10 < 0 ∧ 1 < 0
∨ 10 < 0 ∧ X₀ < 9 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 10 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 9 ∧ 9 ≤ X₀
∨ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 1 < 0
∨ 10 ≤ 0 ∧ 0 ≤ 10 ∧ X₀ < 9 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 10 ≤ 0 ∧ 0 ≤ 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 9 ∧ 9 ≤ X₀

Stabilization-Threshold for: X₀ ≤ 9
alphas_abs: X₀+9
M: 0
N: 1
Bound: 2⋅X₀+20 {O(n)}

relevant size-bounds w.r.t. t₂₂:
X₀: 0 {O(1)}
Runtime-bound of t₂₂: 1 {O(1)}
Results in: 23 {O(1)}

8603 {O(1)}

MPRF for transition t₂₇: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, 0) :|: X₂ ≤ 9 ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ of depth 1:

new bound:

10 {O(1)}

MPRF:

l4 [9-X₂ ]
l3 [10-X₂ ]

MPRF for transition t₂₉: l4(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ 9 ∧ R+1 ≤ 0 ∧ X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ of depth 1:

new bound:

110 {O(1)}

MPRF:

l4 [X₀+1-X₃ ]
l3 [X₀-X₃ ]

MPRF for transition t₃₀: l4(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ 9 ∧ X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ of depth 1:

new bound:

110 {O(1)}

MPRF:

l4 [X₀+1-X₃ ]
l3 [X₀-X₃ ]

MPRF for transition t₃₁: l4(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂+1, X₃) :|: 10 ≤ X₃ ∧ X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ of depth 1:

new bound:

100 {O(1)}

MPRF:

l4 [X₀ ]
l3 [X₀+1-2⋅X₂ ]

All Bounds

Timebounds

Overall timebound:9166 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 10 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 220 {O(1)}
t₂₆: 8603 {O(1)}
t₂₇: 10 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 110 {O(1)}
t₃₀: 110 {O(1)}
t₃₁: 100 {O(1)}

Costbounds

Overall costbound: 9166 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 10 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 220 {O(1)}
t₂₆: 8603 {O(1)}
t₂₇: 10 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 110 {O(1)}
t₃₀: 110 {O(1)}
t₃₁: 100 {O(1)}

Sizebounds

t₂₂, X₀: 0 {O(1)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₃, X₀: 9 {O(1)}
t₂₃, X₁: 0 {O(1)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₄, X₀: 10 {O(1)}
t₂₄, X₁: 10 {O(1)}
t₂₄, X₂: 0 {O(1)}
t₂₄, X₃: X₃ {O(n)}
t₂₅, X₀: 9 {O(1)}
t₂₅, X₁: 10 {O(1)}
t₂₅, X₂: X₂ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₆, X₀: 10 {O(1)}
t₂₆, X₁: 10 {O(1)}
t₂₆, X₂: X₂ {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₇, X₀: 10 {O(1)}
t₂₇, X₁: 10 {O(1)}
t₂₇, X₂: 9 {O(1)}
t₂₇, X₃: 0 {O(1)}
t₂₈, X₀: 10 {O(1)}
t₂₈, X₁: 10 {O(1)}
t₂₈, X₂: 38 {O(1)}
t₂₈, X₃: 10 {O(1)}
t₂₉, X₀: 10 {O(1)}
t₂₉, X₁: 10 {O(1)}
t₂₉, X₂: 18 {O(1)}
t₂₉, X₃: 10 {O(1)}
t₃₀, X₀: 10 {O(1)}
t₃₀, X₁: 10 {O(1)}
t₃₀, X₂: 18 {O(1)}
t₃₀, X₃: 10 {O(1)}
t₃₁, X₀: 10 {O(1)}
t₃₁, X₁: 10 {O(1)}
t₃₁, X₂: 38 {O(1)}
t₃₁, X₃: 10 {O(1)}