You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


1. Field of the Invention
The present invention relates to a valve system for an engine. In particular, the present invention relates to an improved valve system for an engine, wherein a rocker arm is interlocked with an engine valve and is supported by a rocker shaft fixedly supported by a cylinder head such that it is rockable with the rotation of a camshaft of the engine.
2. Description of Background Art
A valve system of this type has been known, for example, from Japanese Patent Laid-open No. Hei 2000-110516.
The above-described background art valve system is of an overhead cam type, wherein a camshaft is disposed over a cylinder head. In this valve system, to transmit rotational power of the crankshaft to the camshaft at a reduction ratio of 1/2, it is required to ensure a space on one end of the crankshaft for disposing power transmission means, such as a cam chain. This results in the width of the engine increasing in the direction along the axial line of the crankshaft. Accordingly, the weight of the engine is increased.
In view of the foregoing, the present invention has been made, and an object of the present invention is to provide a valve system of an engine, which is capable of reducing the size and weight of the engine.
To achieve the above object, according to a first aspect of the present invention, a valve system for an engine includes a crankshaft rotatably supported by a crankcase such that it is connected to a piston slidably fitted in a cylinder bore. A camshaft has an axial line parallel to an axial line of the crankshaft and is interlocked with the crankshaft at a reduction ratio of 1/2. A rocker arm is interlocked with engine valves and is supported by a rocker shaft fixedly supported by a cylinder head such that it is rockable with the rotation of the camshaft. The camshaft disposed on one side of the crankshaft is rotatably supported by the crankcase. The posture of the rocker shaft is set to have an axial line crossing the axial line of the crankshaft on the projection plane perpendicular to an axial line of the cylinder bore. An input arm extending on the projection plane from the rocker arm to the camshaft side is provided on the side of the rocker arm which is rockably supported by the rocker shaft. A pull rod reciprocating in the axial direction with the rotation of the camshaft is connected to the input arm in order to rock the rocker arm in the valve opening direction when the pull rod is moved to the camshaft side.
With this configuration, since the posture of the rocker shaft is set to have an axial line crossing the axial line of the crankshaft on the projection plane perpendicular to an axial line of the cylinder bore, a space required for disposing the rocker shaft, the rocker arm, and the like constituting part of the valve system can be made smaller in the direction along the axial line of the crankshaft. Also, since the input arm extends from the rocker arm to the camshaft disposed on one side of the crankshaft, and the pull rod reciprocating in the axial direction with the rotation of the camshaft is connected to the input arm, it is not required to enlarge the width of the cylinder head in the direction along the axial line of the crankshaft for disposing the pull rod. This results in the possibility of reducing the size and weight of the engine in the direction along the axial line of the crankshaft.
To achieve the above object, according to the second aspect of the present invention, a valve system for an engine includes a crankshaft which is rotatably supported by a crankcase such that it is connected to a piston slidably fitted in a cylinder bore. A camshaft has an axial line parallel to an axial line of the crankshaft and is interlocked with the crankshaft at a reduction ratio of 1/2. A first rocker arm is interlocked with first engine valves and a second rocker arm is interlocked with second engine valves different in kind from the first engine valves. The first and second rocker arms are respectively supported by a first rocker shaft and a second rocker shaft, which are fixedly supported by a cylinder head, such that they are rockable with the rotation of the camshaft. The camshaft is disposed on one side of the crankshaft and is rotatably supported by the crankcase. The first rocker arm corresponding to a pair of the first engine valves and the second rocker arm corresponding to a pair of the second engine valves are disposed in the cylinder head such that they face the combustion chamber. The first and second rocker arms are rockably supported by the first rocker shaft and the second rocker shaft, respectively. The first and second rocker shafts have axial lines crossing the axial line of the crankshaft on the projection plane perpendicular to an axial line of the cylinder bore and are disposed in parallel to each other. A first input arm and a second input arm extend on the projection plane from the first rocker arm and the second rocker arm to the camshaft side and are provided on the first rocker arm and the second rocker arm, respectively. A push rod reciprocating in the axial direction with the rotation of the camshaft is connected to the first input arm in order to rock the first rocker arm in the valve opening direction when the push rod is moved on the side opposite to the camshaft. A pull rod reciprocating in the axial direction according to the rotation of the camshaft is connected to the second input arm in order to rock the second rocker arm in the valve opening direction when the pull rod is moved on the camshaft side.
With this configuration, since the pair of first engine valves and the pair of second engine valves are disposed in the cylinder head such that they face the combustion chamber, it is possible to improve the suction efficiency and increase the output torque in a low speed rotational range. Since the postures of the first and second rocker shafts are set to have axial lines thereof crossing the axial line of the crankshaft on the projection plane perpendicular to the axial line of the cylinder bore, a space required in the cylinder head for disposing the first and second rocker shafts, the first and second rocker arms, and the like constituting part of the valve system can be made smaller in the direction along the axial line of the crankshaft. Furthermore, since the input arms extend from the first and second rocker arms to the camshaft disposed on one side of the crankshaft and the pull rod and the push rod reciprocating in the axial direction according to the rotation of the camshaft are connected to the input arms of both the rocker arms, it is not required to enlarge the width of the cylinder head in the direction along the axial line of the crankshaft for disposing the pull rod and the push rod. Accordingly, a drive system between the camshaft and the rocker arms can be disposed in good balance. This results in the possibility of reducing the size and weight of the engine in the direction along the axial line of the crankshaft.
Further scope of applicability of the present invention will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description.